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Using multi-objective solving

lexgoalprog.mos: lexicographic goal programming for solving a small production planning example
  • configuration of multiple objectives via 'objconfig' constructors in list form
  • list combining 'mpvar' and 'linctr' types
  • detailed status check via XPRS_SOLVESTATUS and XPRS_SOLSTATUS
markowitzmo.mos: Markowitz portfolio optimization, multi-objective quadratic programming example
  • list combining 'nlctr' and 'linctr' types
  • display of the optimal frontier as SVG graph
multiobjknapsack.mos: Knapsack problem with two objectives
  • configuration of multiple objectives in array structure using priorities
  • multi-objective logging settings
Further explanation of this example: 'Mosel User Guide', Section 12.2 Goal Programming

Source Files
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   Mosel Example Problems

   file lexgoalprog.mos
   An example of lexicographic goal programming using the 
   Xpress multi-objective functionality

   Problem description:
   A company produces two electrical products, A and B. Both require
   two stages of production: wiring and assembly. 
   The production plan must meet several goals:
   1. A profit of $200
   2. A contractual requirement of 40 units of product B
   3. To fully utilize the available wiring department hours
   4. To avoid overtime in the assembly department

   (c) 2022 Fair Isaac Corporation
       author: S. Heipcke, June 2022
model "lexGP" 
 uses "mmxprs"

 public declarations
  ! Decision variables for the number of products to make of each type
   produceA,produceB: mpvar
  ! Deviational variables:
  ! There is a penalty for both under- and over-utilizing each department
   surfeit_wiring, deficit_wiring: mpvar
   surfeit_assembly, deficit_assembly: mpvar
  ! There is no penalty for surfeit in profit or in production of product B,
  ! only for deficits
   deficit_profit, deficit_productB: mpvar
   Goals: list of linctr or mpvar    ! or also:  list of any

 produceA is_integer; produceB is_integer

 ! **** Production constraints:
 ! Meet or exceed profit goal of $200
 ! Profit for products A and B are $7 and $6 respectively
 Profit:= 7 * produceA + 6 * produceB 
 Profit + deficit_profit >= 200
 ! Meet or exceed production goal for product B
 produceB + deficit_productB >= 40
 ! Utilize wiring department:
 ! Products A and B require 2 and 3 hours of wiring, 120 hours are available
 2 * produceA + 3 * produceB - surfeit_wiring + deficit_wiring = 120
 ! Utilize assembly department:
 ! Products A and B require 6 and 5 hours of assembly, 300 hours are available
 6 * produceA + 5 * produceB - surfeit_assembly + deficit_assembly = 300

 ! Objective configuration
 Goals:=[deficit_profit, deficit_productB, surfeit_wiring + deficit_wiring,
         surfeit_assembly + deficit_assembly]
(!  Cfg:= [objconfig("priority=4 abstol=0 reltol=0"),
         objconfig("priority=3 abstol=0 reltol=0"),
         objconfig("priority=2 abstol=0 reltol=0"),
         objconfig("priority=1 abstol=0 reltol=0")] !)
 ! Same as:
 forall(i in 1..4) Cfg+=[objconfig(5-i,1,0,0)]

 ! Uncomment this line to try out the effect of inversing priority order:
 ! forall(i in 1..4) Cfg(i).priority:=i
! setparam("XPRS_VERBOSE", true)

 ! Minimize deviations, in priority order

 ! **** Solution reporting
   SolStat,SolvStat: array(integer) of string    ! Status messages

  ["The solve has not been started.", "Optimization has been interrupted.",
   "Optimization has run into a nonrecoverable problem and failed.",
   "Search completed."] 

  ["No solution available.", "An optimal solution has been found.",
   "A solution that is not proven optimal is found.",
   "No solution exists.", "The problem is unbounded, if feasible."]

 writeln("Problem solve status: ", SolvStat(getparam("XPRS_SOLVESTATUS")), 
         " Solution status: ", SolStat(getparam("XPRS_SOLSTATUS")), 
         " Objectives solved: ", getparam("XPRS_SOLVEDOBJS"))
    getparam("XPRS_SOLVEDOBJS")=4 then
   writeln('Production plan:')
   writeln('Product A: ', produceA.sol, ' units')
   writeln('Product B: ', produceB.sol, ' units')
   writeln('Profit: $', Profit.sol)

   if deficit_profit.sol > 0: 
     writeln('Profit goal missed by $', deficit_profit.sol)
   if deficit_profit.sol > 0:
     writeln('Profit goal missed by $', deficit_profit.sol)
   if deficit_productB.sol > 0:
     writeln('Contractual goal for product B missed by ', deficit_productB.sol, ' units')
   if surfeit_wiring.sol > 0:
     writeln('Unused wiring department hours: ', surfeit_wiring.sol)
   if deficit_wiring.sol > 0:
     writeln('Wiring department overtime: ', deficit_wiring.sol)
   if surfeit_assembly.sol > 0:
     writeln('Unused assembly department hours: ', surfeit_assembly.sol)
   if deficit_assembly.sol > 0:
     writeln('Assembly department overtime: ', deficit_assembly.sol)
   writeln('Problem could not be solved')

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