Randomized methods for the number partitioning problem
Computers and Operations Research
Easily searched encodings for number partitioning
Journal of Optimization Theory and Applications
Computers and Operations Research
A complete anytime algorithm for number partitioning
Artificial Intelligence
Computing Partitions with Applications to the Knapsack Problem
Journal of the ACM (JACM)
Tabu Search
An Electromagnetism-like Mechanism for Global Optimization
Journal of Global Optimization
Integer linear programming model for multidimensional two-way number partitioning problem
Computers & Mathematics with Applications
Applying electromagnetism-like mechanism for feature selection
Information Sciences: an International Journal
Expert Systems with Applications: An International Journal
Computers and Operations Research
Variable neighborhood descent with iterated local search for routing and wavelength assignment
Computers and Operations Research
Gaussian variable neighborhood search for continuous optimization
Computers and Operations Research
Variable neighborhood search for the Vertex Separation Problem
Computers and Operations Research
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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.