Title: A pruned Pareto set for multi-objective optimisation problems via particle swarm and simulated annealing

Authors: Ahmad Abubaker; Adam Baharum; Mahmoud Alrefaei

Addresses: School of Mathematical Sciences, University Sains Malaysia, Penang, Malaysia; Department of Mathematics and Statistics, Al Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia ' School of Mathematical Sciences, University Sains Malaysia, Penang, Malaysia ' Departments of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan

Abstract: A Pareto optimal set, which is obtained from solving multi-objective optimisation problems, usually contain a large number of optimal solutions. This situation poses a challenge for decision makers in choosing a suitable solution from a large number of overlapping and complex Pareto solutions. This paper proposes a new procedure for solving multi-objective optimisation problems by reducing the size of the Pareto set. The procedure is divided into two major stages. In the first stage, the multi-objective simulated annealing algorithm is used to solve a multi-objective optimisation problem by constructing the Pareto optimal set. In the second stage, the automatic clustering algorithm is used to prune the Pareto set. This procedure is implemented to solve two multi-objective optimisation problems, namely, the 0/1 multi-objective multi-dimensional knapsack problem and the multi-objective inventory system. The procedure enables the decision maker to select an appropriate solution efficiently.

Keywords: multi-objective problem; inventory control; simulated annealing; particle swarm optimisation; automatic clustering.

DOI: 10.1504/IJOR.2019.099544

International Journal of Operational Research, 2019 Vol.35 No.1, pp.67 - 86

Received: 06 Apr 2016
Accepted: 07 Jun 2016
Published online: 09 May 2019 *

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