Multi-objective combinatorial optimization problems

Instances for the paper D. An, S. N. Parragh, M. Sinnl, and F. Tricoire, "A matheuristic for tri-objective binary integer programming", arxiv, 2021. The paper consider instances for tri-objective CFLP (Capacitated Facility Location Problems).

These instances are also used in paper N. Forget, and S. N. Parragh, "Enhancing Branch-and-Bound for Multi-Objective 0-1 Programming", arxiv.

Test instances

The instances here are in the .fgt format, i.e. they are reformated to be ran by the algorithm of N. Forget, and S. N. Parragh. They are contained in the folder instances, in the sub-folder fgt. Instances are named An22-CFLP_[I]_[J]_[id].fgt where

• I is the number of facilities.
• J is the number of customers.
• id is the instance id (10 different instances for each I and J).

All instance files are given in fgt format (a text file). An example with 5 customers and 10 customers is:

65 65 3

minsum minsum maxsum

42 65 44 61 49 66 39 82 35 47 31 23 67 18 41 69 80 12 75 32 37 25 65 20 38 63 75 17 70 31 37 29 61 23 35 19 16 80 15 58 7 34 87 35 72 76 67 43 62 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
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2 0
2 0
2 0
2 0
2 0
2 0
2 0
2 0
2 0
2 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 

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.