Multi-swarm hybrid for multi-modal optimization Antonio Bolufé Röhler Dep. Artificial Intelligence and Computer Systems University of Havana Havana, Cuba bolufe@matcom.uh.cu Stephen Chen School of Information Technology York University Toronto, Canada sychen@yorku.ca Abstract—Multi-swarm systems base their search on multiple sub-swarms instead of one standard swarm. The use of diverse sub-swarms increases performance when optimizing multi-modal functions. However, new design decisions arise when implementing multi-swarm systems such as how to select the initial positions and initial velocities, and how to coordinate the different sub-swarms. Starting from the relatively simple multi- swarm system of locust swarms, ideas from differential evolution and estimation of distribution algorithms are used to address the new design considerations that are specific to multi-swarm systems. Experiments show that the new hybrid system can perform better than each of the individual components. Keywords-particle swarm optimization; multi-swarm system; hybridization; estimation distribution algorithms; differential evolution; exploration; exploitation I. INTRODUCTION Multi-swarm systems are based on the utilization of different sub-swarms, and they provide an effective approach to address one of the main concerns of heuristic search: the balance of exploration and exploitation. In multi-swarm systems, it is possible to implement search strategies where the mechanisms for diversifying and intensifying the search can be clearly separated. This is achieved by using each sub-swarm as an intense region-focused search sub-process and a separate diversification strategy which will use a more general procedure to determine where and when to launch the sub- swarms. The development of multi-swarm systems leads to new decisions which did not exist during the original development of particle swarm optimization [1]. Some of these decisions have been previously analyzed – e.g. the number of particles to use in each sub-swarm [2], the effects of non-random initial positions and initial velocities [3], and the optimal value for the constriction factor [4]. From this previous work, several design decisions have well-established guidelines – e.g. the use of non-random initial positions and initial velocities leads to improved results in multi-swarm systems (which is not the case for standard single swarms) [4]. Other design decisions, such as which diversification strategy to use or which specific search method will be used to select the initial positions and initial velocities of a sub-swarm, have less established guidelines. Some of these decisions can be addressed by relatively independent sub-components which allow different optimization techniques to be inserted. Multi- swarm systems thus provide a useful framework for the development of hybrid algorithms. In this paper, a new hybrid multi-swarm system is presented. The new system effectively combines components from particle swarm optimization (PSO) [1], estimation distribution algorithms (EDA) [5], and differential evolution (DE) [6] into a multi-swarm hybrid. Experimental results using the Black Box Optimization Benchmark (BBOB) functions [7] show that the new system performs better than each of the individual optimization methods. The presented system is built upon locust swarms, a multi- swarm system specifically designed for multi-modal problems [8]. In locust swarms the search is guided by a “devour and move on” strategy – after a sub-swarm “devours” a relatively small region of the search space (to find a local optimum) scouts are deployed to look for new promising regions to “move on”. The scouting process (random search) and the selection of the initial velocities (directed away from the previous optima) are key components of locust swarms which the hybrid system aims to improve. Random scouting is substituted by a more methodical search technique, i.e. the Univariate Marginal Distribution Algorithm for continuous domains (UMDA) [5], which does some optimization during the scouting process. To better exploit the gradient information gathered by UMDA, difference vectors from differential evolution are used to select the initial velocities. The paper is organized as follows. In Section II, some background about particle swarm optimization and multi- swarm systems is presented. Locust swarms are introduced in Section III and UMDA in Section IV. The new UMDA-PSO hybrid is described in Section V. The benchmark functions and the computational results are presented in Section VI. An analysis of the key components of the new multi-swarm system is done in Section VII, and a comparison with a previous EDA- PSO hybrid system is performed in Section VIII. Section IX provides some discussion about the new multi-swarm system, and a summary is given in Section X. II. BACKGROUND Particle swarm optimization is based on the principles that guide the behavior of swarms in nature, such as flocks of birds and schools of fish [1]. Each particle represents a member of the swarm and describes a possible solution to the optimization problem. The particles move through the search space taking into account personal and social experience. The personal U.S. Government work not protected by U.S. copyright WCCI 2012 IEEE World Congress on Computational Intelligence June, 10-15, 2012 - Brisbane, Australia IEEE CEC 1759