A multi-objective methodology for multi-criteria engineering design

Abstract

Optimization is more and more significant due to its application in the real engineering problems. The recently proposed imperialist competitive algorithm (ICA) is a successful method in mono-objective optimization. Nevertheless, ICA cannot handle simultaneously the conflicting objectives in multi-objective design problem. In addition, the ICA has the drawback of trapping in local optimum solutions when used for high-dimensional or complex multimodal functions. In order to deal with these situations, in this work, an improved ICA, named modified multi-objective imperialist competitive algorithm (MOMICA) is proposed. In MOMICA, an attraction and repulsion (AR) concept is implemented in the assimilation phase to improve the performances of the algorithm to reach the global optimal position. Moreover, in contrast to ICA, the proposed algorithm integrates the sorting non-dominated strategy (SND) to store the Pareto optimal solutions of multiple conflicting functions. Three performance metrics are used to evaluate the performance of the proposed algorithm: (a) convergence to the true Pareto-optimal set, (b) solutions diversity and (c) robustness, characterized by the variance over 10 runs. The results presented in this paper show that the MOMICA algorithm outperforms the other popular techniques in terms of convergence characteristics and global search ability, for both benchmark functions optimization and multi-objective engineering optimization problems.