### S-metric Based Multi-Objective Fireworks Algorithm

Abstract

Fireworks Algorithm(FWA) is a recently developed swarm intelligence algorithm for single objective optimization problems which gains very promising performances in many areas. In this paper, we extend the original FWA to solve multi-objective optimization problems with the help of S-metric. The S-metric is a frequently used quality measure for solution sets comparison in evolutionary multi-objective optimization algorithms (EMOAs). Besides, S-metric can also be used to evaluate the contribution of a single solution among the solution set. Traditional multi-objective optimization algorithms usually perform a (μ + 1) strategy and update the external archive one by one, while the proposed S-metric based multi-objective fireworks algorithm(S-MOFWA) performs a (μ + μ) strategy, thus converging faster to a set of pareto solutions by three steps: 1)Exploring the solution space by mimicking the explosion of fireworks; 2)Performing a simple selection strategy for choosing the next generation of fireworks according to their S-metric; 3)Utilizing an external archive to maintain the best solution set ever found, with a new archive definition and a novel updating strategy, which can update the archive with μ solutions in a single process. The experimental results on benchmark functions suggest that the proposed S-MOFWA outperforms three other well-known algorithms, i.e. NSGA-II, SPEA2 and PESA2 in terms of the convergence measure and covered space measure.