FICO Xpress Optimization Examples Repository: Robust formulations of the single knapsack problem

FICO Xpress Optimization Examples Repository

Robust formulations of the single knapsack problem

Description

Introductory example from the whitepaper 'Robust Optimization with Xpress'. Alternative robust formulations of a small single knapsack problem:

deterministic version: knapsack_basic.mos
ellipsoidal uncertainty: knapsack_ellipsoid.mos
polyhedral uncertainty: knapsack_polyhedron.mos
historical data used as uncertainty scenario: knapsack_scenario.mos
simple bounded uncertains: knapsack_simplebounds.mos, knapsack_simplebounds_direct.mos

Further explanation of this example: Whitepaper 'Robust Optimization with Xpress', Section 1 Introduction

robknapsack.zip

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Source Files

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knapsack_basic.mos	[download]
knapsack_ellipsoid.mos	[download]
knapsack_polyhedron.mos	[download]
knapsack_scenario.mos	[download]
knapsack_simplebounds.mos	[download]
knapsack_simplebounds_direct.mos	[download]

knapsack_basic.mos

(!******************************************************
   Mosel Example Problems
   ======================   

   Example model for the 
   Robust Optimization with Xpress white paper

   (c) 2014 Fair Isaac Corporation
       
*******************************************************!)
model Knapsack
 uses "mmrobust"                                 ! Load the robust library

 parameters
  NUM=5                                          ! Number of items
  MAXVAL=100                                     ! Maximum value
  MAXWEIGHT=80                                   ! Maximum weight
  WTMAX=102                                      ! Max weight allowed for haul
 end-parameters

 declarations
  Items=1..NUM                                   ! Index range for items
  VALUE: array(Items) of real                    ! Value of items
  WEIGHT: array(Items) of real                   ! Weight of items
  x: array(Items) of mpvar                       ! Decision variables
 end-declarations
 
 setrandseed(5);
 forall(i in Items) do
  VALUE(i):=50+random*MAXVAL
  WEIGHT(i):=1+random*MAXWEIGHT
 end-do
 forall(i in Items) x(i) is_binary               ! All x are 0/1

 MaxVal:= sum(i in Items) VALUE(i)*x(i)          ! Objective: maximize total value
 WtMax:= sum(i in Items) WEIGHT(i)*x(i) <= WTMAX ! Weight restriction

 maximize(MaxVal)

 writeln("Solution:\n Objective: ", getobjval)
 writeln("Item  Weight  Value")
 forall(i in Items)
   writeln(i, ": ", getsol(x(i)), strfmt(WEIGHT(i),8,2), strfmt(VALUE(i),8,2))

end-model