Authors: Kratica, Jozef 
Kojić, Jelena
Savić, Aleksandar
Title: Two metaheuristic approaches for solving multidimensional two-way number partitioning problem
Journal: Computers and Operations Research
Volume: 46
First page: 59
Last page: 68
Issue Date: 1-Jun-2014
Rank: M21
ISSN: 0305-0548
DOI: 10.1016/j.cor.2014.01.003
Abstract: 
In this paper, we address two metaheuristic approaches, a Variable Neighborhood Search (VNS) and an Electromagnetism-like metaheuristic (EM), on an NP-hard optimization problem: Multi-dimensional Two-way Number Partitioning Problem (MDTWNPP). MDTWNPP is a generalization of a Two-way Number Partitioning Problem (TWNPP), where a set of vectors is partitioned rather than a set of numbers. The simple k-swap neighborhoods allow an effective shaking procedure in the VNS search. The attraction-repulsion mechanism of EM is extended with a scaling procedure, which additionally moves EM points closer to local optima. Both VNS and EM use the same local search procedure based on 1-swap improvements. Computational results were obtained on 210 standard instances. Direct comparison with results from the literature confirm the significance of applying these methods to MDTWNPP.
Keywords: Combinatorial optimization | Metaheuristics | Number partitioning
Publisher: Elsevier
Project: Mathematical Modelas and Optimization Methods on Large-Scale Systems 
Graph theory and mathematical programming with applications in chemistry and computer science 

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