Diversity-preserving quantum particle swarm optimization for the multidimensional knapsack problem

Abstract

Quantum particle swarm optimization is a population-based metaheuristic that becomes popular in recent years in the field of binary optimization. In this paper, we investigate a novel quantum particle swarm optimization algorithm, which integrates a distanced-based diversity-preserving strategy for population management and a local optimization method based on variable neighborhood descent for solution improvement. We evaluate the proposed method on the classic NP-hard 0–1 multidimensional knapsack problem. We present extensive computational results on the 270 benchmark instances commonly used in the literature to show the competitiveness of the proposed algorithm compared to several state-of-the-art algorithms. The ideas of using the diversity-preserving strategy and the probabilistic application of a local optimization procedure are of general interest and can be used to reinforce other quantum particle swarm algorithms.