Orthogonal simulated annealing for multiobjective optimization

Abstract The paper proposes a new simulated annealing (SA) based multiobjective optimization algorithm, called orthogonal simulated annealing (OSA) algorithm in this work. The OSA algorithm incorporates an orthogonal experiment design (OED) with a simulated annealing based multiobjective algorithm aiming to provide an efficient multiobjective algorithm. OED involves several experiments based on an orthogonal table and a fractional factorial analysis to extract intelligently the best combination of decision vectors making the classical SA to explore search space effectively, to enhance convergence, and to improve quality of solutions in the Pareto set. These benefits have been tested by comparing the performance of OSA with one state-of-the-art multiobjective evolutionary algorithm (NSGA2) and one classical simulated annealing based multiobjective algorithm (CMOSA) considering multiobjective problems of varying degrees of complexity. The obtained Pareto sets by these three algorithms have been tested using standard methods like measure C, hypervolume comparison, etc. Simulation results show that the performance of and CPU time required by these algorithms are problem dependent, and with some problems, the OSA algorithm outperforms the other two algorithms. In particular, the comparison between OSA and CMOSA suggests that around 70% times OSA outperforms CMOSA and obtains a well diversified set of solutions. In addition, with some problems, OSA captures the Pareto fronts where CMOSA fails. Therefore, the development of OSA is noteworthy, and it provides an additional tool to solve multiobjective optimization problems.