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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
goalobjmo.mos: same as goalobj.mos, using multi-objective solving functionality

Further explanation of this example: 'Mosel User Guide', Section 12.2 Goal Programming

Source Files
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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. Sep. 2022        *
*******************************************************!)

model GoalCtr                       ! Start a new model
uses "mmxprs"                       ! Load the optimizer library
uses "mmsystem"

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

declarations
NGOALS=3                           ! Number of goals
GOALS=1..NGOALS
x,y: mpvar                         ! Variables
dev: array(1..2*NGOALS) of mpvar   ! Deviation from goals
MinDev: linctr                     ! Objective function
Goal: array(GOALS) 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 GOALS)
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 GOALS) 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", textfmt("Target",11), textfmt("Value",7))
forall(g in 1..i)
writeln(formattext("%4d %3s %5g %7g", g, ATypes(Goal(g).type),
-Goal(g).coeff, Goal(g).act-dev(2*g).sol+dev(2*g-1).sol))

printsol

end-procedure

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

procedure archimedian

writeln("\nArchimedian:")

declarations
Penalty: array(GOALS) 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 GOALS) 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", textfmt("Target",11), textfmt("Value",7), textfmt("Penalty",9))
forall(g in GOALS)
writeln(formattext("%4d %3s %5g %7g %7g", g, ATypes(Goal(g).type),
-Goal(g).coeff, Goal(g).act-dev(2*g).sol+dev(2*g-1).sol, Penalty(g)))

printsol

end-procedure

end-model