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Multiobjective Integer Linear Programming Problems -- Originals Taken from moolibrary

Originals are taken from moolibrary and converted to the fgt format specified below. Note that we do NOT claim to have created these instances, we have only converted them to another format.

Test instances

Instances are named Kirlik14_ILP_p-[p]_n-[n]_m-[m]_inst-[id].raw where

  • p is the number of objectives.
  • n is the size of the problem.
  • m is the number of constraints.
  • id: Instance id running within the constraint id.

Fgt format description

All instance files are given in raw format (a text file). An example is:

10 5 4

maxsum maxsum maxsum maxsum 

-10 -100 36 -48 60 16 69 62 20 19
71 86 21 97 34 -8 88 -3 76 67
64 -36 5 6 67 85 76 1 -67 -95
87 -8 92 -3 40 3 48 37 94 80

31 2 66 59 2 64 0 71 64 45
81 36 26 79 55 72 35 41 73 31
94 7 32 45 68 57 21 87 0 19
90 100 99 35 30 -52 99 88 26 7
0 54 51 54 0 27 48 83 -17 44

1 394
1 419
1 341
1 492
1 295

0 0 0 0 0 0 0 0 0 0 
100 100 100 100 100 100 100 100 100 100

The general format is defined as:

n m p

objectiveTypes

objectiveCoefficientMatrix

constraintMatrix

rHSMatrix

lbVector
ubVector

where:

  • n is the number of variables.
  • m is the number of constrains.
  • p is the number of objectives.
  • objectiveTypes is the nature of the objectives to be optimized. An identifier should be added for each objective, and it should be done in the same order as in the objective matrix. Four types are supported:
    • maxsum: maximise a sum objective function
    • minsum: minimise a sum objective function
  • objectiveCoefficientMatrix is a p x n matrix defining the coefficients of the objective functions
  • constraintMatrix is a m x n matrix defining the coefficients of the constraints
  • rHSMatrix is a m x 2 matrix defining the right-hand side of the constraints. For each constraint, two numbers are required:
    • The second number is the actual value of the right-hand side of the constraint
    • The first number is an identifier that is used to define the sign of the constraint. Three identifiers can be used: 0 for >= constraints, 1 for <= constraints and 2 for = constraints.
  • lbVector is a vector of size n containing the lower bound of each variable.
  • ubVector is a vector of size n containing the upper bound of each variable.