A Genetic Algorithm Approach for the Multidimensional Two-Way Number Partitioning Problem

This paper addresses the problem of partitioning a set of vectors into two subsets such that the sums per every coordinate should be exactly or approximately equal. This problem, introduced by Kojic [7], is called the multidimensional two-way number partitioning problem (MDTWNPP) and generalizes the classical two-way number partitioning problem. We propose an efficient genetic algorithm based heuristic for solving the multidimensional two-way number partitioning problem. The performances of our genetic algorithm have been compared with the existing numerical results obtained by CPLEX based on an integer linear programming formulation of the problem. The obtained preliminary results, in the case of medium and large instances, reveal that our proposed methodology performs very well in terms of both quality of the solutions and the computational times compared with the previous method of solving the MDTWNPP.