Pre-emptive and Archimedian goal programming
|
|
|
| Type: | Goal Programming |
| Rating: | 3 (intermediate) |
| Description: | goalctr.mos: goal programming using constraints
goalobj.mos: goal programming using objective functions
|
| File(s): | goalctr.mos, goalobj.mos |
|
|
|
| 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
|
| goalobj.mos |
(!*******************************************************
* Mosel Example Problems *
* ====================== *
* *
* file goalobj.mos *
* ```````````````` *
* Example for the use of the Mosel language *
* (Archimedian and pre-emptive goal programming *
* using objective functions) *
* *
* (c) 2008 Fair Isaac Corporation *
* author: S. Heipcke, 2001 *
*******************************************************!)
model GoalObj ! 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
Type: array(1..NGOALS) of string ! Type of goal objectives
Sense: array(1..NGOALS) of string ! Sense of goal objectives
Weight: array(1..NGOALS) of real ! Weights of goals
Deviation: array(1..NGOALS) of real ! Max. deviation from goals
Target: array(1..NGOALS) of real ! Target (RHS) values for goals
wobj: linctr ! Objective function
goal: array(1..NGOALS) of linctr ! Goal constraints
end-declarations
limit:= 42*x + 13*y <= 100 ! Define a constraint
! Define the goal objectives
Weight::[100, 1, 0.1]
Type:: ["perc", "abs", "perc"]
Sense:: ["max", "min", "max"]
Deviation:: [10, 4, 20]
goal(1):= 5*x + 2*y - 20
goal(2):= -3*x + 15*y - 48
goal(3):= 1.5*x + 21*y - 3.8
archimedian ! Archimedian goal programming
preemptive ! Pre-emptive goal programming
!***********************************************************************
procedure archimedian
writeln("Archimedian:")
! Define the objective function as weighted sum of the goals
forall(g in 1..NGOALS)
if(Sense(g)="max") then
wobj-=Weight(g)*goal(g)
else
wobj+=Weight(g)*goal(g)
end-if
minimize(wobj) ! Solve the LP-problem
! Solution printout
writeln(" Solution: x: ", x.sol, ", y: ", y.sol)
writeln(" Goal", strfmt("Target",9), strfmt("Value",12))
forall(g in 1..NGOALS) do
writeln(strfmt(g,5), strfmt(Sense(g), 9),
strfmt(goal(g).act + goal(g).coeff , 12,6))
end-do
end-procedure
!***********************************************************************
procedure preemptive
writeln("\nPre-emptive:")
(!
Optimize successively the goals. After optimizing a goal turn it
into a constraint.
!)
i:=0
while (i<NGOALS) do
i+=1
case Sense(i) of
"max": do
maximize(goal(i)) ! Optimize the next goal
if(getprobstat<>XPRS_OPT) then
writeln("Cannot satisfy goal ",i)
break
else
Target(i):=getobjval
if (Type(i)="perc") then
Target(i)-= abs(Target(i))*Deviation(i)/100
else
Target(i)-= Deviation(i)
end-if
if(i<NGOALS) then
goal(i):= goal(i) >= Target(i) ! Turn goal into a constraint
else
goal(i).type:=CT_GEQ ! Only for printout
end-if
end-if
end-do
"min": do
minimize(goal(i)) ! Optimize the next goal
if(getprobstat<>XPRS_OPT) then
writeln("Cannot satisfy goal ",i)
break
else
Target(i):=getobjval
if (Type(i)="perc") then
Target(i)+= abs(Target(i))*Deviation(i)/100
else
Target(i)+= Deviation(i)
end-if
if(i<NGOALS) then
goal(i):= goal(i) <= Target(i) ! Turn goal into a constraint
else
goal(i).type:=CT_LEQ ! Only for printout
end-if
end-if
end-do
else writeln("Unknown objective sense")
break
end-case
writeln(" Solution(", i,"): x: ", x.sol, ", y: ", y.sol)
end-do
! Some declarations for a nice printout
declarations
STypes={CT_GEQ, CT_LEQ}
ATypes: array(STypes) of string
end-declarations
ATypes::([CT_GEQ, CT_LEQ])[">=", "<="]
! Solution printout
writeln(" Goal", strfmt("Target",15), strfmt("Value",12))
forall(g in 1..i) do
write(strfmt(g,5), strfmt(ATypes(goal(g).type), 3),
strfmt(Target(g), 12,6))
if(g=NGOALS) then
writeln(strfmt(getobjval, 12,6))
else
writeln(strfmt(goal(g).act+goal(g).coeff+Target(g) , 12,6))
end-if
end-do
end-procedure
end-model
|
© 2001-2020 Fair Isaac Corporation. All rights reserved. This documentation is the property of Fair Isaac Corporation (“FICO”). Receipt or possession of this documentation does not convey rights to disclose, reproduce, make derivative works, use, or allow others to use it except solely for internal evaluation purposes to determine whether to purchase a license to the software described in this documentation, or as otherwise set forth in a written software license agreement between you and FICO (or a FICO affiliate). Use of this documentation and the software described in it must conform strictly to the foregoing permitted uses, and no other use is permitted.