### Table of Contents

For the novice GAMS user, solver usage can be very simple: one runs the model and inspects the listing file to see what the solution is. No knowledge of solver options or solver specific return codes is required. While this is enough for some users, most will quickly find they need some basic knowledge of how to control the solver and interpret the results. Section Controlling a Solver via GAMS Options describes how to set the GAMS options that control a solver. Further, most solvers allow the user to set additional, solver-specific options. These can be set via a solver specific options file, which will be discussed in Section The Solver Options File. However, use of generic GAMS options should be preferred, since a GAMS option setting applies to all solvers and is interpreted by the solvers in a consistent way.

A number of solvers can make use of an initialization of variable and equation values. This will be discussed in Starting Point and Initial Basis.

Further solver specific topics, which are more interesting for advanced users, are discussed in the Sections Solve trace and Branch-and-Cut-and-Heuristic Facility (BCH).

For some hints on how to select a solver, see Choosing an appropriate Solver.

# Controlling a Solver via GAMS Options

GAMS options can be set on the GAMS command line, e.g.,

$ gams trnsport iterlim = 100

Additionally, they can be set by an option statement within a GAMS model, e.g.,

```
option iterlim = 100;
```

Finally, a model attribute can set a GAMS option for an individual model:

```
mymodel.iterlim = 100;
```

The model suffix takes precedence over the option statement, which takes precendence over the command line parameters. If none of these methods is used to set an option, default values apply.

Further, one can unset any model-specific option by assigning it the value `NA`

:

```
mymodel.iterlim = NA;
```

Unfortunately, not every option can be via as command line parameter, option statement, and model attribute. We refer to

- Solver-Related Options for the list of solve-related options that can be set via the command line,
- Options that Control Solver-Specific Parameters and Options that Control the Choice of Solver for the list of solve-related options that can be set via the option statement, and
- Model Attributes Mainly Used Before Solve for the list of solve-related model attributes.

# The Solver Options File

To specify solver-specific options, it is necessary to use a solver option file. Two things are required to do this: one must create an option file having a proper name, and one must tell the solver to read and use this option file.

To tell a solver to use an option file, one can set the `optfile`

model attribute or the optfile option to a positive value. For example,

```
model mymodel /all/;
mymodel.optfile = 1;
solve mymodel using nlp maximizing dollars;
```

The option file takes its name from the solver being used: `solvername.XYZ`

, where `solvername`

is the name of the solver that is specified, and the suffix `XYZ`

depends on the value to which `optfile`

has been set. If its value is 1, the suffix is `opt`

. For example, the option file when calling CONOPT would be called `conopt.opt`

. See the documentation on optfile for more information.

The format of the options file can change marginally from solver to solver. The following illustrates some frequent features of the option file format. However, solvers may vary from this format. Thus, the solver-specific documentation should be checked before using an option file.

- Blank lines in an option file are ignored.
- A comment line might begin with an asterisk (
`*`

) in the first column, is not interpreted by either GAMS or the solver, and is used purely for documentation. - Each non-comment line contains only one option specification.
- The format for specifying options is as follows:
keyword(s) [modifier] [value]

The keyword may consist of one or more words and is not case sensitive. The value might be an integer, a real, or a string. Real numbers can be expressed in scientific format, e.g., 1e-6. Note that not all options require modifiers or values. - Any errors in the spelling of keyword(s) or modifiers will lead to that option being misunderstood and therefore ignored. Errors in the value of an option can result in unpredictable behavior. When detected, errors are either ignored or pushed to a default or limiting value, but not all can or will be detected.

Consider the following CPLEX options file,

* CPLEX options file barrier crossover 2

The first line begins with an asterisk and therefore contains comments. The first option specifies the use of the barrier algorithm to solve the linear programming problem, while the second option specifies that the crossover option 2 is to be used. Details of these options can be found in Summary of CPLEX Options.

Options can also be defined by generating an options file within the GAMS source code. Consider the following code fragment for using MINOS options file,

Model m /all/; Option NLP = MINOS; * MINOS options file $onecho > minos.opt scale option 2 completion partial $offecho m.OptFile = 1; Solve m maximizing z using nlp ;

The first option sets the scale option to a value of 2. In this case, the keyword 'scale option' consists of two words. In the second line, the 'completion' option is set to 'partial'. Details of these options can be found in Summary of MINOS Options.

## Dot Options

Dot options in a solver option file allow users to associate values to variables and equations using the GAMS name of the variables and equations. The general syntax of a dot option in the option file is as follows:

(variable/equation name).optionname (value)

Dot options can be specified for `all`

, a `block`

, a `slice`

, and a `single`

variable and equation. Please note that a specific dot option may only apply to variables or equations (e.g. the GAMS/Gurobi dot option prior applies to variables only). The following example makes the use of the dot option clear.

For example, suppose one has a GAMS declaration:

```
Set i /i1*i5/;
Set j /j2*j4/;
Variable v(i,j);
Equation e(i,j);
```

Consider the following lines in an option file with the imaginary option name `dotopt`

:

Line in option file | Explanation |
---|---|

`variables.dotopt 1` | Sets the value of all variables to `1` |

`equations.dotopt 2` | Sets the value of all equations to `2` |

`v.dotopt 3` | Sets the value of the variables in block `v` to `3` |

`e.dotopt(*,*) 4` | Sets the value of the equations in block `e` to `4` |

`v.dotopt(*,’j2’) 5` | Sets the value of the variables v that have `j2` in the second index position (slice) to `5` |

`e.dotopt(’i3’,*) 6` | Sets the value of the equations e that have `i3` in the first index position (slice) to `6` |

`w.dotopt(’i2’) 7` | Sets the value of the single variables `v(’i2’)` to `7` |

`e.dotopt(’i3’,’j3’) 8` | Sets the value of the single equations `e(’i3’,’i3’)` to `8` |

The values of the dot option are applied in correspondence to the sequence in which they appear in the option file. In the current example, the values of `dotopt`

for the equation `e`

would be as follows:

e.dotopt | i1 | i2 | i3 |
---|---|---|---|

j2 | 4 | 4 | 6 |

j3 | 4 | 4 | 8 |

j4 | 4 | 4 | 6 |

# Starting Point and Initial Basis

## Starting Point

NLP solvers that search for a locally optimal solution of a NLP require an initial point to start their search. Further, the closer this initial point is to a local optimum, the less effort the solver may have to spend. The latter can also be true for solvers that search for global optimal solutions, such as most LP or MIP solver or global MINLP solvers.

Because of this immense importance of a starting point, GAMS always passes a starting point to a solver. By default, the point passed on by GAMS is given by the level and marginal attributes of variables and equations. If these values have not been set yet, default values are used. This default value is zero, except for variables whose bounds would forbid this value. In this case, the bound closest to zero is used.

In addition to setting these values explicitly in a GAMS model, a user can also load them from a save file or a GDX point file via execute_loadpoint. The latter may have been generated by running a related model and using option savepoint. Further, in models with several solve statements, the solution from one solve, if any, is used to initialize the starting point for a succeeding solve. This happens automatically since solutions from a solve statements are also stored in the level and marginal values of variables and equations. Finally, note that model attribute defpoint can be used to force sending the default starting point to a solver.

For some solvers, in particular for MIP or MINLP, an option may have to be set to make use of the starting point. Further, some solvers offer the possibility to make use of a partial starting point or use the starting point as a guide for the search. For details, see the specific solver manuals and look for parameters like `mipstart`

and the use of the GAMS parameter tryint.

## Initial Basis

While for some solvers, the values of a starting point are sufficient to initialize the search, active-set algorithms make use of a different form of starting information. An active-set algorithm tries to identify which constraints are active (or binding) in a feasible or optimal solution, that is, which variables are at one of their bounds and for which equations the activity equals the right-hand-side and the marginal is non-zero. For example, the simplex method for linear programs is an active-set algorithm. The classification of constraints as either active or inactive is closely linked to a *basis*. Active constraints are called *nonbasic* and inactive constraints are called *basic*. A basis that specifies the active and inactive constraints in an optimal solution is called an *optimal basis*.

Active-set algorithms may start by guessing an initial basis and then iteratively updating this basis until an optimal basis is found. Solution time may be reduced substantially if a good approximation of the optimal basis can be identified and passed on to the solver. Such a user-provided initial basis is called an *advanced basis*. However, provision of an advanced basis does not always help. For example, the presolving algorithms used in some solvers may cause the advanced basis to be ignored. Further, solvers may perform poorly when the advanced basis provided is worse than what the solver would otherwise have constructed with its own heuristics. Finally, not all algorithms benefit from the provision of an advanced basis: interior-point algorithms are a notable example.

GAMS provides a hint to the solver to suggest whether a basis can or should be extracted from the initial point. The hint is based on the number of rows (aka single equations) with nonzero marginals and the value of the bratio option and is computed internally as:

hint := (0 == bRatio) or (rowsWithNonzeroMarg > nRows * bratio)

While the setting of the variable level and marginal values is important in specifying an advanced basis, only the *marginal values for the rows* are relevant in computing the basis hint and in choosing a value for bratio. For example, in a problem with 1000 rows and with the default value of bratio (0.25), GAMS would suggest a basis only if at least 250 nonbasic rows exist.

Note that the default starting point - all marginals zero - is usually not sufficient for the construction of an initial basis. If the automatic transfer of a basis from one solve statement to the next leads to poor behavior in the solver, setting the option bratio to 1 will cause the basis hint to be false and suppress the use of an initial basis. Setting the model attribute defpoint to 1 or 2 will achieve the same result. Conversely, setting bratio to 0 will force the basis hint to be true.

Active-set solvers in GAMS typically use the basis hint value to decide whether to extract (and use) the advanced basis available in the starting point. Details can vary by solver, but typically it works as follows:

- Variables with a zero level value are suggested to be nonbasic if and only if they have a non-zero marginal value.
- Variables with a non-zero level value are suggested to be nonbasic if the level value is equal one of the variable bounds. The marginal values may also be used here: nonbasic variables correspond with non-zero marginal values.
- Equations with non-zero marginal are suggested to be nonbasic. Otherwise, they are suggested to be basic.

Thus, a user can attempt to explicitly provide an initial basis by setting a corresponding starting point. That is, one can set a guess for an initial basis by specifying

- non-zero marginals for equations that are predicted to be active in a solution
- non-zero marginals for variables that are predicted to be at their bound in a solution
- non-zero levels for the variables that are predicted to be non-zero in a solution

# Trace Features

Sometimes it might be useful to get certain information about a particular solve statement (or GAMS job) in a compact and customizable format.

- The Trace file facility allows to create files containing information about the "end data" of a GAMS job and the contained solve statements.
- The Solve trace facility can provide more detailed information about the solution progress of a particular solve statement (e.g. objective value of the incumbent solution or the best dual bound every five seconds)

## Trace File

The **trace file** contains information about the "end data" of a GAMS job and the contained solve statements. Creation of a trace file can be activated via command line parameter trace (see example below). The trace feature supports several predefined formatting options, that is differently formatted trace files can be created, depending on what output information is desired. The trace file format option can be set via command line parameter traceOpt. The trace file header defines the contained trace records and the associated trace record fields.

- Note
- Trace information is appended to existing trace files
**in the format of the existing trace file**. That is, if a previous trace file of the same name already exists, then all new trace data will be appended in the initial format, no matter if the current`traceopt`

value actually implies a different format. - Trace file headers can be modified, i.e. the predefined formats can be customized and trace record fields can be added or removed as needed.

- Trace information is appended to existing trace files

### Trace Records

A trace file can contain different types of trace records:

Trace Record Type | Meaning |
---|---|

`GamsStep` | A `GamsStep` refers to a GAMS execution phase (there are potentially multiple phases of GAMS execution in a single GAMS Job). For example, a trace file created with `traceopt=0` for the [TRNSPORT] model, which contains a single solve statement, will contain two GamsSteps, one referring top the GAMS execution phase before the solve statement, the other one referring to the execution phase after the solve statement. Note that this may change depending on the setting of solveLink. |

`GamsExit` | `GamsExit` describes the final `GamsStep` . |

`GamsSolve` | `GamsSolve` describes a trace record referring to a solve statement. If a file has multiple solve statements, the corresponding trace file can have multiple `GamsSolve` trace records. |

### Trace Record Fields

For every trace record, the trace file can contain multiple fields from the following list.

Name of Field | Meaning |
---|---|

`CNS` | CNS solver. |

`ComputerName` | Computer name. |

`Direction` | Direction of optimization: `0=min` , `1=max` . |

`DNLP` | DNLP solver. |

`EMP` | EMP solver. |

`ETAlg` | Elapsed time it took to execute the solve algorithm (see corresponding model attribute etAlg). |

`ETSolve` | Elapsed time it took to execute a solve statement in total (see corresponding model attribute etSolve). |

`ETSolver` | Elapsed time taken by the solver only (see corresponding model attribute etSolver). |

`GamsCloseDownTime` | The time it takes to close down GAMS (which partly depends on command line parameters) including the time to write the file summary, a GDX file, a (obfuscated) save file, a parameter file. |

`GamsCompTime` | Time of the GAMS compilation phase. |

`GamsElapsedTime` | Elapsed time since the start of a GAMS run in seconds. |

`GamsElements` | Number of labels. |

`GamsErrorCount` | Number of compilation and execution errors. |

`GamsExecTime` | GAMS execution time. |

`GamsLineNumber` | Number of lines. This corresponds to the number of lines in the echo print of the input file. |

`GamsReturnCode` | GAMS return code. |

`GamsStartupTime` | The time it takes to start up GAMS including the time to check and dump command line parameters, initialize certain internal data structures, loading a work file, reading a license file. |

`GamsSymbols` | Number of symbols (also called identifiers) including names of intrinsic functions and predefined symbols. |

`GamsTotalTime` | Total time of the corresponding trace record. Does only apply for trace records of type `GamsStep` and `GamsExit` . |

`GamsVersionID` | String that contains a GAMS version ID, e.g. `WEX282-282` for the Windows 64bit version of GAMS 28.2. |

`InputFileName` | GAMS model filename. |

`JobDate` | Day when the job started. |

`JobTime` | Time when the Job started. |

`JulianDate` | Julian date number with start day/time of job. |

`LP` | LP solver. |

`Marginals` | Indicates availability of marginals: `0=no, 1=yes` . |

`MCP` | MCP solver. |

`MINLP` | MINLP solver. |

`MIP` | MIP solver. |

`MIQCP` | MIQCP solver. |

`ModelGenerationTime` | Model generation time. Refers to the last model in the part of the program that corresponds to the trace record. |

`ModelName` | Model name. Refers to the last model in the part of the program that corresponds to the trace record. |

`ModelStatus` | Model status. Refers to the last model in the part of the program that corresponds to the trace record. |

`ModelType` | Model type. Refers to the last model in the part of the program that corresponds to the trace record. |

`MPEC` | MPEC solver. |

`NLP` | NLP solve. |

`NumberOfDiscreteVariables` | Number of discrete variables. Refers to the last model in the part of the program that corresponds to the trace record. |

`NumberOfDomainViolations` | Number of domain violations (see also model attribute domUsd ). |

`NumberOfEquations` | Number of equations. Refers to the last model in the part of the program that corresponds to the trace record. |

`NumberOfInstructions` | Length of non-linear code. |

`NumberOfIterations` | Number of iterations. Refers to the solve of the last model in the part of the program that corresponds to the trace record. |

`NumberOfNodes` | Number of nodes. Refers to the solve of the last model in the part of the program that corresponds to the trace record. Only relevant if some tree search algorithm (e.g. branch-and-bound was used). |

`NumberOfNonlinearNonZeros` | Number of non-zeroes. Refers to the last model in the part of the program that corresponds to the trace record. |

`NumberOfNonZeros` | Number of variables. Refers to the last model in the part of the program that corresponds to the trace record. |

`NumberOfVariables` | Number of variables. Refers to the last model in the part of the program that corresponds to the trace record. |

`ObjectiveValue` | Objective value. Refers to the solve of the last model in the part of the program that corresponds to the trace record. |

`ObjectiveValueEstimate` | Estimate of the best possible solution for a mixed-integer model (aka best bound). Refers to the solve of the last model in the part of the program that corresponds to the trace record. |

`OptionFile` | Solver option file number. Refers to the solve of the last model in the part of the program that corresponds to the trace record. |

`Platform` | Platform ID, e.g. `WEX` for the Windows 64bit. |

`QCP` | QCP solver. |

`RMINLP` | RMINLP solver. |

`RMIP` | RMIP solver. |

`RMIQCP` | RMIQCP solver. |

`RMPEC` | RMPEC solver. |

`SolveLine` | Line number of the last solve statement in the part of the program that corresponds to the trace record. This corresponds to the line number in the echo print of the input file. |

`SolveNumber` | Number of solve statement for a particular model. For example, `solve myModelA...; solve myModelB...; solve myModelA...;` results in solve numbers `1, 1, 2` . |

`SolverCalcTime` | Time spent in function and derivative calculations (deprecated, see also model attribute resCalc). |

`SolverElapsedTime` | Elapsed time taken by the solver when solveLink=0 is used (almost identical to model attribute etSolver). |

`SolverID` | Solver ID number. |

`SolverName` | Name of the solver. Refers to the solve of the last model in the part of the program that corresponds to the trace record. |

`SolverReadTime` | Time to import model (deprecated, see also model attribute resIn). |

`SolverRealTime` | Elapsed time taken by the solver when solveLink=0 is used (almost identical to model attribute etSolver). |

`SolverSignature` | String containing a solver signature, e.g. `IBM ILOG CPLEX 28.2.0 r750fa45 Released Aug 19, 2019 WEI x86 64bit/MS Window` . Refers to the solver used to solve the last model in the part of the program that corresponds to the trace record. |

`SolverStatus` | Solver Status. Refers to the solve of the last model in the part of the program that corresponds to the trace record. |

`SolverTime` | Time used to solve the model in seconds reported by the solver (see also model attribute resUsd). |

`SolverVersion` | Solver Version (see also model attribute sysVer). |

`SolverWriteTime` | Time to export solution (deprecated, see also model attribute resOut). |

`User1` | Content of user1 string. |

`User2` | Content of user2 string. |

`User3` | Content of user3 string. |

`User4` | Content of user4 string. |

`User5` | Content of user5 string. |

`UserName` | User name. |

### Trace Report

GAMS can create **trace reports** from trace files, if started with command line parameter action`=gt`

. The following sequence of commands loads model [TRNSPORT] from the GAMS model library, runs `trnsport.gms`

and creates a tracefile `trc.txt`

, and produces a trace report plus a trace summary from the trace file.

$ gamslib trnsport $ gams trnsport trace=trc.txt $ gams trc.txt a=gt

The **trace file** `trc.txt`

contains the default trace record fields for the `GamsStep`

and `GamsSolve`

trace records:

* Trace Record Definition * GamsStep * JobDate JobTime InputFileName GAMS GamsVersionID GamsReturnCode GamsErrorCount GamsStartupTime GamsCompTime GamsExecTime GamsCloseDownTime GamsTotalTime "User1" * GamsSolve * JobDate JobTime InputFileName ModelType SolverName SolverStatus ModelStatus SolveNumber SolveLine SolverID SolverVersion NumberOfEquations NumberOfVariables NumberOfNonZeros NumberOfNonlinearNonZeros NumberOfInstructions * NumberOfIterations ModelGenerationTime SolverReadTime SolverCalcTime SolverWriteTime ObjectiveValue "User1" * 09/25/19 07:04:00 trnsport.gms GAMS WEX282-282 1 0 0.015 0 0 0.016 0.031 "" 09/25/19 07:04:00 trnsport.gms LP CPLEX 1 1 1 64 23 NA 6 7 19 0 0 4 0 NA NA NA 153.675 "" 09/25/19 07:04:00 trnsport.gms GAMS WEX282-282 0 0 0 0 0 0 0 ""

The **trace summary** `trc.sum`

contains condensed information about the trace records:

Trace Summary with TL=0 for [...]\trc.txt Trace Records = 3, Error Records = 0, First Date = 09/25/19 07:04:00

The **trace report** is created in `trc.lst`

and contains detailed information about the trace records from the underlying trace file including a `ModelSolveStat`

matrix that assigns a score from 0 to 9 to all potential combinations of model status and solver status:

[...] Trace Report for File: [...]\trc.txt Using ModelSolveStat for TL=0 1 2 3 4 5 6 7 8 9 10 11 12 13 1 9 . . . . . . . . . . . . 2 9 9 9 9 9 . . 9 . . . . . 3 9 . . . . . . . . . . . . 4 9 . . . . . . . . . . . . 5 9 . . . . . . . . . . . . 6 . 5 5 5 5 . . 5 . . . . . 7 9 9 9 9 9 . . 9 . . . . . 8 9 9 9 9 9 . . 9 . . . . . 9 . 5 5 5 5 . . 5 . . . . . 10 9 . . . . . . . . . . . . 11 . . . . . . 5 . . . . . . 12 . . . . . . . . . . 3 . 3 13 . . . . . . . . 3 3 . 3 . 14 4 4 4 4 4 6 . 4 . . . 3 . 15 9 . . . . . . . . . . . . 16 9 . . . . . . . . . . . . 17 9 . . . . . . . . . . . . 18 9 . . . . . . . . . . . . 19 9 . . . . . . . . . . . . Marked trace records are listed below: Record Date Time Filename Type Solver Message * Trace Record Definition * GamsStep * JobDate JobTime InputFileName GAMS GamsVersionID GamsReturnCode GamsErrorCount GamsStartupTime GamsCompTime GamsExecTime GamsCloseDownTime GamsTotalTime "User1" * GamsSolve * JobDate JobTime InputFileName ModelType SolverName SolverStatus ModelStatus SolveNumber SolveLine SolverID SolverVersion NumberOfEquations NumberOfVariables NumberOfNonZeros NumberOfNonlinearNonZeros NumberOfInstructions * NumberOfIterations ModelGenerationTime SolverReadTime SolverCalcTime SolverWriteTime ObjectiveValue "User1" * First time stamp = 09/25/19 07:04:00 Last time stamp = 09/25/19 07:04:00 Total trace records = 3 Total comment records = 7 Total GAMS records = 2 all return codes 1 RC= 0 Normal completion 1 RC= 1 Executing subsystem Time (sec) total mean start 0.01 0.01 compile 0.00 0.00 execute 0.00 0.00 closedown 0.02 0.01 total 0.03 0.02 Total SOLVE records = 1 all return codes solvestatus 1 RC= 1 1 Normal Completion modelstatus 1 RC= 1 1 Optimal Numbers total mean equations 6 6.00 variables 7 7.00 nonzeros 19 19.00 nonlinear 0 0.00 instruction 0 0.00 equations 6 6.00 Time (sec) total mean generation 0.00 0.00 input 0.00 0.00 calculation 0.00 0.00 output 0.00 0.00 total solve 0.00 0.00 SOLVESTAT Cross Tabulation 1 2 3 4 5 6 7 8 9 10 11 12 13 tot LP 1 . . . . . . . . . . . . 1 total 1 0 0 0 0 0 0 0 0 0 0 0 0 1 MODELSTAT Cross Tabulation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 tot LP 1 . . . . . . . . . . . . . . . . . . 1 total 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 GTRACE TIME = 0.000 SECONDS VERID WEX282-282 [...]

The trace report may be particularly interesting, if the underlying trace file contains multiple trace records from different solve statements. In combination with command line parameter traceLevel, it is easy to filter for `GamsSolve`

trace records with a low `ModelSolveStat`

score, i.e. undesirable combinations of model status and solver status. If we run [TRNSPORT] again with an iteration limit of 0 (remember that the trace information will be appended to the trace file from the example above) and recreate the trace report as follows

$ gams trnsport trace=trc.txt iterlim=0 $ gams trc.txt a=gt

the trace report shows two solve records and the obtained statuses:

Total SOLVE records = 2 all return codes solvestatus 1 RC= 1 1 Normal Completion solvestatus 1 RC= 2 2 Iteration Interrupt modelstatus 1 RC= 1 1 Optimal modelstatus 1 RC= 6 6 Intermediate Infeasible

A look at the `ModelSolveStat`

matrix from the initial example, tells us that a combination of model status 6 (Intermediate Infeasible) in combination with solve status 2 (Iteration Interrupt) results in a score of 5. If we increase the traceLevel to a value greater than or equal to 5 and recreate the trace report again, e.g. via

$ gams trc.txt a=gt tracelevel=5

the `ModelSolveStat`

matrix at the beginning of the trace report changes such that only the scores greater than 5 for accepted combinations of model and solver status are shown

Using ModelSolveStat for TL=5 1 2 3 4 5 6 7 8 9 10 11 12 13 1 9 . . . . . . . . . . . . 2 9 9 9 9 9 . . 9 . . . . . 3 9 . . . . . . . . . . . . 4 9 . . . . . . . . . . . . 5 9 . . . . . . . . . . . . 6 . . . . . . . . . . . . . 7 9 9 9 9 9 . . 9 . . . . . 8 9 9 9 9 9 . . 9 . . . . . 9 . . . . . . . . . . . . . 10 9 . . . . . . . . . . . . 11 . . . . . . . . . . . . . 12 . . . . . . . . . . . . . 13 . . . . . . . . . . . . . 14 . . . . . 6 . . . . . . . 15 9 . . . . . . . . . . . . 16 9 . . . . . . . . . . . . 17 9 . . . . . . . . . . . . 18 9 . . . . . . . . . . . . 19 9 . . . . . . . . . . . .

and GAMS throws an execution error

--- Starting trace report generation *** Status: Execution error(s)

The trace file facility in combination with the trace report can be particularly useful for automated quality assurance tests where certain expected outcomes should be audited.

## Solve trace

In order to do accurate performance evaluations it may be useful to obtain more detailed information about a solve than the "end data" that the trace file provides. E.g., for a branch-and-bound based solver, one may want to have intermediate information about the values of primal and dual bounds at the root node and subsequent nodes within the search.

The **solve trace** option that is implemented in some of the GAMS solver interfaces allows users to output solve information, e.g., primal and dual bounds, for every `n`

nodes or at every time step. For example, the user may be interested in the objective value of the incumbent solution or the best dual bound on the optimal value every 50 nodes and every five seconds of the solve.

- Note
- The solve trace file format and options may change in a future GAMS release.

The solve trace option is invoked via a GAMS solver options file. Usually, options to specify a filename of the trace file to be created and options to specify time and node intervals are available. Please refer to the GAMS solver manuals for the exact names of these options (search for `solvetrace`

or `miptrace`

).

The solve trace file is written in comma-separated-value (CSV) format, where the entries in each line have the following meaning:

Column Name | Meaning |
---|---|

`lineNum` | a line index |

`seriesID` | indicator why the line was written: S = start of search, N = node frequency, T = time frequency, E = end of search |

`node` | number of enumerated branch-and-bound nodes |

`seconds` | time since the solving started |

`bestFound` | primal bound, i.e., objective value of incumbent solution |

`bestBound` | dual bound, i.e., bound on optimal value |

A sample solve trace file including statistics of a GAMS run using the MIP model [DICE] and the solver XPRESS looks as follows:

* miptrace file miptrace.mtr: ID = XPRESS.1 Instance = dice * fields are lineNum, seriesID, node, seconds, bestFound, bestBound 1, S, 1, 0.078, na, na 2, N, 101, 0.781, 21, 23.9369 3, N, 201, 0.875, 21, 23.5564 4, N, 304, 1.031, 21, 23.5564 5, E, 399, 1.094, 21, 21 * miptrace file miptrace.mtr closed

See also the slides for the presentation Advanced Use of GAMS Solver Links (2013) and the accompanying scripts for some ideas on what to do with the solve trace functionality.

# Branch-and-Cut-and-Heuristic Facility (BCH)

Global search algorithms can sometimes significantly benefit from user supplied routines that support the solution process of an hard optimization problem. For example, branch-and-cut solvers (e.g., CPLEX, Gurobi, SCIP, Xpress) can profit from user-supplied *cutting planes* or *good feasible solutions*. GAMS users could supply these as part of the model given to the solver, by adding a set of constraints representing likely to be violated cuts and an initial solution (possibly in combination with GAMS parameters like tryint and solver-specific options like mipstart in CPLEX). However, this does not allow a dynamic interaction between a running solver and user supplied routines that, for example, use a current relaxation solution to construct cutting planes or feasible solutions. The GAMS Branch-and-Cut-and-Heuristic (BCH) facility attempts to automate all major steps necessary to make callbacks that certain solvers provide for such usage available to the GAMS user. This allows GAMS users to apply complex solution strategies without having to have intimate knowledge about the inner workings of a specific solver.

**Currently, only two solvers support the BCH facility: CPLEX and SBB. ** With GAMS/CPLEX, user supplied GAMS programs that implement primal heuristics and cut generation can be used. With SBB, only primal heuristics are possible.

As the name indicates, the BCH facility has been designed with the solving process of a branch-and-cut solver (e.g., CPLEX, Gurobi, SCIP, Xpress) in mind. Such solvers often allow to call a user supplied routine after a node in the branch-and-bound (B&B) tree has been processed. Within that routine, available information like the solution of a relaxation (often an LP or NLP) at that node and the current incumbent, if any, is exported by the BCH facility into a GDX file using the original GAMS namespace. Next, different user supplied GAMS programs can be called, e.g., for finding cuts which are violated by the relaxation solution (cut generator) or to find new incumbents (primal heuristic). These GAMS programs should import the information from the GDX file and do their computations. After termination, the BCH facility resumes control, reads the findings from the GAMS program and passes them to the solver.

A relaxation solution may be exported into a file `bchout.gdx`

by the BCH facility. This GDX file does not only contain the variable values as level values (`.l`

), but also variable bounds (`.lo`

and `.up`

). For a B&B solver, these are the local bounds at this node. Hence, they reflect branching decisions made in the B&B tree and bound tightenings that were deduced by the solver. In a similar way, the BCH facility may export an incumbent solution to the GDX file `bchout_i.gdx`

. The bounds for the incumbent solution reflect global bounds, i.e., the original bounds, possibly tightened by the solver. GDX files can be imported by the GAMS program using the compile time $load or run time execute_load.

The BCH facility is activated and controlled by setting certain options in the solvers options file. The precise names and meanings of the options may vary from one solver to another. Therefore, also the corresponding GAMS solver manual should be checked. The options that come with the BCH facility can be used to define the calls of the users GAMS programs, to determine when they should be called, and to overwrite the filenames for the GDX files (to avoid name clashes). General BCH related options are the following:

Name | Description | Default |
---|---|---|

`UserGDXIn` | The name of the GDX file read back into the solver. | `bchin.gdx` |

`UserGDXName` | The name of the GDX file exported from the solver with the solution at the node. | `bchout.gdx` |

`UserGDXNameInc` | The name of the GDX file exported from the solver with the incumbent solution. | `bchout_i.gdx` |

`UserGDXPrefix` | Prefix to add to `UserGDXIn` , `UserGDXName` , and `UserGDXNameInc` | empty |

`UserJobID` | Postfix to add to listing and log filenames and to `UserGDXIn` , `UserGDXName` , and `UserGDXNameInc` . Further, `--UserJobID` is added to calls to users GAMS programs. | empty |

`UserKeep` | Calls users GAMS programs with `gamskeep` instead of `gams` . The use of `gamskeep` will preserve the scratch directory similar to the command line option keep | 0 |

In the following, the interface for the available callbacks are explained in more detail and corresponding options are listed.

## Primal Heuristics

In the primal heuristic callback, the user can provide a GAMS program which tries to construct a feasible solution based on the information provided by the solver, e.g., a current relaxation solution and the current incumbent. Thus, the GAMS program could attempt to repair infeasibilities in the relaxation solution or try to improve the incumbent from the solver.

If the GAMS program finds a new solution, it should store it in the level values of variables that correspond to the original variables. For example, if the original model uses binary variable `open(i,t)`

, then at the end of the GAMS program `open.l(i,t)`

should contain a 0 (zero) or a 1 (one). The BCH facility calls the GAMS program and instructs GAMS to store the results in a GDX file at termination. This GDX file is then read in again by the BCH facility and the solution is passed back to the solver. The solver checks this solution for infeasibilities and in case this check is passed and the solution is better than the best known solution, the solver updates it's incumbent.

If the GAMS program cannot find a feasible solution, it can terminate with an execution error triggered by an abort statement to prevent the BCH facility from reading the results from the heuristic run.

BCH parameters to control the primal heuristic call are typically the following:

As an example, for the Oil Pipeline Network Design problem, the BCH options to invoke the primal heuristic in the GAMS program `bchoil_h.inc`

when using GAMS/CPLEX could be

userheurcall bchoil_h.inc mip cplex optcr 0 reslim 10 userheurfirst 5 userheurfreq 20 userheurinterval 1000

## Cutting Planes

In the cut generator callback, the user can provide a GAMS program which tries to find a linear cut (that is, a linear inequality) that is violated by the relaxation solution. The solver would then add these cuts to it's *cut pool*. Typically, it then resolves the relaxation at the node and calls the cut generator again. If no cutting planes are found, the solver will continue, e.g., by processing the next node. Please note that the solver cannot perform validity checks on the provided cuts. Hence, it is possible to cut off areas of the feasible region, including optimal solutions.

Exporting cuts is a little more complicated than a solution because next to the cut coefficients, also the sense and the right-hand-side of the cut inequality needs to be exported. Further, exporting several cuts with one call should be possible. For this purpose, the GAMS program has to define and fill a set `cc`

and parameters `numcuts`

, `rhs_c(cc)`

, and `sense_c(cc)`

appropriately. The set `cc`

is used as a cut index. It can be larger than the number of actually generated cuts.

- Note
- The elements of the cut index set must form a series of integers starting at 1 (
`1, 2, 3,...`

).

Parameter `numcuts`

should specify the number of added cuts. `rhs_c(cc)`

should store the right-hand-side of each cut. Finally, `sense_c(cc)`

should store the sense of each cut, which must be 1 for lower-equal (≤), 2 for equal (=, rather unusual for cuts), and 3 for greater-equal (≥). The corresponding declaration in GAMS code may be

```
$set MaxCuts 100
Set cc 'cuts' / 1 * %MaxCuts% /;
Parameters numcuts 'number of cuts to be added' / 0 /
rhs_c(cc) 'cut rhs'
sense_c(cc) 'the sense of the cuts';
```

The only thing missing are the cut coefficients. As it should be possible to return more than one cut, using variable attributes like level values is not sufficient. Therefore, for each variable that is part of a cut, a new parameter must be added in the GAMS program. The name of the parameter must be the name of the corresponding variable with an additional `_c`

at the end. Further, the parameter must be indexed like the variable, but with the cut index set cc added at the beginning. For example, assume variable `open(i,t)`

should be part of a cut. Then the cut coefficients should be stored in a parameter `open_c(cc,i,t)`

, e.g.,

```
Parameter open_c(cc,i,t) 'coefficients of variable open(i,t) in cut cc';
```

The BCH facility reads all parameters that end in `_c`

, takes the base name and looks for a variable with that name and indices and builds up the cut matrix. A cut cannot introduce a new variable into the model. All cuts added to the model are assumed to be *global cuts*, that is, they need to be valid for the entire problem, not just for the current node.

BCH parameters to control the cut generation call are typically the following:

Name | Description | Default |
---|---|---|

`UserCutFreq` | Determines the frequency of the cut generator call. | 10 |

`UserCutMult` | Determines the multiplier for the frequency of the cut generator call. | 2 |

`UserCutInterval` | Determines the interval when to apply the multiplier for the frequency of the cut generator call. See UserHeurInterval for details. | 100 |

`UserCutFirst` | Calls the cut generator for the first n nodes. | 10 |

`UserCutNewInt` | Whether to call the cut generator if the solver found a new integer feasible solution. | no |

`UserCutCall` | Arguments to the GAMS call to invoke the cut generator GAMS program. | empty |

As an example, for the Oil Pipeline Network Design problem, the BCH options to invoke the cut generator in the GAMS program `bchoil_c.inc`

when using GAMS/CPLEX could be

usercutcall bchoil_c.inc mip cplex usercutfirst 0 usercutfreq 0 usercutnewint yes

## Incumbent Callbacks

The incumbent callbacks can be used to execute a GAMS program when the solver found a new feasible solution that improves the incumbent. Additionally, the incumbent check callback `UserIncbCall`

can be used to notify the solver whether the given feasible solution should be accepted by the solver. This allows to implement a filtering mechanism that forces a solver to search for additional solutions even though an optimal solution might have been found already. Furthermore, the callback `UserLazyConCall`

allows to add lazy constraints after an incumbent has been found.

The following parameters control the incumbent callbacks:

## Examples

The GAMS model library contains a few examples to show to use the BCH facility:

- bchtlbas.gms : Trim Loss Minimization with Heuristic using BCH Facility This model implements a very simple LP/MIP based primal heuristic for the trimloss minimization problem.
- bchfcnet.gms : Fixed Cost Network Flow Problem with Cuts using BCH Facility This model implements simple but difficult to separate cuts for a network design problem. The global solver BARON is used to find violated cuts by solving a non-convex MINLP.
- bchmknap.gms : Multi knapsack problem using BCH Facility This model implements simple cover inequalities for the multi-knapsack problem.
- bchoil.gms : Oil Pipeline Design Problem using BCH Facility This is the most complex example. It implements three different primal heuristics: an initial heuristic based on a simplified cost structure, a rounding heuristic, and a local branching heuristic. In addition, complex cuts are generated by solving regionalized versions of the original problem.
- dicegrid.gms : MIP Decomposition and Parallel Grid Submission - DICE Example This example uses many of the UserJobID option to rename files, since running multiple jobs in parallel requires the use of different filenames. This example also uses the incumbent reporting call UserIncbICall.
- solnpool.gms : Cplex Solution Pool for a Simple Facility Location Problem This example uses the incumbent checking call UserIncbCall as an advanced filter for accepting or rejecting solutions found by CPLEX.

# Choosing an appropriate Solver

For any of the GAMS problem classes (LP, MCP, MINLP, ...), there is no solver that is best on every problem instance. Below, we provide some links to rules of thumb on choosing a solver or solver comparisons.

- T. Koch, T. Achterberg, E. Andersen, O. Bastert, T. Berthold, R. Bixby, E. Danna, G. Gamrath, A. Gleixner, S. Heinz, A. Lodi, H. Mittelmann, T. Ralphs, D. Salvagnin, D. Steffy, K. Wolter, MIPLIB 2010, Mathematical Programming Computations, 3:2 (2011) 103-163. preprint
- M. Bussieck and S. Vigerske, MINLP Solver Software (2014).
- SNOPT vs. IPOPT: P. Gill, M. Saunders, E. Wong, On the Performance of SQP Methods for Nonlinear Optimization, 2015
- H. Mittelmann: Decision Tree for Optimization Software and Benchmarks for Optimization Software

## Relative Merits of MINOS and CONOPT

### How to choose between MINOS and CONOPT

It is almost impossible to predict how difficult it is to solve a particular model. The best and most reliable way to find out which solver to use is to try out both. However, there are a few rules of thumb:

CONOPT is well suited for models with very non-linear constraints. If you experience that MINOS has problems achieving feasibility during the optimization, you should try CONOPT. On the other hand, if your model has few nonlinearities outside the objective function, MINOS and QUADMINOS is probably the best solver.

CONOPT is has a fast method for finding a first feasible solution that is particularly well suited for models with few degrees of freedom (this means: the number of variables is approximately the same as the number of constraints - in other words, models that are almost square). In these cases CONOPT is likely to outperform MINOS while for models with many more variables than equations MINOS is probably more suited.

CONOPT has a preprocessing step in which recursive equations and variables are solved and removed from the model. If you have a model where many equations can be solved one by one, CONOPT will take advantage of this property. Similarly, intermediate variables only used to define objective function terms are eliminated from the model and the constraints are moved into the objective function.

CONOPT has many built-in tests (e.g. tests for detecting poor scaling). Many models that can be improved by the modeler are rejected with a constructive message. CONOPT is therefore a useful diagnostic tool during model development even if another solver is used for the production runs.

### Why serious NLP modelers should have both MINOS and CONOPT

It is almost impossible to predict how difficult it is to solve a particular model. However, if you have two solvers, you can try both. The overall reliability is increased and the expected solution time will be reduced.

On a test set of 196 large and difficult models, many poorly scaled or without initial values, both MINOS and CONOPT failed on 14 models. However only 4 failed on both MINOS and CONOPT. So the reliability of the combined set of solvers is much better than any individual solver.

Many examples of poorly formulated models were observed on which MINOS failed. CONOPT rejected many of the models, but with diagnostic messages pinpointing the cause of the problem. After incorporating the changes suggested by CONOPT, both MINOS and CONOPT could solve the model. Switching between the two solvers during the initial model building and debugging phase can often provide useful information for improving the model formulation.

### Special Offer for two NLP Solvers

In order to encourage modelers to have two NLP solvers, GAMS offers a 50% discount on the second solver when both MINOS and CONOPT are purchased together.

## PATH versus MILES

This document describes some of the differences between the MCP solvers PATH and MILES. MILES is a free solver, that comes with the GAMS/BASE module, while PATH is an optional solver, that is charged for separately.

PATH and MILES are two GAMS solvers capable of solving mixed nonlinear complementarity problems (MCP). Both solvers are based on the sequential linear complementarity algorithm, i.e., they both solve a sequence of linear mixed complementarity problems whose solutions typically converge to the solution of the MCP. To solve each of the linear subproblems (major iterations), both codes use a generalization of an algorithm due to Lemke that is based on a sequence of pivots (minor iterations) similar to those generated by the simplex method for linear programming. To do these pivots efficiently, both codes use the same sparse linear algebra package.

As a result of the above similarities, the performance of the two codes is comparable for many "easy" models. Viewed over a broad range of problems, however, PATH is typically faster and more robust than MILES. While both codes solve all the MCP and MPSGE models in GAMSLIB, PATH significantly outperforms MILES on the MCPLIB test collection found at CPNET.

Most sophisticated MCP and MPSGE modelers prefer to use PATH over MILES. PATH has a crashing scheme that allows it to quickly improve the user given starting point before starting to solve the linear subproblems. This frequently speeds up solution time. PATH automatically attempts to fix "singular" models using a technique based on proximal perturbations. In many cases, this enables the linear subproblems to be solved, leading to a model solution. This typically helps modelers at model development time.

PATH has many more solution options to enable it solve difficult models. The code automatically tries useful options on difficult problems using a restart procedure. PATH has a much more sophisticated "globalization" procedure that typically improves speed and robustness. PATH implements a nonmonotone watchdog technique. Stalling is frequently circumvented by allowing larger steps to be taken toward solutions.

PATH has many more diagnostic features that help uncover problems in a model. In particular, singularities in the model, zero rows and columns and several measures of optimality are returned to the user. Theoretically, PATH has better convergence properties than MILES. In particular, new merit functions are known to allow more reliable and faster convergence.