Variable Neighborhood Descent Branching applied to the Multi-Way Number Partitioning Problem

This paper presents an application of the Variable Neighborhood Descent Branching method to solve the Multi-Way Number Partitioning Problem. This problem consists of distributing the elements of a given sequence into k disjoint subsets such that the sums of each subset elements fit in the shortest interval. It shows a new method to decompose the MWNPP in n-1 subproblems using local branching constraints. This decomposing justifies the neighborhood structure used in the proposed algorithm. The study of parameter settings defines the operation of the proposed algorithm. The results shows that there is no statistically significant difference of objective value between proposed algorithm and mathematical model solved by CPLEX, but the time used by both methods are significantly different.