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AMPL CPLEX 9.0 User Guide

1. nenennunnuenennnnenennnnna 20 Using CPLEX with AMPL 2 0 cece eee eee 23 Problems Handled by CPLEX 0 cee ee cece eee eee eee eens 23 Piecewise linear Programs 0 000 cee ee eee eee 24 Quadratic PrograMS oooooooco se AET ni E EE SE ER RE E E TaS EE Ta ia 24 Q adratic Constraints coi A ee Be eh eee i 25 Specifying CPLEX Directives 0 cece cece eens 26 Using CPLEX for Linear Programming nennnnnnnnnna 29 CPLEX Linear Programming Algorithms enunnununnnnnna 29 Directives for Problem and Algorithm Selection 00 cece neces 30 Directives for Preprocessing cece eee eee eee eee eee 32 Directives for Controlling the Simplex Algorithm nnnnna 35 Directives for Controlling the Barrier Algorithm enenannna 40 Directives for Improving Stability nuneuenannunenenannna 42 Directives for Starting and Stopping 00 eee eee eee eee 43 Directives for Controlling Output 0 2 0 0 cee eee eee 45 Using CPLEX for Integer Programming ennnnunnnnna 47 CPLEX Mixed Integer Algorithm enennuneuannennnnnanna 47 Directives for Preprocessing 0 cece eee eee eee eee eee eee 49 Directives for Algorithmic Control enennununuuannnnua 53 Directives for Relaxing Optimality 00 c cece ee
2. ILOG AMPL CPLEX System Version 9 0 User s Guide Standard Command line Version Including CPLEX Directives September 2003 Copyright 1987 2003 by ILOG S A All rights reserved ILOG the ILOG design CPLEX and all other logos and product and service names of ILOG are registered trademarks or trademarks of ILOG in France the U S and or other countries Java and all Java based marks are either trademarks or registered trademarks of Sun Microsystems Inc in the United States and other countries Microsoft Windows and Windows NT are either trademarks or registered trademarks of Microsoft Corporation in the U S and other countries All other brand product and company names are trademarks or registered trademarks of their respective holders AMPL is a registered trademark of AMPL Optimization LLC and is distributed under license by ILOG CPLEX is a registered trademark of ILOG Printed in France Chapier 1 Chapter 2 Chapter 3 Table of Contents Introduction x5 25155041 a eh ee vee eo ee ee ee aca 1 Welcome to AMPL 02 cece cece eenueuueeuae nen nene nan nen nen nan naa 1 Using this Guide s cocos mir a dan a ma eee avita A aa 1 Installing AMPL xeruenuannannanunennen enn nan nen nen nn nunn na 2 Requirements ni A Ea a pk AS 2 Unix Installations ccc a tuld A ie ee ed Oe ees 3 Windows Installation 0 0 cent a a E a 3 AMPL and Parallel CPLEX 0 0 0 00 eee ete 4 LICENS
3. In extreme cases the basis may have to be refactored every few iterations and the algorithm will be very slow Given adequate memory CPLEX s performance is relatively insensitive to changes in refactorization frequency For a few extremely large difficult problems you may be able to improve performance by reducing i from the value that CPLEX chooses net find i default 1 This directives governs the method used by the CPLEX network optimizer to extract a network from the linear program The value of i influences the size of the network extracted potentially reducing optimization time The default value i 1 extracts only the natural network from the problem CPLEX then invokes its network simplex method on the extracted network In some cases CPLEX can extract a larger network by multiplying rows by 1 reflection scaling and rescaling constraints and variables so that more matrix coefficients are plus or minus 1 Setting the netfind directive to 2 enables reflection scaling only while setting it to 3 allows reflection scaling and general scaling ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE xxxstart i default 0 Set this parameter to 1 to instruct CPLEX to start the optimization from one of the xxx format basis files generated by CPLEX when it last solved this problem see the description of the basisinterval directive above for more information Note that these xxx format files are for the presolved problem so one should not s
4. In some cases even though the current tree size is within system resource limits it may be that there is considerable memory fragmentation and as a result poor performance because of the way in which the tree was built To combat that fragmentation it can be helpful to write a tree file and resolve reading in the tree file Some parts of the branch amp bound tree can be stored in compressed files when the nodefile directive is used Storing part of each node in files will allow more nodes to be explored in a given t reememl im limit but file access may be slower than physical memory access This feature may be especially useful if you use steepest edge pricing for subproblem simplex pricing strategy because the pricing information consumes a lot of memory The best approach to reduce memory usage is to modify the solution process Switching to a higher backtrack parameter value and best estimate node selection strategy or depth first search node selection which is even more extreme often works Depth first search rarely generates a large unexplored node list since CPLEX will be diving deep into the branch amp bound tree rather than jumping around within it This narrowly focused search also often results in faster individual node processing times Overall efficiency is sometimes worse than with best bound node selection since each branch is exhaustively searched to the deepest level before fathoming it in favor of better branches Another
5. ampl option cplex options crash 0 dual ampl feasibility 1 0e 8 scale 1 ampl lpiterlim 100 If you use the latter approach be sure to include spaces at the beginning or end of the individual strings so that the identifiers will be separated by spaces when all of the strings are concatenated 12 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Often you will want to add solver options to the set you are currently using If you simply type acommand such as option solver options new options however you will overwrite the existing option settings To avoid this problem you can use AMPL s notation for options the symbol option name is replaced by the current value of option name To add an optimality tolerance to the CPLEX options in the above example you would write ampl option cplex options cplex options ampl optimality 1 0e 8 Initial Variable Values and Solvers Some optimizers including most nonlinear solvers but excluding simplex based linear solvers make use of initial values for the decision variables as a starting point in their search for an optimal solution A good choice of initial values can greatly speed up the solution process in some cases Moreover in nonlinear models with multiple local optima the optimal solution reported by the solver may depend on the initial values for the variables AMPL passes initial values for decision variables and dual values if available to the solver You can set i
6. at its lower bound at optimality You can change a variable s basis status using AMPL s 1et command This may be useful in instances where you want to provide an initial basis to jump start CPLEX ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 79 80 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE CPLEX Synonyms The following list contains alternative names for certain CPLEX directives The use of primary names is recommended Table A 1 CPLEX Synonyms Synonym agglim dense display doperturb endbasis endvector growth heuristic iterations mipsolutions Primary Directive aggfill densecol Ipdisplay perturb writebasis writevector bargrowth rootheuristic Ipiterlim solutionlim ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 81 82 Synonym nodes nodesel presolvedual startalg startalgorithm startbasis startvector subalgorithm time treememory varsel writeprob ILOG AMPL CPLEX SYSTEM 9 0 Primary Directive nodelim nodeselect predual mipstartalg mipstartalg readbasis readvector mipalgorithm timelimit treememlim varselect file USER S GUIDE Symbols symbol notation for options 13 syntax set initial values 13 A absmipgap directive 60 advance directive 35 aggcutlim directive 49 aggfill directive 32 aggregate directive 32 algorithm directives for selection 30 mixed integer 47 algorithmic control directives 53 AMPL notation for options 13 and P
7. choice of algorithm 29 cplex options option 26 linear programs 29 memory reguirement for linear programs 30 mixed integer algorithm 47 optimization methods 29 problems handled by CPLEX 23 specifying CPLEX directives 26 crash directive 36 crossover directive 41 current suffix 69 cutpass directive 50 cuts generate 50 polyhedral 50 cutsfactor directive 51 D densecol directive 41 dependency directive 33 devex pricing 37 dgradient directive 37 direction suffix 67 directive absmipgap 60 advance 35 aggcutlim 49 aggfill 32 84 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE aggregate 32 autoopt 31 backtrack 53 baralg 40 barcorr 40 bardisplay 45 bargrowth 40 bariterlim 43 barobjrange 40 baropt 31 baroutofcore 40 barstart 41 barthreads 4 31 41 basisinterval 36 bbinterval 53 boundstr 49 branch 54 cliguecuts 50 clocktype 43 61 coeffreduce 50 comptol 41 concurrentopt 31 covercuts 50 crash 36 crossover 41 cutpass 50 cutsfactor 51 densecol 41 dependency 33 dgradient 37 disjcuts 50 doperturb 42 dual 30 dualopt 31 dualthresh 30 endtree 61 feasibility 43 file 45 finalfactor 51 flowcuts 50 flowpathcuts 50 fraccand 51 fraccuts 50 fracpass 51 gubcuts 50 heuristicfreg 55 iisfind45 impliedcuts 50 integrality 60 logfile45 lowercutof f 60 lowerob j 44 lpdisplay 45 lpiterlim44 markowitz 43 maximize 32 minimize 32 mipalgorithm 55 mipcrossover 55 mipcuts 50 mipdisplay 63 mipemphasi
8. 42 down suffix 69 dual directive 30 dual pricing indicator 37 dual simplex algorithm 29 dualopt directive 31 dualthresh directive 30 E editing using a text editor 7 end AMPL session 7 endtree directive 61 F feasibility directive 43 file creating auxiliary 15 predefined commands 20 file directive 45 files load several files 9 temporary directory 17 86 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE finalfactor directive 51 flowcuts directive 50 flowpathcuts directive 50 fraccand directive 51 fraccuts directive 50 fracpass directive 51 G global thread limit 31 gubcuts directive 50 H heuristicfreg directive 55 iis suffix 70 iisfind directive 45 impliedcuts directive 50 installation 2 AMPL and Parallel CPLEX 4 Unix 3 Windows 3 integer programs 23 integrality directive 60 L launching AMPL 7 licensing 4 linear programs 23 CPLEX solution method 29 logfile directive 45 lowercutoff directive 60 lowerobj directive 44 lpdisplay directive 45 lpiterlim directive 44 markowitz directive 43 Markowitz threshold 43 Markowitz tolerance 43 maximize directive 32 memory reguirement for linear programs 30 running out 64 memory usage execute solver outside AMPL 16 messages termination 76 minimize directive 32 MIP difficult subproblems 66 mip priorities option 55 mipalgorithm directive 55 mipcrossover directive 55 mipcuts directive 50 mipdisplay
9. GUIDE prereduce directive 34 prerelax directive 52 presolve directive 34 presolvenode directive 52 prestats directive 34 pricing directive 38 primal directive 30 primal simplex algorithm 29 primal dual barrier algorithm 29 primalopt directive 31 priorities directive 63 priority suffix 67 probe directive 52 problem file ASCII format 15 binary format 15 problem files 13 Q gcpconvergetol directive 42 guadratic programming 24 R RAM reguirement for linear programs 30 readbasis directive 44 readvector directive 44 refactor directive 38 relax optimality 60 relax directive 32 relobjdiff directive 60 requirements AMPL 2 rinsheur directive 57 round directive 58 S save output 14 saving temporary files 14 scale directive 35 search directives for stopping and starting 61 sensitivity directive 46 siftopt directive 31 simplex algorithm basic solution 29 directives 35 singular directive 44 solution display information 14 save output 14 saving a solution 14 solution command 14 solution file ASCTI format 15 binary format 15 solution files 13 solutionlim directive 63 solve codes 75 76 solver add solver options 13 choosing 11 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 89 display solution information 14 execute outside AMPL 16 interface 11 multiline options 12 options 12 problem files 13 set initial values 13 solution files 13 specify op
10. for AMPL CPLEX DLL used by cplexamp exe Directory of examples see Examples below File used by the Windows uninstall procedure Utility program invoked by AMPL for DOS shells File containing additional information on the directory Sample AMPL models Most of these correspond to examples in the AMPL book More information on some of the examples is provided in the readme file in this directory Advanced sample AMPL models A description of each is provided in the readme file in this directory More samples The industries directory is sub divided into industry specific subdirectories The models have been brought together from a variety of sources Together they provide a palette of AMPL models that you may use as a starting point for your projects USER S GUIDE 5 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Using AMPL Running AMPL If you have added the AMPL installation directory to the search path you can run AMPL from any directory Otherwise run AMPL by moving to the AMPL directory and typing amp1 at the shell prompt At the amp1 prompt you can type any AMPL language statement or any of the commands described in Section A 13 of the book AMPL A Modeling Language for Mathematical Programming To end the session type quit at the amp1 prompt Using a Text Editor Generally you will edit your model and data both expressed using AMPL language statements in a text editor and type commands at the amp1
11. from the file 1 which must also be in the standard MPS basis format This basis determines the initial solution If the writebasis directive is specified CPLEX writes a record of the final simplex basis to the file named 2 in the standard MPS basis format Normally this is an optimal basis but it may be otherwise if an optimum does not exist or could not be found by the chosen algorithm or if the iterations were terminated prematurely by one of the directives described below readvector f1 writevector f2 These directives are used to take a barrier algorithm solution and write it to or read it from a CPLEX vec file Because AMPL always instructs CPLEX to take its barrier method solution and apply a hybrid method to obtain a basic solution this feature can only be used if a barrier iteration limit is exceeded If the readvector directive is specified CPLEX will read in a vec file named 1 and use it to initiate the hybrid crossover method that results in an optimal basic solution Note that CPLEX will not perform additional barrier iterations after reading in the vec file Similarly if the writevector directive is specified CPLEX will write out vec file named 2 singular i default 10 CPLEX will attempt to repair the basis matrix up to i times when it finds evidence that the matrix is singular Once this limit is exceeded CPLEX terminates with the current basis set to the best factorizable basis that has been found ti
12. i default 2100000000 CPLEX stops after i barrier method iterations and returns its current solution whether or not it has determined that the solution is optimal clocktype i default 1 The default setting of clockt ype 1 means that CPLEX will measure time in terms of CPU seconds A setting of 2 means that CPLEX will measure time in terms of elapsed wall clock seconds ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 43 lpiterlim i default 2 1e 9 or larger CPLEX stops after i simplex method iterations and returns its current solution whether or not it has determined that the solution is optimal lowerobj r1 default 1 0e 75 upperobj r2 default 1 0e 75 CPLEX stops at the first iteration where the solution is feasible in the constraints and the objective value is below r1 or above r2 At their default values these directives have no practical effect Setting r1 for a minimization or r2 for a maximization to a good value for the objective will cause CPLEX to stop as soon as it achieves this value readbasis f1 writebasis f2 Current versions do not reguire you to explicitly save the basis to hot start CPLEX variable status is automatically stored and used between CPLEX invocations The readbasis and writebasis directives are included for backward compatibility with previous versions of CPLEX for AMPL which did not use variable status information Ifthe readbasis directive is specified then the initial basis is instead read
13. in the discussion below To append new directives to cplex_options use this form ampl option cplex_options cplex_options amp1 optimality 1 0e 8 crash 1 A in front of an option name denotes the current value of that option so this statement just appends more directives to the current directive string As a result the string contains two directives for crash but the new one overrides the earlier one ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 27 28 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Using CPLEX for Linear Programming CPLEX Linear Programming Algorithms For linear programs CPLEX employs either a simplex method or a barrier method to solve the problem Refer to a linear programming textbook for more information on these algorithms Four distinct methods of optimization are incorporated in the CPLEX package A primal simplex algorithm that first finds a solution feasible in the constraints Phase I then iterates toward optimality Phase II A dual simplex algorithm that first finds a solution satisfying the optimality conditions Phase I then iterates toward feasibility Phase ID A network primal simplex algorithm that uses logic and data structures tailored to the class of pure network linear programs A primal dual barrier or interior point algorithm that simultaneously iterates toward feasibility and optimality optionally followed by a primal or dual crossover routine that produce
14. memory conserving strategy is to use strong branching variable selection using the varselect directive When using strong branching substantial computational effort is made at each node to determine the best branching variable As a result many fewer nodes are generated reducing the overall demand on memory Often strong branching is faster as well as using less memory On some problems the automatic generation of cuts results in excessive use of memory with little benefit in speed In such cases it is expedient to turn off cut generation by setting the covers and cliques directives to 1 Failure To Prove Optimality One frustrating aspect of the branch amp bound technique for solving MIP problems is that the solution process can continue long after the best solution has been found In these situations the branch amp bound tree is being exhaustively searched in an effort to guarantee that the current integer feasible solution is indeed optimal Remember that the branch amp bound tree may be as large as 2n nodes where n equals the number of binary variables A problem containing only 30 binary variables could produce a tree having over 1 billion nodes If no other stopping criteria have been set the process might continue until the search is complete or your computer s memory is exhausted ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 65 In general you should set at least one limit on the number of nodes processed number of impr
15. optimization nodefile i default 1 workfilelim r default 128 workfiledir f The list of unprocessed nodes in the branch amp bound tree typically dominates CPLEX s memory usage when solving integer programs A setting of 0 for the nodefile directive causes CPLEX to store all nodes in physical memory The default value of 1 creates a compressed version of the node file in memory Writing nodes to disk i 2 3 enables CPLEX to process more nodes before running out of memory This is typically more efficient than relying on the operating system s generic swapping procedure If i 2 an uncompressed node file is written to disk Compressing the file 1 3 adds computation time but allows more efficient use of memory ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE When the nodefile directive instructs CPLEX to write nodes to a node file the workfilelim directive specifies the maximum size of RAM to be consumed before writing to disk takes place Although node files are designed for efficiency the speed of RAM is always superior to that of disk and you should take advantage of what memory your computer has The default value of 128 a reasonable value for most computers means that 128 megabytes of RAM will be devoted to storing the tree and requirements beyond that will begin to go to files on disk A related directive is treememl im described below which serves to place a limit on the total size of the tree The default value of the treememl
16. program which is a function of the numbers of variables and constraints and the sparsity of the coefficient matrix The factorization of the basis matrix also requires an allocation of memory the amount is problem specific depending on the sparsity of the factorization When memory is limited CPLEX automatically makes adjustments that reduce its requirements but that usually also reduce its optimization speed The CPLEX directives in the following subsections apply to the solution of linear programs including network linear programs The letters i and r denote integer and real values respectively Directives for Problem and Algorithm Selection 30 CPLEX consults several directives to decide how to set up and solve a linear program that it receives The default is to apply the dual simplex method to the linear program as given substituting the network variant if the AMPL model contains node and arc declarations The following discussion indicates situations in which you should consider experimenting with alternatives dualthresh i default 32000 primal dual Every linear program has an equivalent opposite linear program the original is customarily referred to as the primal LP and the equivalent as the dual For each variable and each constraint in the primal there are a corresponding constraint and variable respectively in the dual Thus when the number of constraints is much larger than the number of variables in the primal th
17. r discourage backtracking yielding a strategy that is more nearly depth first Successive subproblems are more similar nodes are processed faster and integer solutions are often quickly found deep in the search tree Considerable time may be wasted in searching the descendants of one node however before backtracking to a better part of the tree The default value of 01 gives a moderately breadth first search and represents a good compromise Lower values often pay off when the LP subproblems are expensive to solve Setting i2 to 0 chooses a pure depth first strategy regardless of r CPLEX automatically uses this strategy to search for an initial feasible integer solution at the outset of the branch amp bound procedure branch il default 0 The branch directive determines the direction in which CPLEX branches on the selected fractional variable When branching on a variable x that has fractional value r CPLEX creates one subproblem that has the constraint x gt ceil r and one that has the constraint x lt floor r these are the up branch and down branch respectively By default 11 0 CPLEX uses an internal heuristic to decide whether it should first process the subproblem on the up branch or on the down branch You may instead specify consistent selection of the up branch i1 1 or down branch i1 1 Sometimes one of these settings leads the algorithm to examine and discard the poorer branches high in the tree reducing the tr
18. repeated successive branchings produce the tree structure shown above If there are more than a few integer variables the branching process has the potential to create more nodes than any computer can hold There are two key circumstances however in which branching from a particular node can be discontinued The node s subproblem has no fractional valued integer variables It thus provides a feasible solution to the original integer program If this solution yields a better objective value than any other feasible solution found so far it becomes the incumbent and is saved for future comparison The node s subproblem has no feasible solution or has an optimum that is worse than a certain cutoff value Since any subproblems under this node would be more restricted they would also either be infeasible or have an optimum value worse than the cutoff Thus none of these subproblems need be considered In these cases the node is said to be fathomed Because subproblems become more restricted with each branching the likelihood of fathoming a node becomes greater as the algorithm gets deeper into the tree So long as nodes are not created by branching much faster than they are inactivated by fathoming the tree can be kept to a reasonable size When no active nodes are left CPLEX is finished and it reports the final incumbent solution back to AMPL If the cutoff value has been set throughout the algorithm to the objective value of the curre
19. the value to a positive integer may improve the numerical stability of the algorithm probably at the expense of computation time barobjrange r default 1e 15 This directive sets the maximum absolute value of the objective function CPLEX s barrier algorithm looks at this value to detect unbounded problems Any positive value is acceptable input However care should be taken to avoid choosing a value so small that CPLEX will conclude a problem is unbounded when it is not baroutofcore i default 0 workfilelim r default 1e 15 workfiledir f The largest component of memory usage in the barrier algorithm is generally for the Cholesky factorization The baroutofcore directive when set to 1 specifies that the barrier optimizer should use out of core storage using files on disk for this array The default value for this directive is 0 meaning that all arrays are to be kept in RAM When baroutofcore 1 the workfilelim directive specifies the maximum amount of RAM that may be used for the Cholesky factorization before files are used for the remainder of memory needs The default is 128 which means CPLEX will use 128 megabytes of RAM before using disk space These temporary barrier files are created in the directory specified by the value of the workfiledir directive If no value is specified the directory specified by the TMPDIR on Unix or TMP on Windows environment variable is used ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE If TMP
20. tolerance r1 gt 0 specifies the degree to which a linear program s basic variables may violate their bounds You may wish to lower r1 after finding an optimal solution if there is any doubt that the solution is truly optimal but if it is set too low CPLEX may falsely conclude that the problem has no feasible solution Valid values for r1 lie between 1e 9 and 0 1 The Markowitz threshold r2 lt 1 influences the order in which variables are eliminated during basis factorization Increasing r2 may yield a more accurate factorization and consequently more accurate computations during iterations of the simplex algorithm Too large a value may produce an inefficiently dense factorization however Valid values for r2 lie between 0 0001 and 0 99999 The optimality tolerance r3 gt 0 specifies how closely the optimality or dual feasibility conditions must be satisfied for CPLEX to declare an optimal solution Valid values for r3 lie between 1e 9 and 0 01 Directives for Starting and Stopping Normally CPLEX uses an internal procedure to determine a starting point for the simplex algorithm then iterates to optimality The following directives override these conventions so that you can start from a saved basis and can stop when a certain criterion is satisfied Command line versions of CPLEX for AMPL can also be stopped by using break typically by pressing the Control and C keys simultaneously The best solution found so far is returned bariterlim
21. 0 bands 2 25 4 26 1e 20 bands 3 24 9 27 213 bands 4 10 27 29 1 coils 1 29 2857 30 30 8571 coils 2 33 35 1e 20 coils 3 35 2857 37 1e 20 4 35 2857 39 1e 20 coils r ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 69 For constraints the interpretation is similar except that it applies to a constraint s constant term the so called right hand side value ampl display time down time current ampl time up time down time current time up 1 37 8071 40 66 3786 2 37 8071 40 47 8571 3 25 32 45 4 30 40 62 5 r Diagnosing Infeasibilities For a linear program that has no feasible solution you can ask CPLEX to find an irreducible infeasible subset or IIS of the constraints and variable bounds By definition members of an IIS have no feasible solution but dropping any one of them permits a solution to be found to the remaining ones Clearly knowing the composition of an IIS can help localize the source of the infeasibility The associated suffix is lis You turn on the IIS finder using the iisfind option described in Directives for Controlling Output on page 45 An associated option iis table set up and displayed automatically by CPLEX shows the strings that may be associated with iis and gives brief descriptions of what they mean 70 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE The following example shows how IIS finding might be applied to the infeasible diet problem from chapter 2 of the AMPL book After solve d
22. 0 turn off dependency checking 1 turn on only at the beginning of preprocessing 2 turn on only at the end of preprocessing 3 turn on at the beginning and at the end of preprocessing precompress i default 0 This directive specifies whether CPLEX should compress the original model after presolve is performed This can save considerable storage space for large models Under the automatic setting i 0 CPLEX decides whether to perform the compression based on model characteristics Setting i 1 switches precompress off setting i 1 switches it on predual i default 0 By default after presolving the problem CPLEX decides whether to solve the primal or dual problem based on which problem it determines it can solve faster Setting i 1 explicitly instructs CPLEX to solve the dual problem while setting it to 1 explicitly instructs CPLEX to solve the primal problem ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 33 Regardless of the problem CPLEX solves internally it still reports primal solution values This is often a useful technique for problems with more constraints than variables prereduce i default 3 This directive determines whether primal reductions dual reductions or both are performed during preprocessing By default CPLEX performs both Set this directive to 0 to prevent all reductions 1 to only perform primal reductions and 2 to only perform dual reductions While the default usually suffices performing only one kind or the ot
23. DIR or TMP are not set either the current working directory is used Temporary barrier files are deleted automatically when CPLEX terminates normally barstart i default 1 This directive controls the starting point CPLEX uses to initiate the barrier method The default setting of 1 will suffice for most problems Consider other values 2 3 and 4 if the barrier method appears to converge slowly or when the predual directive is specified barthreads i default the value of the global threads directive This directive only applies to users of parallel CPLEX solvers It specifies the number of parallel processes used during the barrier method optimization comptol r default 1e 8 This directive specifies the complementarity tolerance used by the barrier algorithm to test convergence The barrier algorithm will terminate with an optimal solution if the relative complementarity is smaller than this value Any positive number larger than 1e 10 is acceptable input crossover i default 1 On a linear problem by default i 1 CPLEX initiates the crossover algorithm to convert the barrier solution to a basic or vertex solution using a primal simplex like method If i 2 a dual simplex like method is used for the crossover The crossover algorithm can be turned off by setting i 0 densecol i default 0 CPLEX uses this directive to distinguish dense columns in the constraint matrix Because barrier algorithm performance can improve dramatical
24. ING SS ee a Sok ee ae ee a ean de ee RSS oa del Leds we Beeson eee ea G 4 Usage Notes viii Oe eee A ys Foe eee i a AA VS er ee 4 Installed Files 2 2 4 ties A AE AAA E A As Rete ee 5 Using AMPE crac a A a heme maja ant Mo ae ep ama es 7 R nnihg AMPE i 54555 02055 Ses arate areca ed ele cert a Wate tee sala im ut eck ote eee rete 7 Using a Text Editor neeeneenaneenuenu nen nen nn nunnu enne n ne 7 Running AMPL in Batch Mode oocoocooccn nan nn nne 8 AMPL Solver Interaction ooococcoocncconoo enne 11 Ghoosing aSolVBr fee kesi a n easi e lle h teete a an aata diate eld akte 11 Specifying Solver Options nnnnenennunenennnnnnnn anna 12 Initial Variable Values and SolvVerS oooocococccncco nunna 13 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE v Chapter 4 Chapter 5 Chapter 6 Chapter 7 vi Problem and Solution Files vvrrununnunnnannenennnn ann na 13 Saving temporary files syta aea aa aa aAa E a A a A E O o i aa 14 Creating Auxiliary Files anuanua nanea aa 15 Running Solvers Outside AMPL 0000 c eee eee eee eee 16 Using MPS File Format oooococccnccoon enn nna 16 Temporary Files Directory 0 eee eee eee eee nn na 17 Customizing AMPL nennannenunnnenna nan nun 19 Command Line Switches enneneuennunennuennenananea 19 Persistent Option Settings
25. LEX to automatically determine the number of passes and should suffice for most problems Set it to a positive integer to specify a particular number of passes mipstartstatus il default 1 mipstartvalue i2 default 1 These directives control how existing MIP solution information is used by CPLEX The default value of i1 1 tells CPLEX to use incoming variable and constraint statuses Incoming statuses can be ignored by setting i1 0 Note however that mipstartstatus is normally overridden by the AMPL option send_statuses which can take on the following values Table 7 1 Values of the AMPL Option send_statuses 0 gt gt send no solver status values 1 default gt gt send statuses if there are no integer variables 2 gt send statuses even if there are integer variables ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 51 52 By default i2 1 variable values are checked to see if they provide an integer feasible solution before the problem is optimized If an integer feasible solution is found the objective function value is used as a cutoff during branch amp bound To ignore existing values set i2 0 prerelax i default 0 Setting i 1 invokes the CPLEX presolve for the linear program associated with the initial relaxation of a mixed integer program All other presolve settings apply Sometimes additional reductions can be made beyond any previously performed MIP presolve reductions presolvenode i default 0 The presolvenode
26. M manual and a license key that enables the use of AMPL and or CPLEX Follow the instructions in that manual for details on how to install the license key Usage Notes The CPLEX solver for AMPL is named cplexamp cplexamp exe on Windows This version of AMPL will use this solver by default Older versions of the CPLEX solver for AMPL were simply named cplex cplex exe on Windows Some users of that version may have specified the solver in their model or run files like this option solver cplex If you have models containing settings like this you will encounter errors or the old version of the solver might be invoked There are two ways to fix this Ideally you should change these lines to option solver cplexamp If that is not practical you can copy the file cplexamp to cplex If you do the latter you must remember to copy it again the next time you upgrade cplexamp ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Installed Files Unix systems ampl cplexamp amplcplex90userguide pdf examples Windows Systems ampl exe cplexamp exe cplex90 d411 examples AMPLCPLEX isu exhelp32 exe Examples readme txt models looping industries industries finance industries logistic industries product industries purchase industries schedule ILOG AMPL CPLEX SYSTEM 9 0 AMPL The CPLEX solver for AMPL User s Manual for AMPL CPLEX Directory of examples see Examples below AMPL The CPLEX solver
27. PLEX indicating that the linear program has been perturbed more than once r is probably too large reduce it to a level where only one perturbation is required The default doperturb value of i1 0 selects CPLEX s automatic perturbation strategy If an automatic perturbation occurs early in the solution process consider setting i1 1 to select perturbation at the outset This alternative will save the time of first allowing the optimization to stall before activating the perturbation mechanism but is useful only rarely for extremely degenerate problems The perturblimit parameter governs the number of stalled iterations CPLEX allows before perturbing the problem The default value of 12 0 causes CPLEX to determine this number based on the characteristics of the particular problem being solved Setting i2 toa positive integer value identifies a specific number of stalled iterations to tolerate before perturbing the problem ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE feasibility r1 default 1 0e 6 markowitz r2 default 0 01 optimality r3 default 1 0e 6 If a problem is making slow progress through Phase I or repeatedly becomes infeasible during Phase II numerical difficulties have arisen Adjusting the algorithmic tolerances controlled by these directives may help Decreasing the feasibility tolerance increasing the optimality tolerance and or increasing the Markowitz tolerance will typically improve numerical behavior The feasibility
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29. aints however as the number of calculations required per iteration in this situation is usually too large to afford any advantage ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE If devex pricing helps you may wish to try steepest edge pricing 1 2 This alternative incurs a substantial initialization cost and is computationally the most expensive per iteration but may dramatically reduce the number of iterations so as to produce the best results on exceptionally difficult problems The variant using slack norms i 3 is a compromise that sidesteps the initialization cost it is most likely to be advantageous for relatively easy problems that have a low number of iterations or time per iteration Full reduced cost pricing i 4 is a variant that computes a reduced cost for every variable and selects as entering variable one having most negative reduced cost or most positive as appropriate Compared to CPLEX s standard reduced cost pricing 1 1 full reduced cost pricing takes more time per iteration but in rare cases reduces the number of iterations more than enough to compensate This alternative is supplied mainly for completeness as it is proposed in many textbook discussions of the simplex algorithm dgradient i default 0 This directive governs the dual simplex algorithm s choice of a pricing procedure that determines which variable is selected to leave the basis at each iteration Your choice is likely to make a substantial diffe
30. anding model applications around the world AMPL helps you create models with maximum productivity By using AMPL s natural algebraic notation even a very large complex model can often be stated in a concise often less than one page understandable form As its models are easy to understand debug and modify AMPL also makes maintaining models easy Using this Guide This brief guide describes starting up AMPL reading a model and supplying data and solving optimizing the model using CPLEX The first three sections cover issues such as using command line options and environment variables and using AMPL on different operating systems Later sections provide a detailed description of CPLEX directives ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 1 This document does not provide full installation and set up instructions Documentation describing other AMPL compatible solvers distributed by ILOG is also available separately This Guide does not teach you the AMPL language To learn and effectively use the features of the AMPL language you should have a copy of the book AMPL A Modeling Language for Mathematical Programming by Robert Fourer David M Gay and Brian W Kernighan ISBN 0 534 50983 5 first published in 1993 by The Scientific Press now published by Duxbury Press This book includes a tutorial on AMPL and optimization modeling models for many classical problems such as production transportation blending and scheduling di
31. aralle CPLEX installing 4 batch mode 8 command line switches 19 configuration table 2 description 1 end session 7 execute solver outside AMPL 16 installing 2 launching AMPL 7 learning the AMPL language 2 let command 79 licensing 4 requirements 2 solver interface 11 ampl prompt 7 append directives 27 ASCII format problem and solution files 15 autoopt directive 31 auxiliary files creating 15 B backtrack directive 53 baralg directive 40 barcorr directive 40 bardisplay directive 45 bargrowth directive 40 bariterlim directive 43 barobjrange directive 40 baropt directive 31 baroutofcore directive 40 barrier algorithm ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Index 83 directives 40 barstart directive 41 barthreads directive 4 31 41 basic solution simplex algorithm 29 basis simplex algorithm 29 basisinterval directive 36 batch mode 8 bbinterval directive 53 bestnode suffix 68 binary format problem and solution files 15 boundstr directive 49 branch directive 54 C cliguecuts directive 50 clocktype directive 43 61 coeffreduce directive 50 command let 79 option 12 19 option solver 11 predefined commands 20 solution 14 write 14 15 command line switches 19 commands display 14 comptol directive 41 concurrentopt directive 31 configuration 2 covercuts directive 50 CPLEX append directives 27 barrier algorithm 23 barrier algorithm OP extension 25
32. btain the solution Note that the MPS format does not provide a way to distinguish between objective maximization and minimization However CPLEX assumes that the objective is to be minimized There is no standardization on this issue other solvers may assume maximization Thus it is incumbent upon the user of the MPS format to ensure that the objective sense in the AMPL model corresponds to the solver s interpretation Temporary Files Directory If the TMPDIR option is not set AMPL writes the problem and solution files and other temporary files to the current directory You can give a specific location for the temporary files by setting option TMPDIR to a valid path On a PC you might use ampl option TMPDIR D temp On a Unix machine a typical choice would be ampl option TMPDIR tmp ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 17 18 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Command Line Switches Customizing AMPL Certain AMPL options normally set with the opt ion command during an AMPL session can also be set when AMPL is first invoked This is done using a command line switch consisting of a hyphen and a single letter followed in some cases by a numeric or string value You will find these switches most useful when you have one or more model data or run file that you want AMPL to process using different option settings at different times without actually editing the files themselves The table bel
33. by actually solving subproblems for different choices of branching variable The variable yielding the best results is then chosen Strong branching requires more time for each node but usually fewer nodes to solve the problem This strategy works especially well on binary problems where the number of binary variables is significantly greater than the number of rows It is also useful when memory is limited creating fewer nodes requires less memory Pseudo reduced costs i 4 are related to pseudocosts i 2 but are less expensive to compute They may therefore be advantageous on models whose LP relaxation contains many hundreds or thousands of fractional variables that are potentially to be branched upon ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 59 Directives for Relaxing Optimality 60 In dealing with a difficult integer program you may need to settle for a good solution rather than a provably optimal one The following directives offer various ways of weakening the optimality criterion for CPLEX s branch and bound algorithm absmipgap r1 default 0 0 mipgap r2 default 1 0e 4 The optimal value of your integer program is bounded on one side by the best integer objective value found so far and on the other side by a value deduced from all the node subproblems solved so far The search is terminated when either best nod best integer lt rl or best nod best integer 1 0 best node lt r2 Thus the re
34. ceive any useful solution in response to the solve command after a reasonable amount of time and are in doubt as to how to proceed consult the troubleshooting tips at the end of this section Directives for Preprocessing All of the preprocessing directives described in Using CPLEX for Linear Programming are also applicable to problems that specify integer valued variables The following directives control additional preprocessing steps that are applicable to certain mixed integer programs only aggcutlim i default 3 This directive controls the number of constraints that can be aggregated for generating flow cover and mixed integer rounding cuts In most cases the default setting of 3 will be satisfactory Set it to 0 to prevent any aggregation boundstr i default 1 Bound strengthening tightens the bounds on variables in mixed integer programs This may enable CPLEX to fix the variable and remove it from consideration during the branch amp bound algorithm By default i 1 CPLEX automatically decides whether to perform bound strengthening This reduction usually improves performance but occasionally takes a long time due to its iterative nature In cases where the time required for bound strengthening outweighs any subsequent reduction in run time disable this feature by setting i 0 To turn on bound strengthening set i 1 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 49 mipcuts i default 0 cliquecuts il default 0 covercu
35. ctive values of the best integer solution found so far and of the best unprocessed node subproblem The optimal value lies between these two When i1 2 a more detailed log line is displayed once every i2 nodes as well as for each node where an integer solution is found A indicates lines of the latter type The default of i2 1 gives a complete picture of the branch amp bound process which may be instructive for small examples With a larger choice of 12 this setting can be very useful for evaluating the progress of long runs the log line includes a count of the number of active nodes which gives an indication of the rate at which the search tree is growing or shrinking in memory When 11 3 CPLEX also prints information on node cut and node presolve The LP iteration log for the root node 1 1 4 and for all subproblems i 1 5 can also be displayed timing i default 0 This directive can be used to display a summary of processing times It works the same for integer programming as for linear programming as described in Using CPLEX for Linear Programming on page 29 Common Difficulties 64 The following discussion addresses the difficulties most often encountered in solving integer programs with CPLEX Running Out of Memory The most common difficulty when solving MIP problems is running out of memory This problem arises when the branch amp bound tree becomes so large that insufficient memory is available to solve an LP
36. d number of iterations before switching to barrier Set the simplex iteration limit to a reasonably low number of dual iterations and then invoke this hybrid solutions strategy by setting the mipalgorithm directive to 5 Remember that setting a simplex iteration limit apples to all invocations of the simplex solvers If the iteration limit is set too low it might prematurely terminate cleanup iterations sometimes needed at the conclusion of a crossover operation Since the dual simplex solver will most often be the best method specify a sufficient number of iterations before forcing a switch to barrier For either of the above mipalgorithm strategies it is beneficial to set the barrier algorithm option to settings 1 or 2 Either of these nondefault choices is better at detecting infeasibility a frequent characteristic of MIP subproblems ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Defined Suffixes for CPLEX The most common use of AMPL suffixes is to represent solver result values that correspond to variables constraints and other model components Yet only the most standard kinds of results such as reduced costs given by X rc where x is a variable name and slacks given by C slack where C is a constraint name are covered by the built in suffixes To allow for solver specific optimization results AMPL permits solvers to define new suffixes and to associate solution result information with them Similarly users can also define su
37. des Note that CPLEX takes 91 nodes and 601 simplex iterations to find the optimal integer solution Now let us provide CPLEX with branching priorities for all variables as well as a preferred branching direction for a single variable Note that before we re run CPLEX we set mipstartvalue to discard the existing solution ampl option cplex_options mipstartvalue 0 ampl suffix priority IN integer gt 0 lt 9999 ampl suffix direction IN integer gt 1 lt 1 ampl let i in ORIG j in DEST s ampl Use i j priority ampl sum p in PROD demand j p ampl let Use GARY FRE direction 1 ampl solve CPLEX 9 0 optimal integer solution objective 235625 446 simplex iterations 64 branch and bound nodes Indeed CPLEX now requires fewer nodes 64 and fewer simplex iterations 446 to reach optimality While this is not a dramatic improvement larger cases where directing branch and bound in this manner makes the difference between unsolvability and finding the solution in a few minutes are well known Another form of algorithmic control is provided by the suffix bestnode of your model s objective function which returns the best node value at the present state of optimization after control is returned to AMPL from the solve command If the optimization terminates for some reason other than a proved optimum such as a time limit or other limit the bestnode suffix in comparison with the solution val
38. different solver termination conditions All valid solve codes with the corresponding termination message from CPLEX are listed in the table below Table 9 2 Solve Codes and Termination Messages Number Message at termination 0 optimal solution 1 primal has unbounded optimal face 2 optimal integer solution 3 optimal integer solution within mipgap or absmipgap 100 best solution found primal dual feasible 200 infeasible problem 201 infeasible with phase II singularities ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Table 9 2 Solve Codes and Termination Messages Continued Number Message at termination 202 infeasible with phase singularities 203 optimal with unscaled infeasibilities 204 converged dual feasible primal infeasible 205 converged primal and dual infeasible 206 best solution found primal infeasible 207 best solution found primal dual infeasible 208 infeasible or unbounded in presolve 220 integer infeasible 300 unbounded problem 301 converged primal feasible dual infeasible 302 best solution found dual infeasible 400 phase II objective limit exceeded 401 phase ll iteration limit 402 phase iteration limit 403 phase II time limit 404 phase time limit 405 primal objective limit reached 406 dual objective limit reached 410 node limit with no integer solution 411 time limit with no integer solution 412 treememory limit with no integer solution 420 mixed integer solutions limit 421 node limit with integer solu
39. ding on the value at the current most recently created active node CPLEX either branches from that node or else backtracks to the node that has the best bound 12 1 or best estimate 12 2 or i2 3 among all active nodes ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 53 When used in conjunction with best estimate node selection i12 2 the bbinterval setting i1 controls the interval for selecting the best bound node Decreasing this interval may be useful when best estimate finds good solutions but makes little progress moving the bound Conversely increasing i1 may help when the best estimate node selection does not find any good integer solutions The backtracking decision is made by comparing the value bound or estimate at the current node with the values at parent nodes in the tree If the value of the current node has degraded increased for a minimization decreased for a maximization by at least a certain amount relative to the values at parent nodes then a backtrack is performed The cutoff for degradation is determined by an internal heuristic that is regulated by the value of r Lower values of r which can range from 0 to 1 favor backtracking resulting in a strategy that is more nearly breadth first The search jumps around fairly high in the tree solving somewhat dissimilar subproblems Good solutions are likely to be found sooner through this strategy but the processing time per node is also greater Higher values of
40. directive 63 mipemphasis directive 55 mipgap directive 60 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 87 mipinterval directive 63 mipstartstatus directive 51 mipstartvalue directive 51 mipthreads directive 4 31 56 mircuts directive 50 N netfind directive 38 netopt directive 32 network primal simplex algorithm 29 nodefile directive 56 nodelim directive 63 nodeselect directive 53 nonlinear quadratic programs 23 numeric result codes interpretation 76 O objdifference directive 60 optimality directives for relaxing 60 optimality directive 43 optimization methods available in CPLEX 29 option cautions 19 eexit 19 funcwarn 20 gentimes 20 linelim20 mip_priorities 55 outopt 20 presolve 20 randseed 20 substout 20 times 20 version 20 options add options 13 persistent settings 20 preserve settings 21 set options 19 specify solver options 12 ordering directive 41 ordertype directive 57 out of memory 16 output directives for controlling 63 directives for controlling output 45 p Parallel CPLEX installing with AMPL 4 persistent option settings 20 perturbation directive 42 perturblimit directive 42 pgradient directive 36 piecewise linear programs transformation 24 plconpri directive 57 plobjpri directive 57 precompress directive 33 predual directive 33 preprocessing directives 32 directives integer programs only 49 88 ILOG AMPL CPLEX SYSTEM 9 0 USER S
41. directive determines how CPLEX applies its presolve to the LP subproblems at the nodes of the branch and bound tree By default CPLEX decides automatically Set i 1 to force node presolve Set i 1 to prevent it The default setting usually works best probe i default 0 This directive controls whether CPLEX should perform probing before solving the MIP Probing can lead to dramatic reductions in the problem size but can also consume large amounts of time By default 1 0 CPLEX automatically decides whether to perform probing To disable probing set i 1 To enable probing set it to a value of 1 2 or 3 A larger value results in an increased level of probing More probing can lead to greater reductions in problem size but also significant increases in probing time sosl i default 1 An optimization problem containing restrictions that at most one of a specified group of variables can take a nonzero value is a form of discrete optimization that can be handled by an equivalent mixed integer program When i is at its default value of 1 this conversion is performed using a structure known as a special ordered set of type 1 If i is changed to 0 the conversion is made instead to an equivalent formulation using multiple binary variables sos2 i default 1 An optimization problem containing piecewise linear terms may have to be converted to an equivalent mixed integer program as explained in Piecewise linear Programs on page 24 When i is at
42. e 08 scale 1 lpiterlim 100 CPLEX 9 0 optimal solution objective 88 2 1 iterations 0 in phase I CPLEX confirms each directive it will display an error message if it encounters one that it does not recognize CPLEX directives consist of an identifier alone or an identifier followed by an sign and a value a space may be used as a separator in place of the You may store any number of concatenated directives in cplex_options The example above shows how to type all the directives in one long string using the character to indicate that the string continues on the next line Alternatively you can list several strings which AMPL will automatically concatenate ampl option cplex_options crash 0 dual amp1 feasibility 1 0e 8 scale 1 ampl lpiterlim 100 In this form you must take care to supply the space that goes between the directives here we have put it before feasibility and iterations If you have specified the directives above and then want to try setting say optimalit y to 1 0e 8 and changing crash to 1 you could use ampl option cplex options ampl optimality 1 0e 8 crash 1 However this will replace the previous cplex_options string The other previously specified directives such as feasibility and iterations will revert to their default values 26 ILOG AMPL CPLEX SYsTEM 9 0 USER S GUIDE CPLEX supplies a default value for every directive not explicitly specified defaults are indicated
43. e bounds By definition members of an IIS have no feasible solution but dropping any one of them permits a solution to be found to the remaining ones Clearly knowing the composition of an IIS can help localize the source of the infeasibility Setting i 2 generates a potentially smaller IIS at the cost of greater computation time When iisfindis used CPLEX uses the iis suffix to specify which variables and constraints are in the IIS as explained in Diagnosing Infeasibilities on page 70 logfile f1 This directive instructs CPLEX to create a log file named 1 that will contain output from the optimization The amount of output in the log file will depend on other directives such as the display directive described above lpdisplay i default 0 The default choice of i 0 produces a minimal few lines of output from CPLEX summarizing the results of the run When i 1 a log line recording the iteration number and the scaled infeasibility or objective value is displayed after each refactorization of the basis matrix Additional information on the operation of the network simplex algorithm is also provided if applicable This is often the appropriate setting for tracking the progress of a long run ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 45 When i 2 a log line is displayed after each iteration This level of output is occasionally useful for diagnosing problems of degeneracy or instability in the simplex algorithm sensitivity When sp
44. e dual has a much smaller basis matrix and CPLEX may be able to solve it more efficiently ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE The primal and dual directives instruct CPLEX to set up the primal or the dual formulation respectively The dualthresh directive makes a choice the dual LP if the number of constraints exceeds the number of variables by more than i and the primal LP otherwise autoopt dualopt baropt primalopt siftopt concurrentopt The autoopt directive instructs CPLEX to select an appropriate algorithm to solve the problem You can specify a particular algorithm by the dualopt baropt and primalopt directives which invoke dual simplex barrier and primal simplex methods respectively The autoopt directive will most frequently select the dual simplex method The two simplex variants use similar basis matrices but employ opposite strategies in constructing a path to the optimum Any of the algorithms can be applied regardless of whether the primal or the dual LP is set up as explained above in general the six combinations of primalopt dualopt baropt and primal dual perform differently Consider trying the barrier method or the primal simplex method if CPLEX s dual simplex method reports problems in its display or if you simply wish to determine whether another algorithm will be faster Few linear programs exhibit poor numerical performance in both the primal and the dual algorithms In general the barrier method te
45. e eee eee 60 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Chapter 8 Chapter 9 Directives for Halting and Resuming the Search eee eee 61 Directives for Controlling Output 0 0 0 0 cee eee eee eee 63 Common Difficulties sz ceiien a tne he hat A cae a o Se ek eae 64 Running Out of Memory 00 0 cette eee tees 64 Failure To Prove Optimality 0 0 0 2 65 Difficult MIP Subproblems niiin cieei deka eee ee a hed pate Renate Da 66 Defined Suffixes for CPLEX 00 0c e eee eee 67 Algorithmic Control sisita saana ti Pees VG Gd nee ee ee 67 Sensitivity Ranging 222 0660 bie ete at a eee eee ete a ea 69 Diagnosing Infeasibilities 0 0 0 ccc eee eee eee 70 Direction of Unboundedness ccoocccccc nan naa 72 CPLEX Status Codes in AMPL nenuannannna 75 Solve Codes c 5 cece eee eee vk m ed chee eee ee a 75 Basis Status ic ii a a ol ias 78 A A A A a i A A a ora eee ee 83 ILOG AMPL CPLEX SYsTEM 9 0 USER S GUIDE vii viii ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 1 1 3 1 4 1 6 1 6 2 6 3 6 4 7 1 7 2 7 3 7 4 7 5 9 1 9 2 A 1 List of Tables AMPL GonfigurationTable s oc sssaaa o a e a tee date Sete le bee eee ieee ceo eee le 2 A xiliary FOSA heck egal a al ice a aaa A bs ak te a ia 15 AMPL Option Names for Command Line Switches 0 00 eee e eee eee eee 19 Settings for the dependency Directive e ueruenuenunn
46. ecified this directive instructs CPLEX to output sensitivity ranges corresponding to the optimal solution For variables the suffix current provides the corresponding objective function coefficient in the current problem and down and up specify the smallest and largest values for which the current basis remains optimal For constraints the suffixes apply to the constant value or right hand side Details on CPLEX defined suffixes are provided in Defined Suffixes for CPLEX on page 67 timing i default 0 When this directive is changed to 1 from its default value of 0 a summary of processing times is displayed to standard output Input 0 06 CPU 0 06 Wall Solve 6 42 CPU 6 42 Wall Output 0 05 CPU 0 05 Wall Input is the time that CPLEX takes to read the problem from a file that has been written by AMPL Solve is the time that CPLEX spends trying to solve the problem Output is the time that CPLEX takes to write the solution to a file for AMPL to read CPU values provide processor time whereas Wa11 values provide elapsed time Setting i 2 writes the timing information to standard error and setting i 3 directs the information to both the standard output and the standard error The latter two options are only interesting for Unix CPLEX for AMPL users version This directive causes the display of the CPLEX version being used to solve the problem ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Using CPLEX for Integer Programm
47. ee size and overall solution time Branching control can also be exercised using the direction suffix described in Algorithmic Control on page 67 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE heuristicfreq i3 default 0 Use the heuristicfreg directive to specify the frequency with which CPLEX applies a rounding heuristic at the nodes This can help find solutions missed using other settings The default value 13 0 instructs CPLEX to use internal logic to decide when to apply the heuristic To suppress application of the heuristic at all nodes let 13 1 To specify the node frequency with which CPLEX applies the heuristic set 13 to a positive integer mipalgorithm il default 0 mipcrossover i2 default 1 This directive specifies the algorithm or combination of algorithms that CPLEX will apply to solve the LP subproblem at each branch amp bound node The recognized values of i1 are Table 7 2 Settings for the mipcrossover Directive 0 Automatic 1 Primal simplex 2 Dual simplex 3 Network simplex 4 Barrier 5 Sifting The default strategy chooses the algorithm by using an internal heuristic based on the type of subproblem Typically CPLEX will use the dual simplex method when the problem is linearly constrained and the barrier method when it is a quadratically constrained program For linear programming subproblems the default settings usually perform well but other strategies may significantly reduce the time per node except
48. ely recognized format for linear and integer programming problems Although it is a standard supported by many solvers and modeling systems including AMPL MPS file format is neither compact nor easy to read and understand AMPL s binary file format is a much more efficient way for modeling systems and solvers to communicate Also MPS file format cannot be used for nonlinear problems and not all MPS compatible solvers support exactly the same format particularly for mixed integer problems ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE AMPL does have the ability to translate a model into MPS file format as outlined below With this feature you may be able to solve AMPL models with a solver that reads its problem input in MPS file format If you choose to use this feature you will find AMPL s ability to produce auxiliary files very useful since these files can be used to relate the MPS file format information to the sets variables constraints and objectives defined in the AMPL model However you will not be able to bring the solution variable values dual values and so on back into AMPL further work with the solution must be performed outside of AMPL To translate your model into MPS file format use the write command as outlined above with m as the first letter of the filename To illustrate the command shown below creates a file named steel mps ampl write msteel In most cases you will need to run your solver separately to o
49. em the objective at this second solution is lower than at the first To continue past this point with all the same CPLEX directives you need only type solve ampl solve CPLEX 9 0 solutionlim 1 varselect 1 starttree multmip tre endtree multmip tre CPLEX 9 0 optimal integer solution objective 235625 601 simplex iterations 142 branch and bound nodes ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE We see here that the objective value from the second solution 235625 was optimal but that CPLEX had to process an additional 18 nodes to prove optimality This is not by chance The branch amp bound procedure must often examine many nodes to prove optimality after it has found an optimal solution nodelim i default 2 1e9 The search is terminated after i linear programming subproblems have been solved The default value can vary depending on the hardware priorities i default 0 This directive instructs CPLEX to generate an automatic priority order based on characteristics of the model it has received for solving The default of priorities 0 means that no such priority order will be built and CPLEX will use its own methods for branching variable selection A value of priorities 1 means variables will be ordered according to decreasing or increasing objective function value for a minimization or maximization problem A value of priorities 2 means variables will be ordered by the range of their possible values so that for instanc
50. es any fractional binary variables will be branched upon before other fractional integer variables A value of priorities 3 means variables will be ordered according to increasing or decreasing objective function cost per coefficient count in the constraint matrix for a minimization or maximization problem solutionlim i default 2 1e9 The search is terminated after i feasible solutions satisfying the integrality requirements have been found timelimit r default 1 0e75 The search is terminated after r seconds of computing time treememlim r default 1 0e75 The total size of the branch amp bound tree is limited to r megabytes Directives for Controlling Output When invoked by solve CPLEX normally returns just a few lines to your screen to summarize its performance The following directives let you choose more output which may be useful for monitoring the progress of a long run or for comparing the effects of other directives on the behavior of the branch amp bound algorithm Output normally comes to the screen but may be redirected to a file by specifying solve gt filename mipdisplay il default 0 mipinterval i2 default 1 The default of 11 0 produces a minimal few lines of output from CPLEX summarizing the results of the run ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 63 When 11 1 a single log line is displayed for every integer solution found The information includes the number of nodes processed and the obje
51. ete variables are present then the model is termed Mixed Integer QCP or MIQCP The Q matrix for each quadratic constraint must be positive semi definite just as for a quadratic objective function to ensure that the feasible space remains convex Most of the comments regarding CPLEX features in section Quadratic Programs above also pertain to QCP with the additional observation that only the barrier optimizer applies to continuous models that have any quadratic constraints and therefore barrier is also the only choice for subproblem solution of MIQCP models ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 25 Specifying CPLEX Directives In many instances you can successfully apply CPLEX by simply specifying a model and data setting the solver option to cplex and typing solve For larger linear programs and especially the more difficult integer programs however you may need to pass specific options also referred to as directives to CPLEX to obtain the desired results To give directives to CPLEX you must first assign an appropriate character string to the AMPL option called cplex options When CPLEX is invoked by solve it breaks this string into a series of individual directives Here is an example ampl model diet mod ampl data diet dat ampl option solver cplexamp ampl option cplex options crash 0 dual ampl feasibility 1 0e 8 scale 1 ampl lpiterlim 100 ampl solve CPLEX 9 0 crash 0 dual feasibility l
52. etects that there is no feasible solution it is repeated with the iisfind directive ampl model diet mod ampl data diet2 dat ampl option solver cplexamp ampl solve CPLEX 9 0 infeasible problem 7 iterations 7 in phase 1 ampl option cplex_options iisfind 1 ampl solve CPLEX 9 0 iisfind 1 CPLEX 9 0 infeasible problem 0 iterations Returning iis of 7 variables and 2 constraints suffix iis symbolic OUT option iis_table 0 non not in the iis 1 low at lower bound 2 fix fixed 3 upp at upper bound You can use display to look at the iis values that have been returned ampl display _varname _var iis _conname amp1 _con iis _varname _var iis _conname con iis 1 Buy BEEF upp diet A non 2 Buy CHK low diet B1 non 3 Buy FISH low diet ea low 4 Buy HAM upp N rst CM non 5 Buy TMCH Y non diet i upp 6 Buy MTL upp diet CAL non 7 Buy SPG low 8 Buy TUR low This information indicates that the IIS consists of four lower and three upper bounds on the variables plus the constraints providing the lower bound on B2 and the upper bound on NA in the diet Together these restrictions have no feasible solution but dropping any one of them will permit a solution to be found to the remaining ones Of course in our example we shouldn t actually drop the lower bounds on the Buy variable we could end up with negative values However we could
53. ex options presolve 0 ampl solve CPLEX 9 0 presolve 0 CPLEX 9 0 unbounded problem 30 iterations 0 in phase I variable unbdd returned suffix unbdd OUT ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE The suffix message indicates that unbdd has been created automatically You can use this suffix to display the direction of unboundedness which is quite simple in this case ampl display Supply Price unbdd Supply_Price unbdd 1 1 6 1 11 1 Le 1 21 1 ap 7 1 12 1 17 1 220 1 1 8 1 13 1 18 1 231 9 1 14 1 19 51 241 2 1 10 1 15 1 20 1 25 1 ds uN r ampl display Demand Price unbdd Demand_Price unbdd A3 1 A6 1 A8 1 A9 1 B2 1 B4 1 r ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 73 74 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Solve Codes CPLEX Status Codes in AMPL When CPLEX returns control to AMPL after a solve command built in AMPL parameters and an AMPL option provide information on the outcome of the optimization as shown ampt ampt ampt ampl Pp Pp Pp Pp sol sol ampt model oil mod data oil dat option solver cplexamp display solve_result_num solve_result ve_result_num 1 ve result solve CPLEX 9 0 optimal solution objective 12 20834324 3 7 ampt iterations 0 in phase I display solve_result_num solve_result solve_result_num 0 solve_result solved ampt option so
54. ffixes to control the solver User defined suffixes understood by CPLEX and suffixes defined by CPLEX are described in this section Algorithmic Control For each integer variable in a problem CPLEX recognizes a preferred branching direction and a branching priority specified by the following two suffixes direction priority Branching direction preference can be specified for each variable by setting its direction suffix to a value between 1 and 1 Variables not assigned a suffix value get a default value of zero A negative value indicates a preference for branching down and a positive value indicates a preference for branching up ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 67 For variables with direction at zero the branching direction is determined by the branching related directives described in Directives for Algorithmic Control on page 53 Each time that CPLEX must choose a fractional valued integer variable on which to branch it gives preference to the fractional variables that have the highest priority value A judicious choice of priorities any number between 0 and 9999 is valid can guide the search in a way that reduces the number of nodes generated For example let us consider a model drawn from pages 300 301 of the AMPL book ampl model models multmip3 mod ampl data models multmip3 dat ampl solve CPLEX 9 0 optimal integer solution objective 235625 601 simplex iterations 91 branch and bound no
55. file called steel run containing the commands model steel mod data steel dat option solver cplexamp solve display Make gt steel ans Note that this assumes that steel run is in the same directory as the model and data files and that AMPL can be found on the path You can then run AMPL as follows C X gt ampl steel run A more flexible approach which is a commonly followed convention among AMPL users 1s to put just the AMPL commands the last three lines in the example above in a file with the run extension You can then type C X gt ampl steel mod steel dat steel run which accomplishes the same thing as C gt ampl ampl include steel mod ampl include steel dat ampl include steel run ampl quit C gt 8 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE If you intend to load several files and solve a problem but you want to type a few interactive commands in the middle of the process type the character in place of a filename AMPL processes the files on the command line from left to right when it encounters the symbol it displays the amp1 prompt and accepts commands until you type end For example you could type C gt ampl steel mod steel dat steel run ampl let avail 50 ampl end This will solve the problem as before but with the parameter avail set to 50 instead of 40 the value specified in steel dat To start AMPL load a model and data file and wait for y
56. for the quadratically constrained case where barrier is the only available choice These settings do not significantly affect the number of nodes that must be visited during the search When the Barrier algorithm is used to solve subproblems i1 4 by default 12 1 CPLEX uses primal simplex for the crossover In certain cases dual simplex may be faster When the subproblems are quadratically constrained programs CPLEX does not perform a crossover so this directive has no effect option mip_priorities vl il v2 i2 From CPLEX 7 0 onwards the mip priorities option has been superseded by the priority suffix Please refer to Algorithmic Control on page 67 for a discussion of setting priorities by individual variable mipemphasis i default 0 This directive guides CPLEX s branch amp bound strategy The default of 0 corresponds to a balance between searching for feasible solutions and proving optimality and works well for most users purposes A setting of 1 shifts the emphasis strongly toward finding new feasible solutions and may be an appropriate setting with difficult models for which a proof of optimality is unlikely to be reached anyway ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 55 56 A setting of 2 shifts the emphasis slightly more toward the proof of optimality and away from finding new feasibles A setting of 3 shifts the emphasis very aggressively toward the optimality proof by concentrating on moving the best bou
57. h and without presolve On the other hand if CPLEX consistently reports that presolve eliminates no variables or constraints you can save a little processing time by turning presolve off To request a report of the number of eliminations performed by presolve see the prestats directive below prestats i default 0 When this directive is changed to 1 from its default of 0 CPLEX reports on the activity of the aggregation and presolve routines Presolve eliminated 1645 rows and 2715 columns in 3 passes Aggregator did 22 substitutions Presolve Time 1 70 sec During the development of a large or complex model it is a good idea to monitor this report and to turn on its AMPL counterpart by setting option show stats to 1 An unexpectedly large number of eliminated variables or constraints may indicate that the formulation is in error or can be substantially simplified ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE scale i default 0 This directive governs the scaling of the coefficient matrix The default value of i 0 implements an equilibration scaling method which is generally very effective You can turn off the default scaling by setting i 1 A value of 1 invokes a modified more aggressive scaling method that can produce improvements on some problems Since CPLEX has internal logic that determines when it need not scale a problem setting the scale directive to 1 rarely improves performance Directives for Controlling t
58. h commands such as display For example if you have just solved a problem created from steel mod and steel dat you could type ampl display Make Time To save this output in a file you can use redirection ampl display Make Time gt mysol txt Note that when you simply mention the name of a constraint in a display statement AMPL will display the dual value shadow price of that constraint not its left hand side value You can use the AMPL suffix notation to display the left hand side value as described in the book AMPL A Modeling Language for Mathematical Programming Saving temporary files AMPL deletes the temporary problem n1 and solution sol files after a solver is finished so no permanent record of the solution is kept unless you save the output yourself for example using display with redirection as illustrated above To override the deletion of temporary files you can use the AMPL write command For example C gt ampl ampl model steel mod data steel dat ampl write bsteel ampl solve CPLEX 9 0 optimal solution objective 192000 2 iterations 0 in phase I ampl quit The first letter b in the filename portion of the write command is interpreted specially as explained below If you now display the files in the current directory with a command such as dir steel you will find the problem file stee1 n1 and the solution file steel sol To later view the solution values you would use
59. h double quotation marks Persistent Option Settings 20 If you have many option settings or other commands that you would like performed each time AMPL starts you may create a text file containing these commands in AMPL language syntax Then set the environment variable name OPTIONS IN to the pathname of this text file For example on a Windows PC you should type C gt set OPTIONS_IN c amplinit txt If you are using a C shell on a Unix machine you would type something like setenv OPTIONS IN ijr amplinit txt AMPL reads the file referred to by OPTIONS IN and executes any commands therein before it reads any other files mentioned on the command line or prompts for any interactive commands ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE If you want AMPL to preserve all of your option settings from one session to the next you can cause AMPL to write the options into a text file named by setting the AMPL option OPTIONS_INOUT ampl option OPTIONS INOUT c lamplopt txt Before exiting AMPL writes a series of option commands to the file named by OPTIONS_INOUT which when read will set all of the options to the values they had at the end of the session To use this text file set the corresponding environment variable to the same filename C gt set OPTIONS_INOUT c amplopt txt After you do this AMPL will read and execute the commands in amplopt t xt when it starts up When you end a session AMPL will write the curre
60. he Simplex Algorithm Several key strategies of the primal and dual simplex algorithms can be changed through CPLEX directives If you are repeatedly solving a class of linear programs that requires substantial computer time experimentation with alternative strategies can be worthwhile advance i default 0 By default 1 0 the advanced basis indicator is off You can set it according to Table 6 2 Table 6 2 Settings for the advance Directive Setting Effect 0 This is the default value The advanced basis indicator is off 1 The advanced indicator is on ILOG CPLEX uses an advanced basis supplied by the user Preprocessing is skipped The advanced indicator is on and ILOG CPLEX will crush an advanced basis or starting vector supplied by the user If this parameter is set to 1 or 2 ILOG CPLEX uses advanced starting information when optimization is initiated If you anticipate the advanced basis to be a close match for your problem so that relatively few iterations will be needed or if you are unsure then setting 1 is a good choice because it avoids some overhead processing If you anticipate that the simplex optimizer will require many iterations even with the advanced basis or if the model is large and preprocessing typically removes much from the model then setting 2 may yield a faster solution by giving you the advantages of preprocessing However in such cases you might also consider n
61. he first integer solution that CPLEX finds for example you can set solutionlim 1 together with endt ree and any other directives you like ampl model multmip3 mod ampl data multmip3 dat ampl option solver cplexamp ampl option cplex options ampl solutionlim 1 varselect 1 amp1 endtree multmip tre ampl solve CPLEX 9 0 solutionlim 1 varselect 1 endtree multmip tre CPLEX 9 0 mixed integer solutions limit objective 238225 251 simplex iterations 64 branch and bound nodes ampl display Trans gt multmip sol A display of the Trans variables at the values they take in the first integer solution has been directed to the file multmip sol for future examination You could also browse through the values interactively at this point When you are ready to continue you need only set starttree to the same file as endt ree and make any other changes to the branch amp bound directives that you wish Then give the solve command again ampl option cplex_options ampl solutionlim 1 varselect 1 ampl starttree multmip tre ampl endtree multmip tre ampl solve CPLEX 9 0 solutionlim 1 varselect 1 starttree multmip tre endtree multmip tre CPLEX 9 0 mixed integer solutions limit objective 235625 596 simplex iterations 124 branch and bound nodes ampl display Trans gt multmip so2 CPLEX s counts of the numbers of iterations and nodes are cumulative Since this is a minimization probl
62. her may be useful when diagnosing infeasibility or unboundedness presolve i default 1 Prior to invoking any simplex algorithm CPLEX applies transformations that reduce the size of the linear program without changing its optimal solution In this presolve phase constraints that involve only one non fixed variable are removed either the variable is fixed and also dropped for an equality constraint or a simple bound for the variable is recorded for an inequality Each inequality constraint is subjected to a simple test to determine if there exists any setting of the variables within their bounds that can violate it if not it is dropped as nonconstraining Further iterative tests attempt to tighten the bounds on primal and dual variables possibly causing additional variables to be fixed and additional constraints to be dropped AMPL s presolve phase as described in Section 10 2 of the AMPL book also performs many but not all of these transformations To see how many variables and constraints are eliminated by AMPL s presolve set option show_stats to 1 To suppress AMPL s presolver so that all presolving is done in CPLEX set option presolve to 0 CPLEX s presolve can be suppressed by changing i to 0 from its default of 1 In rare cases the presolved linear program although smaller is actually harder to solve Thus if CPLEX reports that many variables and constraints have been eliminated by presolve you may want to compare runs wit
63. ice is likely to make a substantial difference to the tradeoff between computational time per iteration and the number of iterations As a rule of thumb if the number of iterations to solve your linear program exceeds three times the number of constraints you should consider experimenting with alternative pricing procedures The recognized values of i are as follows Table 6 3 Settings for the pgradient Directive 1 Reduced cost pricing Hybrid reduced cost devex pricing Devex pricing Steepest edge pricing Steepest edge pricing in slack pace AA OUO N O Steepest edge with unit initial norms The reduced cost procedures are sophisticated versions of the pricing rules most often described in textbooks The devex and steepest edge alternatives employ more elaborate computations which can better predict the improvement to the objective offered by each candidate variable for entering the basis Compared to the default of i 0 the less compute intensive reduced cost pricing i 1 may be preferred if your problems are small or easy or are unusually dense say 20 to 30 nonzeros per column Conversely if you have more difficult problems which take many iterations to complete Phase I consider using devex pricing i 1 Each iteration may consume more time but the lower number of total iterations may lead to a substantial overall reduction in time Do not use devex pricing if your problem has many variables and relatively few constr
64. im directive is effectively infinity which means CPLEX will continue to write nodes to disk until it solves the problem or exhausts available disk space or encounters some other limit Disk node files are created in the temporary directory specified by the value of the workfiledir directive If no value is specified the directory specified by the TMPDIR on Unix or TMP on Windows environment variable is used If TMPDIR or TMP are not set either the current working directory is used Node files are deleted automatically when CPLEX terminates normally ordertype i default 0 CPLEX can automatically generate certain priority orders which determine the choice of branching variable based on specific problem features Use ordertype to specify the type of priority order The default value i 0 bypasses order generation Setting i 1 generates a priority order where variables with larger costs receive higher priority Setting i 2 generates a priority order where variables with smaller bound ranges receive higher priority This setting tends to be useful for models with binary variables that represent a logical decision and associated general integer variables that represent resource levels enabled by the outcome of the decision Setting i 3 tends to help set covering problems In such problems setting a binary variable to 1 covers a group of rows but incurs a cost Binary variables with smaller costs per row covered are good choices to set to 1 A
65. ing CPLEX Mixed Integer Algorithm For problems that contain integer variables CPLEX uses a branch amp bound approach The optimizing algorithm maintains a hierarchy of related linear programming subproblems referred to as the search tree and usually visualized as branching downward YN O Figure 7 1 CPLEX Mixed Integer Algorithm the Search Tree There is a subproblem at each node of the tree and each node is explored by solving the associated subproblem ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 47 48 The algorithm starts with just a top or root node whose associated subproblem is the relaxation of the integer program the LP that results when all integrality restrictions are dropped If this relaxation happened to have an integer solution then it would provide an optimal solution to the integer program Normally however the optimum for the relaxation has some fractional valued integer variables A fractional variable is then chosen for branching and two new subproblems are generated each with more restrictive bounds for the branching variable For example if the branching variable is binary or 0 1 one subproblem will have the variable fixed at zero the other node will have it fixed at one In the search tree the two new subproblems are represented by two new nodes connected to the root Most likely each of these subproblems also has fractional valued integer variables in which case the branching process must be
66. ing this tolerance to a smaller value may result in greater numerical precision of the solution but also increases the chance of a convergence failure in the algorithm and consequently may result in no solution at all Therefore caution is advised in deviating from the default setting For LPs and QPs that is when all the constraints are linear see the compto1 directive Directives for Improving Stability 42 CPLEX is highly robust and has been designed to avoid problems such as degenerate stalling and numerical inaccuracy that can occur in the simplex algorithm However some linear programs can benefit from adjustments to the following directives if difficulties are encountered doperturb il default 0 perturbation r default 1 0e 6 perturblimit i2 default 0 The simplex algorithm tends to make very slow progress when it encounters solutions that are highly degenerate in the sense of having many basic variables lying at one of their bounds rather than between them When CPLEX detects degenerate stalling it automatically introduces a perturbation that expands the bounds on every variable by a small amount thereby creating a different but closely related problem Generally CPLEX can make faster progress on this less constrained problem once optimality is indicated the perturbation is removed by resetting the bounds to their original values The value of r determines the size of the perturbation If you receive messages from C
67. ions You can specify option settings for a particular solver through the AMPL opt ion command CPLEX specific directives are described later in this document Since all solvers provide default settings for their options this is necessary only when your problem requires certain nondefault settings in order to solve or when certain settings yield improved performance or solution accuracy To specify solver options enter option solver_options settings where solver is replaced by the name of the solver you are using This approach allows you to set up different options for each solver you use and to switch among them by simply choosing the appropriate solver with the option solver command For example ampl option cplex options relax scale 1 Solver options consist of an identifier alone or an identifier followed by an sign and a value Some solvers treat uppercase and lowercase versions of an option identifier as eguivalent while others are sensitive to case so that RELAX is not the same as relax for example Solver option settings can easily become long enough to stretch over more than one line In such cases you can either continue a single guoted string by placing a character at the end of each line as in ampl option cplex options crash 0 dual ampl feasibility 1 0e 8 scale 1 ampl lpiterlim 100 Or you can write a series of individually quoted strings which will be concatenated automatically by AMPL as in
68. ions the benefit is highly dependent on problem structure it is best to try experimenting with both i 0 and i 1 relax This directive instructs CPLEX to ignore any integrality restrictions on the variables The resulting linear program is solved by whatever algorithm the above directives specify maximize minimize While AMPL completely specifies the problem and its objective sense it is possible to change the objective sense after specifying the model The two directives instruct CPLEX to set the objective sense to be minimize or maximize respectively Directives for Preprocessing Prior to applying any simplex algorithm CPLEX modifies the linear program and initial basis in ways that tend to reduce the number of iterations required The following directives select and control these preprocessing features aggregate il default 1 aggfill i2 default 10 When il is left at its default value of 1 CPLEX looks for constraints that possibly after some rearrangement define a variable x in terms of other variables two variable constraints of the form x y b constraints of the form x 2 y where x appears in less than i2 other constraints 32 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Under certain conditions both x and its defining equation can be eliminated from the linear program by substitution In CPLEX s terminology each such elimination is an aggregation of the linear program When il is 1 CPLEX decides how many pa
69. is section contain the entire AMPL CPLEX System not just the AMPL language processor After you have located the files read the CD booklet for instructions on setting up the distribution ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 3 FTP After downloading the files execute SETUP EXE from the Run dialog or in an MS DOS window Follow the instructions presented by the setup program To access the Run dialog box on Windows click on the Start button and select Run AMPL and Parallel CPLEX If you have purchased AMPL and Parallel CPLEX follow the above instructions for the appropriate media You will use the same programs to run in serial or parallel mode To make use of multiple threads refer to the documentation on the threads mipthreads and barthreads directives Licensing AMPL is licensed in the same way as CPLEX If you have already activated a license for the CPLEX Suite on this machine and you are not adding AMPL as a new feature then AMPL is already licensed and you should skip these licensing instructions Updating an Existing License If you are upgrading from a previous version of CPLEX please refer to the CPLEX License Update Instructions provided separately or contact the CPLEX License Administrator You should skip any installation steps that would establish a new license New Installation If you are installing CPLEX or AMPL for the first time you will receive an ILOG License Manager IL
70. its default value of 1 this conversion results in only one extra variable per piecewise linear breakpoint All of the extra variables associated with a particular piecewise linear term are marked as belonging together so that CPLEX s branch amp bound procedure knows to treat them specially Variables so marked have come to be known as a special ordered set of type 2 whence the name sos2 for this directive When i is changed to 0 from its default of 1 the conversion creates a larger number of variables but does not employ the special ordered set feature This alternative has no known advantages and is supplied for completeness only ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Directives for Algorithmic Control CPLEX has default values for the algorithmic control directives that often work well for solving a wide range of mixed integer programs However it is sometimes necessary to specify alternative values for one or more of the following directives to improve solution times You can view each of these directives as corresponding to a particular decision faced at each step in the branch amp bound procedure To be specific imagine that an LP subproblem has just been solved The sequence of decisions and the corresponding directives are then as follows Branch next from which node in the tree backtrack nodesel Branch by constraining which fractional variable at the selected node mip_priorities ordertype varselect refe
71. lex you should consider experimenting with the steepest edge procedures e The standard procedure i 2 and the variant in slack space i 3 have similar computational costs often their overall performance is similar as well though one or the other can be advantageous for particular applications e The variant using unit initial norms i 4 is a compromise that sidesteps the initialization cost it is most likely to be advantageous for relatively easy problems that have a low number of iterations or time per iteration Devex pricing i 5 is new in AMPL 9 0 pricing i default 0 To promote efficiency when using reduced cost pricing in primal simplex CPLEX considers only a subset of the nonbasic variables as candidates to enter the basis The default of i 0 selects a heuristic that dynamically determines the size of the candidate list taking problem dimensions into account You can manually set the size of this list to i gt 0 but only very rarely will this improve performance refactor i default 0 This directive specifies the number of iterations between refactorizations of the basis matrix At the default setting of i 0 CPLEX automatically calculates a refactorization frequency by a heuristic formula You can determine the frequency that CPLEX is using by setting the display directive described below to 1 Since each update to the factorization uses more memory CPLEX may reduce the factorization frequency if memory is low
72. lve_result_table option solve_result_table 0 100 200 300 400 500 YA r ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE solved solved infeasible unbounded limit failure 75 76 The session log shows that the built in AMPL parameter solve_result_numis 1 initially and parameter solve_result is The solve invocation resets these parameters however so that they describe CPLEX s status at the end of its run the solve_result_num parameter by a numeric code and solve_result by a message string In the example shown solve_result_numis set to 0 and solve_result to solved indicating normal termination The AMPL option solve result table lists the valid combinations of solve_result_num and solve_result for CPLEX These combinations should be interpreted as shown below Table 9 1 Interpretation of Numeric Result Codes Number String Interpretation 0 99 solved optimal solution found 100 199 solved optimal solution indicated but error likely 200 299 infeasible constraints cannot be satisfied 300 399 unbounded objective can be improved without limit 400 499 limit stopped by a limit such as on iterations 500 599 failure stopped due to solver error Status ranges are normally used to control algorithmic flow in AMPL scripts where solve result num can be tested to distinguish among cases that must be handled in different ways It is occasionally useful however to make fine distinctions among
73. ly if dense columns are treated separately changing this value may improve optimization time Columns with more nonzeros than this setting are considered to be dense If left at the default value CPLEX will automatically determine a value considering factors such as the size of the problem Any nonnegative integer is acceptable input ordering i default 0 This directive selects the method used to permute the rows of the constraint matrix in order to reduce fill in the Cholesky factor There is a trade off between ordering speed and sparsity of the Cholesky factor The automatic default setting usually chooses the best ordering for the problem The approximate minimum degree AMD algorithm i 1 balances speed and fill The approximate minimum fill AMF algorithm i 2 usually generates slightly better orderings than AMD at the cost of more ordering run time The nested dissection ND algorithm triggered by using i 3 sometimes reduces Barrier run time dramatically ten fold reductions have been observed for some problems This option sometimes produces worse orderings though and it requires much more ordering run time ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 41 gcpconvergetol default le 6 This directive sets the tolerance on complementarity for convergence in quadratically constrained problems QCP The barrier algorithm terminates with an optimal solution if the relative complementarity is smaller than this value Chang
74. melimit r default 1 0e 75 CPLEX stops after r seconds of computation time and returns its current solution whether or not it has determined that the solution is optimal ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Directives for Controlling Output When invoked by solve CPLEX normally returns just a few lines to your screen to summarize its performance The following directives let you choose a greater amount of output which may be useful for monitoring the progress of a long run or for comparing the effects of other directives on the detailed behavior on CPLEX s algorithms Output normally comes to the screen but it may be redirected to a file by specifying solve gt filename bardisplay i default 0 The default choice of i 0 produces a minimal few lines of output from CPLEX summarizing the results of a barrier method run When i 1 a log line recording the barrier iteration number primal and dual objective values and infeasibility information is displayed after each barrier iteration When i 2 additional information about the barrier run is provided This level of output is occasionally useful for diagnosing problems of degeneracy or instability in the barrier algorithm file f1 This directive instructs CPLEX to write a copy of the model it receives for solution into a file named 1 iisfind i default 0 When i 1 for an infeasible problem CPLEX returns an irreducible infeasible subset IIS of the constraints and variabl
75. n i value of 3 gives higher priority to variables with smaller cost per coefficient count This tends to identify such binary variables quickly plconpri il default 1 plobjpri i2 default 2 Certain piecewise linear expressions in AMPL models give rise to auxiliary CPLEX variables in groups known as special ordered sets of type 2 Sos2 variables were discussed in the entry for the sos2 directive above CPLEX takes 11 to be the branching priority for all sos2 variables that arise from piecewise linearities in the constraints and i2 to be the branching priority for all sos2 variables that arise from piecewise linearities in the objective A higher number indicates a higher priority rinsheur default 0 submipnodelim default 500 The rinsheur directive determines how often to apply the relaxation induced neighborhood search heuristic RINS heuristic ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 57 Setting the value to 1 turns off the RINS heuristic Setting the value to 0 the default applies the RINS heuristic at an interval chosen automatically by CPLEX Setting the value to a positive integer applies the RINS heuristic at the requested node interval For example setting RINSHeur to 20 dictates that the RINS heuristic be called at node 0 20 40 60 etc The submipnodel im directive restricts the number of nodes searched during application of the RINS heuristic round default 1 This directive specifies whether to round in
76. nd value and may be an appropriate setting for models resistant to other solution techniques or when feasible solutions without a proof of optimality are of no value None of these emphasis settings changes the fundamental nature of the CPLEX branch amp bound algorithm which is to deliver proved optimal solutions if given enough time the setting merely changes some internal strategies and tactics along the way and represents a way for the user to express his or her aims in a way that is separate from the model formulation A setting of 4 indicates emphasis on hidden feasibles With this setting the MIP optimizer works hard to find high quality feasible solutions that are otherwise very difficult to find Use this setting when you more are interested in a good feasible solution than a provably optimal solution and when feasibility emphasis has difficulty finding solutions of acceptable quality Table 7 3 recapitulates the settings of this parameter Table 7 3 Settings for the mipemphasis Directive Setting Effect 0 default Balance optimality and feasibility 1 Emphasize feasibility over optimality 2 Emphasize optimality over feasibility 3 Emphasize moving best bound 4 Emphasize hidden feasibles mipthreads i default the value of the global threads directive This directive only applies to users of parallel CPLEX solvers It specifies the number of parallel processes used during the branch amp bound
77. nds to work well when the product of the constraint matrix and its transpose remains sparse The siftopt directive instructs CPLEX to use a sifting method that solves a sequence of LP subproblems eventually converging to an optimal solution for the full original model Sifting is especially applicable to models with many more columns than rows when the eventual solution is likely to have a majority of variables placed at their lower bounds The concurrentopt directive instructs CPLEX to make use of multiple processors on your computer by launching concurrent threads to solve your model in parallel The first thread uses dual simplex a second thread uses barrier a third thread if your computer has that many processors uses primal simplex and any additional processors are added to parallelizing barrier On a machine with enough memory this will result in a solution being returned by the fastest of the available algorithms on each problem eliminating the need to choose a single optimizer for all purposes threads i default 1 This directive applies only to users of parallel CPLEX solvers It specifies a global thread limit that is a default thread count for the parallel MIP parallel barrier and concurrentopt optimizers Thread limits for the MIP or barrier optimizer can be set if a finer level of control is desired by the directive mipthreads or barthreads respectively The concurrent optimizer is controlled only by this global thread limi
78. ned to AMPL As mentioned earlier using break on command line versions of CPLEX for AMPL will return the best known solution for integer programs that means the current incumbent You can arrange to save the entire search tree when CPLEX halts so that the search may be resumed from where it left off Directives for this purpose are also listed below clocktype i default 1 The default setting of clocktype 1 means that CPLEX will measure time in terms of CPU seconds A setting of 2 means that CPLEX will measure time in terms of elapsed wall clock seconds endtree f1 starttree f2 CPLEX progressively allocates more memory for the search tree as the branch amp bound procedure creates new nodes it frees all this memory at termination If the endt ree directive is specified CPLEX also writes a record of the final tree to the file named 1 ina compact binary format CPLEX normally starts the branch amp bound procedure from a tree that consists only of the root node as explained at the beginning of this section If the startt ree directive is specified then CPLEX instead starts from the search tree stored in the file named 2 This file must be one that was previously written for the same problem by the endtree directive These directives are particularly useful for large and difficult problems that may take hours or days to solve to optimality ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 61 If you would like to look at t
79. ng branching node appears excessive you may reduce the time per node yet still maintain the performance Conversely if the time per node is reasonable but CPLEX makes limited progress consider increasing the values Users of parallel CPLEX can control the number of threads used in strong branching using the strongthreads directive varselect i default 0 Once a node has been selected for branching this directive determines how CPLEX chooses a fractional valued variable to branch on By default 1 0 the choice is made by an internal heuristic based on the problem and its progress The maximum infeasibility rule i 1 chooses the variable with the largest fractional part This forces larger changes earlier in the tree but it tends to disregard the objective function in doing so The minimum infeasibility rule i 1 chooses the variable with the smallest fractional part This may lead more quickly to a first integer feasible solution but will usually be slower overall to reach the optimal integer solution A pseudocost rule 1 2 estimates the worsening of the objective that will result by forcing each fractional variable to an adjacent integer and uses these degradations in an internal heuristic for choosing a variable to branch on This setting tends to be most effective when the problem embodies complex tradeoffs and the dual variables have an economic interpretation Strong branching i 3 considers several different branches
80. ng of 3 for very aggressive cut generation coeffreduce i default 2 Coefficient reduction during the presolve phase typically improves CPLEX s performance on integer programs by speeding up the solve times of the LP subproblems solved in the branch and bound algorithm However while coefficient reduction will tighten the LP subproblems occasionally it makes them more difficult to solve So if CPLEX solves an integer program in a modest number of nodes but the LP subproblem at each node consumes significant amounts of time solve time may improve by setting i 0 to disable this feature The node count may increase but the savings in time per node may compensate for the increased node count The default setting of i 2 causes CPLEX to perform coefficient reduction whenever possible while i 1 will only reduce coefficients to integer values cutpass i default 0 This directive controls the number of passes CPLEX performs when generating cutting planes for a MIP model By default CPLEX automatically determines the number of passes to perform This setting should suffice for most problems Set the cutpass directive to 1 to stop all cut generation Set it to a positive integer to specify a particular number of passes ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE cutsfactor r default 4 0 The cutsfactor directive controls the number of additional cuts generated by CPLEX While the constraints generated by CPLEX improve performance in most case
81. nitial values using the syntax in the var declaration of your AMPL model When you solve a problem two times in a row the final values from the first solver invocation become the initial values for the second solver invocation unless you override this behavior with statements in your AMPL model In nonlinear models with multiple local optima this can cause some solvers to report a different solution on the second invocation Simplex based solvers typically discard initial values However they can use basis status information if available Basis statuses can be set either within AMPL or by a previous optimization Information on interpreting and setting variable statuses is provided in Chapter 9 CPLEX Status Codes in AMPL Problem and Solution Files When you type solve AMPL processes your model and data to create a temporary problem file such as stee1 n1 which will be read by the solver It then loads and executes the solver program which is responsible for creating a solution file such as steel sol AMPL reads the solution file and makes the solution values available through the variable constraint and objective names you have declared in your AMPL model Unless you specify otherwise AMPL then deletes the temporary problem and solution files ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 13 14 You can display the solution information for example the values of the decision variables and constraints in your AMPL session wit
82. nt incumbent CPLEX s default strategy then the reported solution is declared optimal Other cutoff options described below cannot provide a provably optimal solution but may allow the algorithm to finish much faster CPLEX s memory requirement for solving linear subproblems is about the same as its requirement for linear programs discussed in the previous section In the branch amp bound algorithm however each active node of the tree requires additional memory The total memory that CPLEX needs to prove optimality for an integer program can thus be much larger and less predictable than for a linear program of comparable size ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Because a single integer program generates many LP subproblems even small instances can be very computation intensive and require significant amounts of memory In contrast to solving linear programming problems where little user intervention is required to obtain optimal results you may have to set some of the following directives to get satisfactory results on integer programs You can either change the way that the branch amp bound algorithms work or relax the conditions for optimality as explained in the two corresponding subsections below When experimenting with these possibilities it is also a good idea to include directives that set stopping criteria and display informative output these are described in the next two subsections If you consistently fail to re
83. nt option settings including any changes you have made during the session into this file so that they will be preserved for use in your next session If both the OPTIONS_IN and OPTIONS_INOUT environment variables are defined the file referred to by OPTIONS_IN will be processed first then the file referred to by OPTIONS_INOUT ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 21 22 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Using CPLEX with AMPL Problems Handled by CPLEX CPLEX is designed to solve linear programs as described in Chapters 1 8 and 11 12 of AMPL A Modeling Language for Mathematical Programming as well as the integer programs described in Chapter 15 Integer programs may be pure all integer variables or mixed some integer and some continuous variables integer variables may be binary taking values 0 and 1 only or may have more general lower and upper bounds For the network linear programs described in Chapter 12 CPLEX also incorporates an especially fast network optimization algorithm The barrier algorithmic option to CPLEX though originally designed to handle linear programs also allows the solution of a special class of nonlinear problems namely quadratic programs QPs as described later in this section However CPLEX does not solve general non QP nonlinear programs For instance if you attempt to solve the following nonlinear problem described in Chapter 13 of the AMPL book CPLEX will gene
84. on You might want to do this if you receive an out of memory message from your solver not from AMPL itself When the solver is invoked from within AMPL a fair amount of memory is already used for the AMPL Modeling System program code and for data structures created by AMPL for its own use in memory If you execute the solver alone it can use all available memory To run your solver separately first use AMPL to create a problem file C gt ampl ampl model steel mod data steel dat ampl write bsteel ampl quit Then run your solver with a command like the one below for CPLEX C gt cplexamp steel AMPL solver_options In this example the first argument steel matches the filename after the initial letter b in the AMPL write command The AMPL argument tells the solver that it is receiving a problem from AMPL This may optionally be followed by any solver options you need for the problem using the same syntax used with the option solver_options command but omitting the outer quotes forexample crash 1 relax Assuming that the solver runs successfully to completion it will write a solution file steel sol in this case You can then restart AMPL and read in the results with the solution command as outlined earlier C gt ampl ampl model steel mod data steel dat ampl solution steel sol Using MPS File Format 16 MPS file format originally developed decades ago for IBM s Mathematical Programming System is a wid
85. optimization run possibly after a data change You can refer to a variable s solver status by appending sstatus to its name Initially when no problem has yet been solved all variables have the status none 78 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE After an invocation of a simplex solver the same display lists the statuses of the variables at the optimal basic solution For example consider the following ampl model oil mod ampl data oil dat ampl option solver cplex ampl solve CPLEX 9 0 optimal solution objective 12 20834324 37 iterations 0 in phase I ampl option sstatus table option sstatus table egu nonbasic at equal lower and upper bounds btw nonbasic between bounds 0 none no status assigned 1 bas basic 2 sup superbasic 3 low nonbasic lt normally lower bound 4 upp nonbasic gt normally upper bound 5 6 1 ampl display InCr sstatus InCr sstatus MID_C bas W_TEX low r A table of the recognized CPLEX status values is stored in the AMPL option sstatus_table displayed above Numbers and short strings representing status values are given in the first two columns The numbers are mainly for communication between AMPL and CPLEX though you can access them by using the suffix sstatus_num in place of sstatus The entries in the third column are comments The output of the display command shows that variable Incr MID_C is in the basis and InCr W_TEX
86. ot using the advanced basis by setting this parameter to O instead on the grounds that the basis may not be giving you a helpful starting point after all Setting 2 may also be effective for MIPs in which the percentage of integer constraints is low It may also reduce the solution time of fixed MIPs ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 35 basisinterval i default 50000 This directive controls the frequency with which CPLEX automatically writes a basis file to disk This is a safeguard against unanticipated events such as power failures interrupting a run By using the resulting basis file in conjunction with the xxxstart directive described below one can resume the run from the most recently written basis files crash i default 1 This directive governs CPLEX s procedure for choosing an initial basis except when the basis is read from a file as specified by the directive readbasis described below A value of i 0 causes the objective to be ignored in choosing the basis whereas values of 1 and 1 select two different heuristics for taking the objective into account The best setting for your purposes will depend on the specific characteristics of the linear programs you are solving and must be determined through experimentation pgradient i default 0 This directive governs the primal simplex algorithm s choice of a pricing procedure that determines which variable is selected to enter the basis at each iteration Your cho
87. our interactive commands type C X gt ampl steel mod steel dat ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 9 10 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE AMPL Solver Interaction Choosing a Solver AMPL s solver interface supports linear nonlinear and mixed integer models with no built in size limitations This interface is rich enough to support many of the features used by advanced solvers to improve performance and solution accuracy such as piecewise linear constructs representation of network problems and automatic differentiation of nonlinear functions To take advantage of these features solvers must be written to utilize AMPL s interface ILOG provides no support for the usage of AMPL with solvers not distributed by ILOG You choose a solver for a particular problem by giving its executable filename in the AMPL option solver command For example to use the AMPL compatible CPLEX solver type ampl option solver cplexamp Most solvers have algorithmic options such as CPLEX with its Mixed Integer and Barrier options In these cases you give the solver executable name to AMPL for example with option solver cplexamp the solver will determine from the problem characteristics as passed by AMPL for example a quadratic objective or integer variables as well as solver options you specify which algorithmic options will be used ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 11 Specifying Solver Opt
88. oved solutions found or total processing time using the CPLEX directives given above Setting limits ensures that the tree search will terminate in reasonable time You can then inspect the solution and if necessary re run the problem using different directive settings Consider some of the shortcuts described above for improving performance particularly those for relaxing optimality They may provide you with an optimal or very nearly optimal solution even though a proof of optimality would require more computer resources than you have available Difficult MIP Subproblems Certain classes of MIP problems occasionally produce very difficult subproblems The subproblems may be dual degenerate Or an alternative algorithm such as primal simplex or barrier may perform better with the particular model If the subproblems are dual degenerate consider setting mipalgorithm to choose primal simplex for solving subproblems If the subproblems are taking many iterations per node to solve consider setting dgradient to use a stronger dual pricing algorithm Most often one would use dual steepest edge pricing In cases where the barrier algorithm is selected to solve the initial LP relaxation it may be useful to apply it on the subproblems using one of two options The first is to use barrier on all subproblems Since the barrier algorithm cannot utilize a basis often a better choice is to allow the dual simplex algorithm to run for a predetermine
89. ow summarizes the command line switches and their equivalent names when set with the AMPL option command Table 4 1 AMPL Option Names for Command Line Switches Switch AMPL Option Description Cn Cautions n n 0 suppress caution messages n 1 report caution messages default n 2 treat cautions as errors en eexit n n gt 0 abandon command after n errors n lt 0 abort AMPL after n errors n 0 report any number of errors ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 19 Switch AMPL Option Description f funcwarn 1 do not treat unavailable functions of constant arguments as variable P presolve 0 turn off AMPL s presolve phase S substout 1 use defining equations to eliminate variables L linelim 1 fully eliminate variables with linear defining equations so model is recognized as linear T gentimes 1 show time to generate each model component t times 1 show time taken in each model translation phase ostr outopt str set problem file format b g m and stub name to display more possibilities use 0 S randseed use current time for random number seed sn randseed n use n for random number seed V version display the AMPL software version number If you type amp1 at the shell prompt AMPL will display a summary list of all the command line switches On some Unix shells is a special character so you may need to use 2 wit
90. pecify xxx files in readbasis and writebasis directives ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 39 Directives for Controlling the Barrier Algorithm 40 Several key strategies of the barrier algorithm can be changed through CPLEX directives If you are repeatedly solving a class of linear programs that requires substantial computer time experimentation with alternative strategies can be worthwhile baralg i default 0 The automatically determined choice of barrier algorithm i1 0 is usually the fastest However on primal or dual infeasible problems the infeasibility estimate start algorithm i1 1 or the infeasibility constant start algorithm 11 2 may improve numerical stability possibly at the cost of speed Setting i1 3 selects the standard barrier algorithm bargrowth r default 1e 8 This directive is used to detect unbounded optimal faces At higher values the barrier algorithm will be less likely to conclude that the problem has an unbounded optimal face but more likely to have numerical difficulties if the problem does have an unbounded face Any positive number is acceptable input barcorr i default 1 CPLEX may perform centering corrections if it encounters numerical difficulties during the barrier method optimization By default i 1 the barrier solver automatically computes an estimate for the maximum number of centering corrections done at each iteration If the automatic estimate is computed to be 0 setting
91. prompt to load your model and data solve a problem and inspect the results Although you could type in the statements of a model at the amp1 prompt AMPL does not include a built in text editor so you cannot use AMPL commands to edit the statements you have previously entered Microsoft Windows users on PCs and XWindows users on Unix systems should open separate windows for editing files and running AMPL ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 7 If you cannot open multiple windows on your desktop you can use AMPL s shell command to invoke an editor from within AMPL You can use any editor that saves files in ASCII format Windows command line DOS users can use edit or notepad and Unix users vi or emacs If you are using edit under DOS for instance you can type ampl shell edit steel dat Use editor menus and commands to edit your file then save it and exit the editor At the ampl prompt you can type new AMPL commands such as ampl reset data ampl data steel dat Note that editing a file in a text editor does not affect your AMPL session until you explicitly reload the edited file as shown above Running AMPL in Batch Mode If you have previously developed a model and its data and would like to solve it and display the results automatically you can create a file containing the commands you would like AMPL to execute and specify that file at the command line when you run AMPL For example you might create a
92. r to the discussion on setting priorities by variable in Algorithmic Control on page 67 Investigate which of a fractional variable s two resulting branches first branch refer to the discussion on setting branching preference by variable in Algorithmic Control on page 67 Solve the resulting new subproblem by which LP algorithm mipalgorithm Explore rounded subproblem solutions how often heuristicfreg It is often hard to predict which combination of directives will work best Some experimentation is usually required your knowledge of the problem structure may also suggest certain choices of branch amp bound strategy backtrack r default 0 9999 bbinterval il default 7 nodeselect i2 default 1 These directives determine the criterion for choosing the next node from which to branch once a feasible integer solution has been found Depending on whether i2 is set to 1 2 or 3 CPLEX associates a value with each node and chooses a node based on these values For 12 1 a node s value is the bound on the integer optimum that is given by solving the LP subproblem at that node For i2 2 or i2 3 a node s value is an estimate of the best integer objective that can be achieved by branching from that node estimates of node objective values are derived from so called pseudocosts which are in turn derived from the solutions to the LP subproblems Settings 2 and 3 differ regarding the exact nature of the estimated objective Depen
93. ram to CPLEX and converts the solution into user defined variables The conversion has the effect of adding a variable to correspond to each linear piece when the above rules are not satisfied additional integer variables and constraints must also be introduced Quadratic Programs This user guide provides but a brief description of quadratic programming In effect it is assumed that you are familiar with the area Interested users may wish to consult a good reference such as Practical Optimization by Gill Murray and Wright Academic Press 1981 for more details A mathematical description of a quadratic program is given as renee 1 T T minimize 3 Ox cx subject to Ax b I lt x lt u where represents lt gt or operators In the above formula Q represents a matrix of quadratic objective function coefficients Its diagonal elements Q are the coefficients of the quadratic terms ae The nondiagonal elements Q and Q are added together to be the coefficient of the term x x ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE The CPLEX linear programming algorithms incorporate an extension for quadratic programming For a problem to be solvable using this option the following conditions must hold 1 All constraints must be linear 2 The objective must be a sum of terms each of which is either a linear expression or a product of two linear expressions 8 For any values of the variables whether or not they satisfy
94. rate an error message ampl model models nltransd mod ampl data models nltrans dat ampl option solver cplexamp ampl solve at0 nl contains a nonlinear objective ampl ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 23 24 This restriction applies if your model uses any function of variables that AMPL identifies as not linear even a function such as abs or min that shares some properties of linear functions Piecewise linear Programs CPLEX does solve piecewise linear programs as described in Chapter 14 if AMPL transforms them to problems that CPLEX solvers can handle The transformation to a linear program can be done if the following conditions are met Any piecewise linear term in a minimized objective must be convex its slopes forming an increasing sequence as in Ii do 29p Hl Op lense KL Any piecewise linear term in a maximized objective must be concave its slopes forming a decreasing sequence as in lt lt 1 3 1 54 0 9 0 25 gt 2 gt XII Any piecewise linear term in the constraints must be either convex and on the left hand side of a lt constraint or equivalently the right hand side of a gt constraint or else concave and on the left hand side of a gt constraint the right hand side of a lt constraint In all other cases the transformation is to a mixed integer program AMPL automatically performs the appropriate conversion sends the resulting linear or mixed integer prog
95. reduce certain lower bounds to zero ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 71 Direction of Unboundedness 72 For an unbounded linear program one that effectively has a minimum objective value of Infinity or a maximum of Infinity the solution is characterized by a feasible point together with a direction of unboundedness from that point On return from CPLEX the values of the variables define the feasible point The direction of unboundedness is given by an additional value associated with each variable through the associated solver defined suffix unbdd An application of the direction of unboundedness can be found in our example of Benders decomposition applied to a transportation location problem One part of the decomposition scheme is a subproblem obtained by fixing the variables Build i which indicate the warehouses that are to be built to trial values build i When all values build i are set to zero no warehouses are built and the primal subproblem is infeasible As a result the dual formulation of the subproblem which always has a feasible solution is unbounded When this dual problem is solved from the AMPL command line CPLEX returns the direction of unboundedness in the expected way ampl model trnlocid mod ampl data trnlocl dat ampl problem Sub Supply Price Demand Price ampl Dual Ship Cost Dual Ship ampl let i in ORIG build i 0 ampl option solver cplexamp ampl option cpl
96. rence to the tradeoff between computational time per iteration and the number of iterations As a rule of thumb if the number of iterations to solve your linear program exceeds three times the number of constraints you should consider experimenting with alternative pricing procedures The dual pricing indicator allows you to indicate devex pricing Table 6 4 lists the valid settings for this directive Table 6 4 Dual Pricing Indicator dgradient Setting Effect 0 Let CPLEX determine automatically 1 Standard dual pricing 2 Steepest edge pricing 3 Steepest edge pricing in slack space 4 Steepest edge pricing unit initial norms 5 Devex pricing These settings can be further described as follows The default value 1 0 lets CPLEX choose a dual pricing procedure through an internal heuristic based on problem characteristics Standard dual pricing i 1 described in many textbooks selects as leaving variable one that is farthest outside its bounds ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 37 The three steepest edge alternatives employ more elaborate computations which can better predict the improvement to the objective offered by each candidate for leaving variable Steepest edge pricing involves an extra initialization cost but its extra cost per iteration is much less in the dual simplex algorithm than in the primal Thus if you find that your problems solve faster using the dual simp
97. s in some problems the additional memory to store them and time required to solve the larger LP subproblems may outweigh the performance gains from the tighter problem formulation In such cases use this directive to limit the number of cuts that CPLEX generates CPLEX will generate no more than r times the number of rows in the problem finalfactor i default 1 When preprocessing changes to the model prior to optimization a reverse operation uncrush occurs at termination to restore the full model with its solution With default settings the simplex optimizers perform a final basis factorization on the full model before terminating If you turn off this parameter the final factorization after uncrushing will be skipped on large models this can save considerable memory but computations that require a factored basis after optimization for example for the computation of the condition number Kappa may be unavailable depending on the operations performed during preprocessing If you run out of memory at the end of a simplex optimization consider turning off final factorization fraccand i default 200 This directive limits the number of candidate variables CPLEX will examine when generating fractional cuts on a MIP model For most purposes the default of 200 will be satisfactory fracpass i default 0 This directive controls the number of passes CPLEX performs when generating fractional cuts on a MIP model The default of 0 instructs CP
98. s 55 mipgap 60 mipinterval 63 mipstartstatus 51 mipstartvalue 51 mipthreads 4 31 56 mircuts 50 net find 38 netopt 32 nodefile 56 nodelim63 nodeselect 53 objdifference 60 optimality 43 ordering 41 ordertype 57 perturbation 42 perturblimit 42 pgradient 36 plconpri 57 plobjpri 57 precompress 33 predual 33 prereduce 34 prerelax 52 presolve 34 presolvenode 52 prestats 34 pricing 38 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 85 primal 30 primalopt 31 priorities 63 probe 52 gcpconvergetol 42 readbasis 44 readvector 44 refactor 38 relax 32 relobjdiff 60 rinsheur 57 round 58 scale 35 sensitivity 46 siftopt 31 singular 44 solutionlim63 sos1 52 sos2 52 startalgorithm 58 starttree 61 strongcand 58 strongit 58 strongthreads 58 submipnodelim 57 threads 4 31 timelimit 44 63 timing 46 64 treememlim 63 uppercutoff 60 upperobj 44 varselect 59 version 46 workfiledir 40 56 workfilelim 40 56 writebasis 44 writevector 44 xxxstart 39 directives algorithmic control 53 append additional CPLEX directives 27 control barrier algorithm 40 control output 45 63 control simplex algorithm 35 CPLEX directives 26 CPLEX directives for linear programs 30 halt and resume search 61 improving stability 42 preprocessing 32 preprocessing integer programs only 49 relax optimality 60 select algorithm 30 starting and stopping 43 store multiple 26 disjcuts directive 50 display command 14 doperturb directive
99. s a basic optimal solution see below CPLEX normally chooses one of these algorithms for you but you can override its choice by the directives described below The simplex algorithm maintains a subset of basic variables or a basis equal in size to the number of constraints A basic solution is obtained by solving for the basic variables when the remaining nonbasic variables are fixed at appropriate bounds ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 29 Each iteration of the algorithm picks a new basic variable from among the nonbasic ones steps to a new basic solution and drops some basic variable at a bound The coefficients of the variables form a constraint matrix and the coefficients of the basic variables form a nonsingular square submatrix called the basis matrix At each iteration the simplex algorithm must solve certain linear systems involving the basis matrix For this purpose CPLEX maintains a factorization of the basis matrix which is updated during most iterations and is occasionally recomputed The sparsity of a matrix is the proportion of its elements that are not zero The constraint matrix basis matrix and factorization are said to be relatively sparse or dense according to their proportion of nonzeros Most linear programs of practical interest have many zeros in all the relevant matrices and the larger ones tend also to be the sparser The amount of RAM memory required by CPLEX grows with the size of the linear
100. scussions of modeling concepts such as linear nonlinear and piecewise linear models integer linear models and columnwise formulations and a reference section AMPL is continuously undergoing development and while we strive to keep users updated on language features and capabilities the official reference to the language is the AMPL book which is naturally revised less frequently Installing AMPL Please read these instructions in their entirety before beginning the installation Remember that most distributions will operate properly only on the specific platform and operating system version for which they were intended If you upgrade your operating system you may need to obtain a new distribution All AMPL installations include cplexamp cplexamp exe on Windows the CPLEX solver for AMPL This combined distribution is known as the AMPL CPLEX system Note that cplexamp may not be licensed for a few users with unsupported solvers However most AMPL installations will include the use of cplexamp Requirements AMPL may be installed and run on the following configurations Table 1 1 AMPL ConfigurationTable Computer Operating System Release DEC Alpha Compag Tru64 UNIX 5 1 and higher HP PA RISC HP UX 11 and higher Intel PC Linux 2 3 and higher Intel PC Windows NT4 2000 XP RS6000 or PowerPC AIX 5 1 and higher 2 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Table 1 1 AMPL ConfigurationTable Continued Computer Operating Sys
101. sses to perform Set il to 0 to prevent any such aggregations Set il to a positive integer to specify the precise number of passes Aggregation can yield a substantial reduction in the size of some linear programs such as network flow LPs in which many nodes have only one incoming or one outgoing arc If 12 gt 2 however aggregation may also increase the number of nonzero constraint coefficients resulting in more work at each simplex iteration The default setting of 12 10 usually makes a good tradeoff between reduction in size and increase in nonzeros but you may want to experiment with lower values if CPLEX reports that many aggregations have been made If CPLEX consistently reports that no aggregations can be performed on the other hand you can set il to 0 to turn off the aggregation routine and save memory and processing time To request a report of the number of aggregations see the prestats directive later in this section dependency i default 1 By default i 1 CPLEX chooses automatically when to use dependency checking This parameter offers several settings that make it possible for a user to control dependency checking more precisely Table 6 1 shows you the possible settings of the parameter that controls dependency checking and indicates their effects Table 6 1 Settings for the dependency Directive Setting Effect 1 default automatic let CPLEX choose when to use dependency checking
102. subproblem As memory gets tight you may observe warning messages while CPLEX attempts to navigate through various operations within limited memory If a solution is not found shortly the solutions process will be terminated with an error termination message The tree information saved in memory can be substantial CPLEX saves a basis for every unexplored node When utilizing the best bound or best estimate method of node selection the list of unexplored nodes can become very long for large or difficult problems How large the unexplored node list can become is entirely dependent on the actual amount of physical memory available the size of the problem and the solution algorithm selected Certainly increasing the amount of memory available extends the problem solving capability Unfortunately once a problem has failed because of insufficient memory you cannot project how much further the process needed to go or how much memory would be required to ultimately solve it ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE To avoid out of memory failures we recommend resetting the t reemem1 im parameter to stop the solution process prior to consuming all available memory This limit parameter value should be set to a number slightly less than the total available memory which can include the swap file Remember that not all installed memory is available the operating system and other active processes can reduce the amount of memory available to CPLEX
103. t directive ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 31 netopt i default 1 CPLEX incorporates an optional heuristic procedure that looks for pure network constraints in your linear program If this procedure finds sufficiently many such constraints CPLEX applies its fast network simplex algorithm to them Then if there are also non network constraints CPLEX uses the network solution as a start for solving the whole LP by the general primal or dual simplex algorithm whichever you have chosen The default value of i 1 invokes the network identification procedure if and only if your model uses node and arc declarations and CPLEX sets up the primal formulation as discussed above Setting i 0 suppresses the procedure while i 2 requests its use in all cases You can have CPLEX display the number of network nodes constraints and arcs variables that it has extracted by setting the prestats directive described with the preprocessing options below to 1 CPLEX s network simplex algorithm can achieve dramatic reductions in optimization time for pure network linear programs defined entirely in terms of node and arc declarations For a pure network LP every arc declaration must contain at most one from and one to phrase and these phrases may not specify optional coefficients In the case of linear programs that are mostly defined in terms of node and arc declarations but that have some side constraints defined by subject to declarat
104. teger variables to integral values before returning the solution and whether to report that CPLEX returned noninteger values for integer values Table 7 4 Settings for the round Directive value meaning round nonintegral integer variables do not modify solve_result RM do not modify solve_message 8 modify even ifmaxerr lt le 9 Modifications take place only if CPLEX assigned nonintegral values to one or more integer variables and for round lt 8 only if the maximum deviation from integrality maxerr exceeded the minimum integrality tolerance 1e 9 startalgorithm i default 0 This directive specifies the algorithm that CPLEX will apply to solve the initial LP relaxation The recognized values of i are Table 7 5 Settings for the startalgorithm Directive 0 Automatic 1 Primal simplex 2 Dual simplex 3 Network simplex 4 Barrier 5 Sifting 6 Concurrent strongcand i1 default 10 strongit i2 default 0 strongthreads i3 default 1 These three directives impact strong branching see varsel directive below ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE The st rongcand directive controls the size of the candidate list for strong branching The strongit parameter limits the number of iterations performed on each branch in strong branching The default setting of 12 0 which allows CPLEX to determine the iteration parameter will generally suffice You can use low values of i1 and i2 if the time per stro
105. tem Release SGI 32 bit MIPS3 Irix 6 5 and higher SGI 64 bit MIPS4 Irix 6 5 and higher Sun Ultra Solaris 2 8 and higher Unix Installation On Unix systems AMPL is installed into the current working directory We recommend that you perform the installation in an empty directory After installation make sure the executable files have read and execute privileges turned on for all users and accounts that will use AMPL CD ROM The ILOG CD contains the AMPL CPLEX system for several different platforms First read the file INFO_UNX TXT The section titled AMPL Modeling Language contains information to help you locate the distribution for your platform Note that the files listed in this section contain the entire AMPL CPLEX System not just the AMPL language processor After you have located the files read the CD booklet for instructions on extracting the distribution FTP Execute gzip dc lt path ampl tgz tar xf where path is the full path name into which amp1 tgz was downloaded Windows Installation On Windows systems AMPL is installed into a directory which you can specify during the installation the default location is C AMPL CD ROM The ILOG CD contains the AMPL CPLEX system for several different platforms First read the file INFO_PC TXT The section titled AMPL Modeling Language contains information to help you locate the distribution for your version of Windows Note that the files listed in th
106. the constraints the quadratic part of the objective must have a nonnegative value if a minimization or a nonpositive value if a maximization The last condition is known as positive semi definiteness for minimization or negative semi definiteness for maximization CPLEX automatically recognizes nonlinear problems that satisfy these conditions and invokes the barrier algorithm to solve them Nonlinear problems of any other kind are rejected with an appropriate message Most CPLEX features applying to continuous LP models apply also to continuous QP models likewise most features applying to linear MIP models also apply to mixed integer QP models MIQP In cases where the nature of QP dictates different behavior from a directive usually the result is that the directive is ignored and default behavior remains in effect An example of this would be the dual directive to specify that CPLEX solves the explicit dual formulation for QP the default primal formulation will be used anyway In almost every case such differences will result in best performance and will require no user intervention Quadratic Constraints A model containing one or more quadratic constraints of the form T ax x OxsSr is called a Quadratically Constrained Program QCP and can be solved using the CPLEX barrier algorithm Linear constraints may also be present in a QCP and a positive semi definite quadratic term in the objective function is permitted If discr
107. the solution command For example C gt ampl ampl model steel mod data steel dat ampl solution steel sol CPLEX 9 0 optimal solution objective 192000 2 iterations 0 in phase I ampl display Make Make bands 6000 coils 1400 r ampl quit You must include the model and data statements as shown above so that AMPL knows the definitions of symbolic names like Make But solution then retrieves the earlier results from steel sol without running a solver ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE if you use b as the first character of the filename portion of the write command AMPL uses a compact and efficient binary format for the problem and solution files If you use g instead AMPL writes the files in an ASCII format that may be easier to transmit electronically over systems like the Internet In technical support and consulting situations ILOG may ask you to send a file using this format If you use m AMPL writes the problem in MPS format and the filename ends in mps for example steel mps This is described further in Using MPS File Format on page 16 Creating Auxiliary Files AMPL can create certain human and program readable auxiliary files that help relate the various set variable constraint and objective names used in your AMPL model to the column and row indices that are written to the problem file and seen by the solver This is particularly valuable when the AMPL presolve phase ac
108. tion 422 time limit with integer solution 423 treememory limit with integer solution ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Basis Status Table 9 2 Solve Codes and Termination Messages Continued Number Message at termination 500 unrecoverable failure 501 aborted in phase II 502 aborted in phase 503 aborted in barrier dual infeasible 504 aborted in barrier primal infeasible 505 aborted in barrier primal and dual infeasible 506 aborted in barrier primal and dual feasible 507 aborted in crossover 510 unrecoverable failure with no integer solution 511 aborted no integer solution 520 unrecoverable failure with integer solution 521 aborted integer solution exists 522 integer optimal with unscaled infeasibilities 523 out of memory no tree solution may exist Following optimization CPLEX also returns an individual status for each variable and constraint This feature is intended mainly for reporting the basis status of variables after a linear program is solved either by the simplex method or by an interior point barrier method followed by a crossover routine In addition to the variables declared by var statements in an AMPL model solvers also define slack or artificial variables that are associated with constraints Solver statuses for these latter variables are defined in a similar way The major use of solver status values from an optimal basic solution is to provide a good starting point for the next
109. tions 12 use of initial values 13 sosl directive 52 sos2 directive 52 stability directives for improving 42 startalgorithm directive 58 starting directives 43 statttres directive 61 stopping directives 43 strongcand directive 58 strongit directive 58 strongthreads directive 58 submipnodelim directive 57 suffix bestnode 68 current 69 direction 67 down 69 iis 70 priority 67 unbdd 72 up 69 switches Cn 19 command line 19 en 19 f 20 L 20 ostr 20 P 20 s 20 s 20 sn 20 T 20 t 20 v 20 T temporary files directory 17 saving 14 termination messages 76 text editor using 7 text file predefined commands 20 threads directive 4 31 time to find solution 46 to read problem 46 to write solution 46 timelimit directive 44 63 timing directive 46 64 treememlim directive 63 troubleshooting common difficulties 64 U unbdd suffix 72 Unix installation 3 up suffix 69 uppercutoff directive 60 90 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE upperob j directive 44 usage notes 4 Vv varselect directive 59 version directive 46 W Windows installation 3 workfiledir directive 40 56 workfilelim directive 40 56 write command 14 15 writebasis directive 44 writevector directive 44 X xxxstart directive 39 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 91 92 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE ILOG WO
110. ts i2 default 0 disjcuts i3 default 0 flowcuts i4 default 0 flowpathcuts i5 default 0 fraccuts i6 default 0 gubcuts i7 default 0 impliedcuts i8 default 0 mircuts i9 default 0 Integer programming solve times can often be improved by generating new constraints or cuts based on polyhedral considerations These additional constraints tighten the feasible region reducing the number of fractional variables to choose from when CPLEX needs to select a branching variable CPLEX can generate cuts based on different combinatorial constructs corresponding to the directives listed above By default CPLEX decides whether to generate cuts Typically the default setting yields the best performance To disable a particular family of cuts set its directive to 1 To enable moderate cut generation set the appropriate directive to 1 To enable aggressive cut generation set it to 2 To set all these classes of cuts to one common value for instance 1 to disable all cuts use the directive mipcuts Cuts directives are applied in the order in which they are encountered so for instance mipcuts 1 fraccuts 2 first turns off all cuts and then turns fractional cuts back on The reverse cae of fraccuts 2 mipcuts 1 results in all cuts being disabled as though the fraccuts 2 directive is not present Using more aggressive cut generation causes CPLEX to make more passes through the problem to generate cuts The disjcuts directive also supports a setti
111. tually eliminates variables and constraints before the problem is sent to the solver To create the auxiliary files you set the AMPL option auxfiles to a string of letters denoting the combination of auxiliary files you would like produced and then use the write command to create and save the auxiliary files along with the problem n1 file For example the command ampl option auxfiles cr will cause the write command to create auxiliary files containing the names of the variables columns and constraints rows as sent to the solver The table below shows the types of auxiliary files that can be created and the letter you use to request them via the AMPL option auxfiles Table 3 1 Auxiliary Files Letter Extension Description a adj adjustment to objective for example to compensate for fixed variables eliminated by presolve col AMPL names of the variables columns sent to the solver fix names of variables fixed by presolve and the values to which they are fixed r Tow AMPL names of the constraints rows sent to the solver s sile names of slack constraints eliminated by presolve because they can never be binding u UNV names of variables dropped by presolve because they are never used in the problem instance ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE 15 Running Solvers Outside AMPL With the write and solution commands you can arrange to execute your solver outside the AMPL sessi
112. turned objective value will be no more than rl from the optimum and will also be within about 100 r2 percent of the optimum if the optimal value is significantly greater than 1 in magnitude Increasing r1 or r2 allows a solution further from optimum to be accepted The search may be significantly shortened as a result Valid values for r2 lie between 1e 9 and 1 0 integrality r default 1 0e 5 In the optimal solution to a subproblem a variable is considered to have an integral value if itlies within r of an integer For some problems increasing r may give an acceptable solution faster This parameter may be set to 0 to improve the robustness of MIP solutions most commonly with little if any impact on the performance of the optimizer lowercutoff rl default 1 0e75 uppercutoff r2 default 1 0e75 These directives specify alternative cutoff values a node is fathomed if its subproblem has an objective less than rl for maximization problems or greater than r2 for minimization problems As a result any solution returned by CPLEX will have an optimal value at least as large as rl or as small as r2 This feature can be useful in conjunction with other limits on the search but too high a value of rl or too low a value of r2 may result in no integer solution being found objdifference r1 default 0 0 relobjdiff r2 default 0 0 This directive automatically updates the cutoff to more restrictive values Normally the incumbent integer sol
113. ue may provide some indication of the quality of the solution or the nearness of a proof of optimality ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Sensitivity Ranging When the sensitivity directive described in Directives for Controlling Output on page 45 is included in CPLEX s option list classical sensitivity ranges are computed and are returned in the following three suffixes current down up Let us illustrate the use of these suffixes using an example model from Section 4 3 of the AMPL book ampl model steelT mod ampl data steelT dat ampl option solver cplexamp ampl option cplex_options sensitivity ampl solve CPLEX 9 0 sensitivity CPLEX 9 0 optimal solution objective 515033 18 iterations 1 in phase I suffix up OUT suffix down OUT suffix current OUT The three lines at the end show the suffix commands executed by AMPL in response to the results from CPLEX These commands are invoked automatically you do not need to type them For variables suffix current indicates the objective function coefficient in the current problem while down and up give the smallest and largest values of the objective coefficient for which the current simplex basis remains optimal CPLEX returns 1e 20 for down and 1e 20 for up to indicate minus infinity and plus infinity respectively ampl display Sell down Sell current ampl Sell up 4 Sell down Sell current Sell up bands 1 23 3 25 1le 2
114. uenuan anna nn unum na 33 Settings for the advance Directive ueruenuennenunnu enn an nan nan annan mnt 35 Settings for the pgradient Directives s is siii iaai to Ae aienea dia odia a a E EEDE poa a E a nunnana nan annan mnt 36 Dual Pricing Indicator dgradient 0 cee eee eee eee eee eee 37 Values of the AMPL Option send_statuS S 2 2 cece eee eee 51 Settings for the mipcrossover Directive ooooooocrrcrrnrnnr nan ann nnnn mnn 55 Settings for the mipemphasis Directive 0 ce ee eee 56 Settings for the round Directies srs drage ai oi a a ele miki amil ats gata mala wales de Cause aita ecole a 58 Settings for the startalgorithm Directive 0 eee 58 Interpretation of Numeric Result Codes nuuerunenunnuenuannana anu nen nn na 76 Solve Codes and Termination Messages neueuunnunennnennn na nan enn naa 76 GPEEX SYNONYMS s simaa taal a eer ala eee a a Cee ened ma a ee ee 81 ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE ix ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE Introduction Welcome to AMPL Welcome to the AMPL Modeling System a comprehensive powerful algebraic modeling language for problems in linear nonlinear and integer programming AMPL is based upon modern modeling principles and utilizes an advanced architecture providing flexibility most other modeling systems lack AMPL has been proven in commercial applications and is successfully used in dem
115. ution s objective value is used as the cutoff for subsequent nodes When r1 gt 0 the cutoff is instead the incumbent s value r1 if minimizing or r1 if maximizing This forces the mixed integer optimization to ignore integer solutions that are not at least r1 better than the one found so far As a result there tend to be fewer nodes generated and the algorithm terminates more quickly but the true integer optimum may be missed if its objective value is within r1 of the best integer objective found ILOG AMPL CPLEX SYSTEM 9 0 USER S GUIDE If r1 0 r2 is used to adjust the objective function value during the optimization For a maximization problem r2 times the absolute value of the objective function value is added to the best feasible objective value obtained so far Similarly if the objective is to be minimized r2 times the absolute value is subtracted from the best so far feasible objective value Subsequent nodes are ignored if their linear relaxations have optimal values worse that this adjusted value Positive values of r2 usually speed the search but may cause the true optimum to be missed Directives for Halting and Resuming the Search There is usually no need to make exhaustive runs to determine the impact of different search strategies or optimality criteria While you are experimenting consider using one of the directives below to set a stopping criterion in advance In each case the best solution found so far is retur

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