A diploid genetic algorithm for solving the multidimensional multi-way number partitioning problem

In this paper, we explore the Multidimensional Multi-way Number Partitioning Problem (MDMWNPP), which is a more complex version of the number partitioning problem. In MDMWNPP, we aim to partition a set of vectors into a given number of subsets, such that the sums of each subset's elements are as close to equal as possible for all vector coordinates. To address this problem, we propose a diploid genetic algorithm (DGA) that maintains population diversity and enhances the performance of genetic algorithms (GA). We also integrate an efficient local search (LS) procedure to guide the search towards promising solution regions. Our approach is compared to the classical (haploid) GA and state-of-the-art results for MDMWNPP on 96 benchmark instances from the literature. The results indicate that our method outperforms the classical GA and is highly competitive with the state-of-the-art approaches.