A Variable Neighborhood Search Approach for Solving the Multidimensional Multi-Way Number Partitioning Problem

This paper presents an implementation of the Variable Neighborhood Search (VNS) metaheuristic for solving the optimization version of the Multidimensional Multi-Way Number Partitioning Problem (MDMWNPP). This problem consists in distributing the vectors of a given sequence into k disjoint subsets such that the sums of each subset form a set of vectors with minimum diameter. The proposed VNS for solving MDMWNPP has a good performance over instances with three and four subsets. A comparative study of results found from this proposed VNS and an implementation of Memetic Algorithm (MA) is carried out, running in the same proportional time interval. Although the average results are different, the statistical tests show that results of the proposed VNS are not significantly better than MA in a set of instances analyzed.

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