FICO Xpress Optimization Examples Repository: Basic LP tasks: problem statement and solving; solution analysis

The first model (file chess.mos) is a small, introductory problem to modeling with Mosel that shows the basic features of the Mosel language:

formulation of a simple LP/IP problem
solving an optimization problem
solution printout

The second model (file chess2.mos) shows some more advanced features of Mosel, namely the data structures set and array:

formulating and solving a simple LP problem
defining a set of variables and an array of descriptions for the variables (to be used in the output printing)

Detailed solution information for MIP problems as may be required when performing sensitivity analysis, such as dual and reduced cost values (file chessfixg.mos) or ranging information for variables and constraints (file chessrng.mos), is not immediately available during or after the branch-and-bound search. The following procedure needs to be used to generate the sensitivity analysis data:

Solve the MIP problem.
Fix all discrete variables to their solution values.
Re-solve the remaining LP problem.
Retrieve the solution information.

Further explanation of this example: 'Mosel User Guide', Chapter 1 Getting started with Mosel and Section 8.1 Initializing sets, or the book 'Applications of optimization with Xpress-MP', Section 1.3 Solving the chess set problem.

(!****************************************************** Mosel Example Problems ====================== file chessfixgcb.mos ```````````````````` Display solution information for a MIP problem. (c) 2008 Fair Isaac Corporation author: S. Heipcke, Dec. 2007, rev. Sep. 2022 *******************************************************!) model "Chess (fixmipentities)" uses "mmxprs" forward procedure printsol public declarations R = 1..2 ! Index range DUR, WOOD, PROFIT: array(R) of real ! Coefficients x: array(R) of mpvar ! Array of variables ifusesoft: mpvar ! Whether soft wood is used CtrSet: set of linctr ! Set of constraints MTime, Wood: linctr ! Constraints end-declarations DUR :: [3, 2] ! Initialize data arrays WOOD :: [1, 3] PROFIT:: [5, 20] Wood:= sum(i in R) WOOD(i)*x(i) <= 200 ! Limit on raw material ! Add. capacity if using soft wood MTime:= sum(i in R) DUR(i)*x(i) <= 160 + 40*ifusesoft ifusesoft is_binary CtrSet:= {MTime, Wood} Profit:= sum(i in R) PROFIT(i)*x(i) ! Set the integer solution callback setcallback(XPRS_CB_INTSOL, ->printsol) ! setparam("XPRS_verbose", true) setparam("realfmt","%.4g") ! Set real number display format maximize(Profit) writeln("\nAfter MIP: Solution: ", getobjval) fixmipentities ! Fix discrete variables maximize(XPRS_LIN, Profit) ! Solve reduced problems as LP writeln("\nAfter fixmipentities: Solution: ", getobjval) writeln("Ctr: \tDual \t Slack + Activity = RHS") forall(c in CtrSet) writeln(" ", getname(c), ":\t", getdual(c), "\t ", getslack(c), "\t", getact(c), "\t", -1*getcoeff(c)) writeln("Var: Solution\t RCost") forall(i in R) writeln(" x(", i, "): ", getsol(x(i)), "\t ", getrcost(x(i))) !****************************************************************** ! Definition of the integer solution callback procedure printsol writeln("CB: Solution: ", getsol(Profit)) writeln("Ctr: \tDual \t Slack + Activity = RHS") forall(c in CtrSet) writeln(" ", getname(c), ":\t", getdual(c), "\t ", getslack(c), "\t", getact(c), "\t", -1*getcoeff(c)) writeln("Var: Solution\t RCost") forall(i in R) writeln(" x(", i, "): ", getsol(x(i)), "\t ", getrcost(x(i))) end-procedure end-model