Optimising the bi-objective multidimensional integer knapsack problem using non-dominated sorting particle swarm optimisation

Jafar Bagherinejad and Mina Dehghani

International Journal of Industrial and Systems Engineering, 2016, vol. 23, issue 3, 263-289

Abstract: The knapsack problem (KP) and its multidimensional version are basic problems in combinatorial optimisation. In this paper, we consider the bi-objective multidimensional integer knapsack problem (BOMIKP), for which the aim is to approximate the set of non-dominated solutions using an evolutionary algorithm named non-dominated sorting particle swarm optimisation (NSPSO). The proposed methodology is based on a new variant of particle swarm optimisation (PSO) specialised in multi-objective optimisation. To aid the decision maker choosing the best compromise solution from the Pareto front, the fuzzy-based mechanism is employed for this purpose. For ensuring the robustness of the proposed method, the computational results are compared with those obtained by non-dominated sorting genetic algorithm II (NSGA-I) and multi-objective particle swarm optimisation (MOPSO) algorithm. Results show the advantages and effectiveness of the used procedures in reporting the optimal Pareto front. In addition, the results indicate that while MOPSO is able to generate Pareto solutions in significantly less amount of time, NSPSO and NSGA-II are capable of providing better quality results and better distribution of solutions in the trade-off surface.

Keywords: integer knapsack problem; multidimensional; bi-objective optimisation; particle swarm optimisation; non-dominated sorting PSO; NSPSO; NSGA-II; MOPSO; genetic algorithms; fuzzy logic. (search for similar items in EconPapers)
Date: 2016
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