mmxprs

Topics covered in this chapter:

The mmxprs module provides access to FICO^® Xpress Optimizer from within a Mosel model and as such it requires the Xpress Optimizer library (XPRS) to be installed on the system. To use this module, the following line must be included in the header of the Mosel model file:

 uses 'mmxprs'

A large number of optimization-related routines are provided, ranging from those for finding a solution to the problem, to those for setting callbacks and cut manager functions. Whilst a description of their usage is provided in this manual, further details relating to the usage of these may be found by consulting the Xpress Optimizer Reference Manual.

New functionality for the Mosel language

The problem type mpproblem.xprs

This module exposes its functionality through an extension to the mpproblem problem type. As a consequence, all routines presented here are executed in the context of the current problem. In particular, the setting of a control parameter is applied only to the current problem and each problem has its own set of settings and solution information. However, when a new problem instance is created, the value of the control parameters XPRS_colorder, XPRS_enummaxsol, XPRS_enumduplpol, XPRS_loadnames and XPRS_verbose are initialised with the settings of the main problem.

The type basis

The module mmxprs defines the type basis to represent solution basis in the Mosel Language. This new type is used to store a basis computed by the optimizer during its solution process (savebasis). A basis can then be loaded again into the optimiser with loadbasis, inspected (by getting the basis status of each variable/constraint it includes with getbstat) or modified (by changing this basis status using setbstat). The type basis supports assignment and test of equality. This comparison only checks whether two basis contain the same information, it does not indicate whether the basis are equivalent.

The type mpsol

The type mpsol characterises a solution of an MP problem by associating a value to each decision variable (type mpvar) of the problem. Initialising such an object can be achieved by saving the current solution found by the optimiser (savesol or savemipsol) or by building it one variable at a time (setsol). Various routines requiring solution information support the solution object. For instance getsol may be used to evaluate an expression on a specific solution; loadmipsol and addmipsol accept this object as input. A solution might be saved into a file using writesol and the resulting file can be loaded into the optimiser with readsol. The type mpsol supports assignment and test of equality.

The type boolvar

An entity of type boolvar is a pseudo boolean decision variable. This type supports operators and, or and not for building logical expressions and can be combined with ordinary Boolean variables. A logical constraint is specified either by associating a pseudo boolean variable to a logical expression using the following syntax:

boolvar = logical_expression

or by forcing the truth value (i.e. true or false) of an expression as follows:

logical_expression = boolean

When a logical expression is used on its own as a statement it is implicitly turned into a constraint (forced to true) and added to the constraint store.

Each boolvar is represented in the MIP problem by two binary variables (mpvar): one for the value itself and another one for its negation. These decision variables can be accessed from the model using the function getvar such that they can be used in linear constraints. The solution value of a boolvar is of type boolean and can be obtained using getsol.

The type logctr

The type logctr represents either a logical expression over linear constraints, a logical expession/constraint over pseudo boolean decision variables (boolvar) or an indicator constraint (see indicator). Logical expressions can be built using standard operators (and, or, not) or with the help of the dedicated functions implies and xor (for logical expressions over linear constraints only). These logical constructs are handled like linear constraints: they are associated to the current problem, can be (re)defined via assignments and hidden using sethidden. Note however that logical constructs are not shown by exportprob although the mmxprs routine writeprob will report them.

If logical expressions over linear constraints are employed in a model, the loading of the problem into the optimizer requires the use of the helper package "advmod":

uses 'advmod'

This package is not necessary when a model uses only logical constraints over pseudo boolean variables or indicator constraints directly.

Control parameters

This module extends the getparam function and the setparam procedure in order to access all the control and problem parameters of Optimizer (for example the problem attribute LPSTATUS is mapped to the mmxprs control parameter XPRS_lpstatus). In addition to these, the following control parameters are also defined:

XPRS_colorder	Reorder matrix columns before loading the problem.
XPRS_enumduplpol	Handling of duplicate solutions during an enumeration.
XPRS_enummaxsol	Maximum number of solutions to be saved during an enumeration.
XPRS_enumsols	Number of solutions found during the last enumeration.
XPRS_fullversion	Optimizer version number.
XPRS_loadnames	Enable/disable loading of MPS names into the Optimizer.
XPRS_maxupdc	Size of the pool of matrix updates.
XPRS_problem	Optimizer problem pointers.
XPRS_probname	Read/set the problem name used by the Optimizer.
XPRS_verbose	Enable/disable message printing by the Optimizer.

Example:

setparam("XPRS_verbose", true)      ! Turn on message printing
pstat:= getparam("XPRS_lpstatus")   ! Get the problem LP optimization status
writeln("Best bound=", getparam("XPRS_bestbound")) ! Display the best bound value

Procedures and functions

This section lists in alphabetical order the functions and procedures that are provided by the mmxprs module.

addmipsol	Add a MIP solution to the optimizer.
basisstability	Get basis stability information.
calcsolinfo	Calculates a property of an mpsol solution.
clearmipdir	Delete all defined MIP directives.
clearmodcut	Delete all defined model cuts.
command	Execute an Optimizer command.
copysoltoinit	Copy solution values to initial values of an NL problem.
crossoverlpsol	Crosses over a previously loaded LP solution to a basic solution.
defdelayedrows	Define the set of constraints to be treated as delayed rows.
defsecurevecs	Define the variables and constraints to be preserved.
estimatemarginals	Estimate better marginal values for variables and constraints for degenerate problems.
fixglobal	Fix values of discrete entitites.
getbstat	Get the status of a variable or constraint in a basis.
getcomputeallowed	Get whether Insight Compute Interface integration is allowed
getdualray	Get a dual ray for an infeasible problem.
getiis	Compute then get the Irreductible Infeasible Sets (IIS).
getiissense	Decode the sense part of an IIS bound type information.
getiistype	Decode the type part of an IIS bound type information.
getinfcause	Returns the variable or constraint causing infeasibility.
getinfeas	Returns sets of infeasible primal and dual variables.
getlb	Get the lower bound of a variable.
getloadedlinctrs	Get the linear constraints loaded into the optimiser.
getloadedmpvars	Get the decision variables loaded into the optimiser.
getmatcoeff	Get the coefficient of a variable or the constant term of a constraint directly from the Optimizer.
getname	Get the name of a decision variable or constraint.
getprimalray	Get a primal ray for an unbounded problem.
getprobstat	Get the Optimizer problem status.
getrange	Get a range value for a variable or constraint.
getscale	Retrieves scaling information about the currently loaded problem.
getsensrng	Get sensitivity ranges for objective function coefficients, RHS coefficients, variable upper bounds or variable lower bounds.
getsize	Get the size of a solution.
getsol	Get the solution value of an expression from a solution object.
getub	Get the upper bound of a variable.
getvar	Get the decision variable associated to a pseudo boolean.
getvars	Get the set of variables of a solution.
hasfeature	Check if a specific feature is supported by the currently used license.
implies	Create an implies expression.
indicator	Create an indicator constraint.
isiisvalid	Check whether an IIS number exists.
isintegral	Check whether a solution value is integral.
loadbasis	Load a previously saved basis.
loadlpsol	Load an LP solution into the optimizer.
loadmipsol	Load a MIP solution into the optimizer.
loadprob	Load a problem into the optimizer.
maximize, minimize	Maximize/minimize the current problem.
postsolve	Postsolve the current matrix.
readbasis	Read a basis from a file.
readdirs	Read directives from a file.
readsol	Read a solution from a file.
refinemipsol	Executes the MIP solution refiner on an mpsol solution.
rejectintsol	Reject a PREINTSOL solution.
repairinfeas	Relaxing bounds to repair infeasibility.
resetbasis	Reset a basis.
resetiis	Reset the search for IIS.
resetsol	Reset a solution.
savebasis	Save the current basis.
savemipsol	Save the current solution into the provided array or solution object.
savesol	Save the current solution into a solution object.
savestate	Save current state of the Optimizer to a file.
selectsol	Select one of the solutions found by solution enumerator.
setarchconsistency	Sets the optimizer architecture control.
setbstat	Set the status of a variable or constraint in a basis.
setcallback	Set optimizer callback functions and procedures.
setcbcutoff	Set cutoff for PREINTSOL callback.
setcomputeallowed	Set whether Insight Compute Interface integration is allowed
setgndata	Update data for GAPNOTIFY callback.
setlb	Set the lower bound of a variable.
setmatcoeff	Set the coefficient of a variable or the constant term directly in the Optimizer.
setmipdir	Set a directive on a variable or Special Ordered Set.
setmodcut	Mark a constraint as a model cut.
setsol	Define the value associated to a decision variabe in a solution object.
setub	Set the upper bound of a variable.
setucbdata	Update data for CHGBRANCH callback.
stopoptimize	Interrupt the optimizer algorithms.
unloadprob	Unload the problem held in the optimizer.
uselastbarsol	Sets up the last barrier solve's solution as the current one if one is available
writebasis	Write the current basis to a file.
writedirs	Write current directives to a file.
writeprob	Write the current problem to a file.
writesol	Write a solution to a file.
xor	Create an exclusive or expression.
xprsmemoryuse	Retrieve memory usage statistics.

Cut Pool Manager

This section contains the functions and procedures of the Xpress Optimizer cut manager. For a detailed description of the cut manager and its functionality the user is referred to the Xpress Optimizer Reference Manual. To run the cut manager from Mosel, it may be necessary to (re)set certain control parameters of the optimizer. For example, switching off presolve and automatic cut generation, and reserving space for extra rows in the matrix may be useful:

setparam("XPRS_presolve", 0);       ! Switch presolve off...
setparam("XPRS_presolveops", 2270); ! ...or use secure setting for presolve
setparam("XPRS_cutstrategy", 0);    ! Switch automatic cut generation off
setparam("XPRS_extrarows", 5000);   ! Reserve space for 5000 extra rows in
                                    ! the matrix

The callback functions and procedures that are relevant to the cut manager are initialized with function setcallback, in common with the other Optimizer callbacks.

It should be noted that cuts are not stored by Mosel but sent immediately to the Optimizer. Consequently, if a problem is reloaded into the Optimizer, any previously defined cuts will be lost. In Mosel, cuts are defined by specifying a linear expression (i.e. an unbounded constraint) and the operator sign (inequality/equality). If instead of a linear expression a constraint is given, it will also be added to the system as an additional constraint.

addcut	Add a cut to the problem in the optimizer.
addcuts	Add an array of cuts to the problem in the optimizer.
delcuts	Delete cuts from the problem in the optimizer.
dropcuts	Drop a set of cuts from the cut pool.
getcnlist	Get the set of cuts active at the current node.
getcplist	Get a set of cut indices from the cut pool.
loadcuts	Load a set of cuts into the problem in the optimizer.
storecut	Store a cut into the cut pool.
storecuts	Store an array of cuts into the cut pool.

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