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Pre-emptive and Archimedian goal programming

Description
goalctr.mos: goal programming using constraints
  • (un)hiding constraints
  • adding and deleting constraint terms
  • getting solution information
  • case statement
  • use of procedures


goalobj.mos: goal programming using objective functions
  • changing constraint type
  • changing the objective function
Further explanation of this example: 'Mosel User Guide', Section 12.2 Goal Programming


Source Files





goalctr.mos

(!*******************************************************
  * Mosel Example Problems                              *
  * ======================                              *
  *                                                     *
  * file goalctr.mos                                    *
  * ````````````````                                    *
  * Example for the use of the Mosel language           *
  * (Pre-emptive and Archimedian goal programming       *
  *  using constraints)                                 *  
  *                                                     *
  * (c) 2008 Fair Isaac Corporation                     *
  *     author: S. Heipcke, 2001, rev. Mar. 2006        *
  *******************************************************!)

model GoalCtr                       ! Start a new model

uses "mmxprs"                       ! Load the optimizer library

forward procedure preemptive        ! Declare some procedures that are
forward procedure archimedian       ! defined later

declarations
 NGOALS=3                           ! Number of goals
 x,y: mpvar                         ! Variables
 dev: array(1..2*NGOALS) of mpvar   ! Deviation from goals
 mindev: linctr                     ! Objective function
 goal: array(1..NGOALS) of linctr   ! Goal constraints
end-declarations
 
 limit:= 100*x + 60*y <= 600        ! Define a constraint
 
! Define the goal constraints
 goal(1):=  7*x + 3*y >= 40
 goal(2):= 10*x + 5*y = 60
 goal(3):=  5*x + 4*y >= 35

                                    ! Some declarations for a nice printout
declarations
 STypes={CT_GEQ, CT_LEQ, CT_EQ}
 ATypes: array(STypes) of string
end-declarations
 
 ATypes(CT_GEQ):= ">="; ATypes(CT_LEQ):= "<="; ATypes(CT_EQ):= "="
  
 preemptive                         ! Pre-emptive goal programming
 archimedian                        ! Archimedian goal programming

!***********************************************************************

procedure printsol
 
  forall(g in 1..NGOALS)
   if(dev(2*g).sol>0) then
    writeln(" Goal(",g,") deviation from target: -", dev(2*g).sol)
   elif(dev(2*g-1).sol>0) then
    writeln(" Goal(",g,") deviation from target: +", dev(2*g-1).sol) 
   end-if
 
end-procedure

!***********************************************************************

procedure preemptive

  writeln("Pre-emptive:")

(! 
  Add successively the goals to the problem and solve it, until all
  goals have been added or a goal cannot be satisfied. This assumes that
  the goals are given ordered by priority.
!)

! Remove (=hide) goal constraint from the problem
  forall(i in 1..NGOALS) goal(i).hidden:=true

  i:=0
  while (i<NGOALS) do
    i+=1
    goal(i).hidden:=false           ! Add (=unhide) the next goal
    case goal(i).type of            ! Add deviation variable(s)
     CT_GEQ: do
              deviation:= dev(2*i)
              mindev += deviation 
             end-do
     CT_LEQ: do
              deviation:= -dev(2*i-1)
              mindev += dev(2*i-1) 
             end-do
     CT_EQ : do
              deviation:= dev(2*i) - dev(2*i-1)
              mindev += dev(2*i) + dev(2*i-1) 
             end-do
     else    writeln("Wrong constraint type")
             break
    end-case  
    goal(i)+= deviation
   
    minimize(mindev)                ! Solve the LP-problem
    writeln(" Solution(", i,"): x: ", x.sol, ", y: ", y.sol)

    goal(i)-= deviation             ! Remove deviation variable(s) from goal
    if(getobjval>0) then
     writeln("Cannot satisfy goal ",i)
     break
    end-if  
  end-do

                                    ! Solution printout
  writeln(" Goal", strfmt("Target",12), strfmt("Value",9))
  forall(g in 1..i) 
   writeln(strfmt(g,5), strfmt(ATypes(goal(g).type),3), 
     strfmt(-goal(g).coeff,9), 
     strfmt( goal(g).act-dev(2*g).sol+dev(2*g-1).sol ,9)) 

  printsol
  
end-procedure

!***********************************************************************

procedure archimedian

  writeln("\nArchimedian:")

 declarations
  Penalty: array(1..NGOALS) of real ! Penalties for goal constraints
 end-declarations

  Penalty:: [8, 3, 1]

  mindev:=0                         ! Re-initialize objective function

! Define the objective as weighted sum of the deviation variables
  forall(g in 1..NGOALS) do
    case goal(g).type of            ! Add deviation variable(s)
     CT_GEQ: do
              deviation:= dev(2*g)
              mindev += Penalty(g)*deviation 
             end-do
     CT_LEQ: do
              deviation:= -dev(2*g-1)
              mindev += Penalty(g)*dev(2*g-1) 
             end-do
     CT_EQ : do
              deviation:= dev(2*g) - dev(2*g-1)
              mindev += Penalty(g)*(dev(2*g) + dev(2*g-1)) 
             end-do
     else    writeln("Wrong constraint type")
             break
    end-case  
    goal(g)+= deviation
  end-do
    
  minimize(mindev)                  ! Solve the LP-problem
  writeln(" Solution: x: ", x.sol, ", y: ", y.sol)

                                    ! Solution printout
  writeln(" Goal", strfmt("Target",12), strfmt("Value",9), strfmt("Penalty",9))
  forall(g in 1..NGOALS) 
   writeln(strfmt(g,5), strfmt(ATypes(goal(g).type),3), 
     strfmt(-goal(g).coeff,9), 
     strfmt( goal(g).act-dev(2*g).sol+dev(2*g-1).sol ,9), 
     strfmt(Penalty(g),9))

  printsol

end-procedure
  
end-model

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