A Multi-objective Particle Swarm Optimizer Hybridized with Scatter Search Luis V. Santana-Quintero, Noel Ram´ ırez, and Carlos Coello Coello CINVESTAV-IPN, Electrical Engineering Department, Computer Science Area, Av. IPN No. 2508, San Pedro Zacatenco, M´ exico D.F. 07360, M´ exico lsantana@computacion.cs.cinvestav.mx, santiago@computacion.cs.cinvestav.mx, ccoello@cs.cinvestav.mx Abstract. This paper presents a new multi-objective evolutionary algo- rithm which consists of a hybrid between a particle swarm optimization (PSO) approach and scatter search. The main idea of the approach is to combine the high convergence rate of the particle swarm optimization algorithm with a local search approach based on scatter search. We pro- pose a new leader selection scheme for PSO, which aims to accelerate convergence. Upon applying PSO, scatter search acts as a local search scheme, improving the spread of the nondominated solutions found so far. Thus, the hybrid constitutes an efficient multi-objective evolution- ary algorithm, which can produce reasonably good approximations of the Pareto fronts of multi-objective problems of high dimensionality, while only performing 4,000 fitness function evaluations. Our proposed ap- proach is validated using ten standard test functions commonly adopted in the specialized literature. Our results are compared with respect to a multi-objective evolutionary algorithm that is representative of the state-of-the-art in the area: the NSGA-II. 1 Introduction Most real world problems involve the simultaneous optimization of two or more (often conflicting) objectives. The solution of such problems (called “multi-objective”) is different from that of a single-objective optimization prob- lem. The main difference is that multi-objective optimization problems normally have not one but a set of solutions which are all equally good. The main aim of this work is to design a MOEA that can produce a reasonably good approxima- tion of the true Pareto front of a problem with a relatively low number of fitness function evaluations. In the past, a wide variety of evolutionary algorithms (EAs) have been used to solve multi-objective optimization problems [1]. In this paper, we propose a new hybrid multi-objective evolutionary algorithm based on par- ticle swarm optimization (PSO) and scatter search (SS). PSO is a bio-inspired optimization algorithm that was proposed by James Kennedy and Russell Eber- hart in the mid-1990s [9], and which is inspired on the choreography of a bird flock. PSO has been found to be a very successful optimization approach both in single-objective and in multi-objective problems [14,9]. In PSO, each solution A. Gelbukh and C.A. Reyes-Garcia (Eds.): MICAI 2006, LNAI 4293, pp. 294–304, 2006. c  Springer-Verlag Berlin Heidelberg 2006