FICO Xpress Optimization Examples Repository: Basic MIP tasks: binary variables; logic constraints

FICO Xpress Optimization Examples Repository

Basic MIP tasks: binary variables; logic constraints

Description

We wish to choose among items of different value and weight those that result in the maximum total value for a given weight limit.

small MIP problem
alternative use of number-valued ranges and sets of strings for indexing variables and data
definition of binary variables
forall statement
formulation of logic constraints using indicators or advmod functionality (burglarl.mos)

Further explanation of this example: 'Mosel User Guide', Section 2.1 The burglar problem.

burglar.zip

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Source Files

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burglar.mos	[download]
burglari.mos	[download]
burglarl.mos	[download]

burglari.mos

(!*******************************************************
  * Mosel Example Problems                              *
  * ======================                              *
  *                                                     *
  * file burglari.mos                                   *
  * `````````````````                                   *
  * Example for the use of the Mosel language           *
  * (Burglar problem)                                   *
  *                                                     *
  * (c) 2008 Fair Isaac Corporation                     *
  *     author: S. Heipcke, 2001                        *
  *******************************************************!)

model "Burglar (index set)"         ! Start a new model

uses "mmxprs"                       ! Load the optimizer library

declarations
 Items={"camera", "necklace", "vase", "picture", "tv", "video",
        "chest", "brick"}           ! Index set for items

 VALUE: array(Items) of real        ! Value of items
 WEIGHT: array(Items) of real       ! Weight of items
 WTMAX=102                          ! Max weight allowed for haul

 x: array(Items) of mpvar           ! 1 if we take item i; 0 otherwise
end-declarations

 VALUE("camera")  := 15;  WEIGHT("camera")  :=  2
 VALUE("necklace"):=100;  WEIGHT("necklace"):= 20
 VALUE("vase")    := 90;  WEIGHT("vase")    := 20
 VALUE("picture") := 60;  WEIGHT("picture") := 30
 VALUE("tv")      := 40;  WEIGHT("tv")      := 40
 VALUE("video")   := 15;  WEIGHT("video")   := 30
 VALUE("chest")   := 10;  WEIGHT("chest")   := 60
 VALUE("brick")   :=  1;  WEIGHT("brick")   := 10
 
 MaxVal:= sum(i in Items) VALUE(i)*x(i)  ! Objective: maximize total value

                                    ! Weight restriction
 WtMax:= sum(i in Items) WEIGHT(i)*x(i) <= WTMAX 

 forall(i in Items) x(i) is_binary  ! All x are 0/1
  
 maximize(MaxVal)                   ! Solve the MIP-problem

                                    ! Print out the solution
 writeln("Solution:\n Objective: ", getobjval)
 forall(i in Items)  writeln(" x(", i, "): ", x(i).sol)

end-model