MULTIOBJECTIVE OPTIMIZATION USING PARALLEL VECTOR EVALUATED PARTICLE SWARM OPTIMIZATION K.E. Parsopoulos, D.K. Tasoulis, M.N. Vrahatis Department of Mathematics, University of Patras Artificial Intelligence Research Center (UPAIRC), University of Patras, GR–26110 Patras, Greece email: kostasp, dtas, vrahatis @math.upatras.gr ABSTRACT This paper studies a parallel version of the Vector Eval- uated Particle Swarm Optimization (VEPSO) method for multiobjective problems. Experiments on well known and widely used test problems are performed, aiming at inves- tigating both the efficiency of VEPSO as well as the advan- tages of the parallel implementation. The obtained results are compared with the corresponding results of the Vector Evaluated Genetic Algorithm approach, yielding the supe- riority of VEPSO. KEY WORDS Particle Swarm Optimization, Multiobjective Optimiza- tion, PVM 1 Introduction Multiobjective optimization (MO) problems consist of sev- eral objectives that need to be achieved simultaneously. Such problems arise in many applications, where two or more, sometimes competing and/or incommensurable ob- jective functions have to be minimized concurrently. Due to the multicriteria nature of MO problems, the “optimal- ity” of a solution has to be redefined, giving rise to the concept of Pareto optimality. In contrast to the single– objective optimization case, MO problems are character- ized by trade–offs and, thus, a multitude of Pareto optimal solutions. Traditional gradient–based optimization techniques can be used to detect Pareto optimal solutions. However, these techniques suffer from two critical drawbacks; (I) the objectives have to be aggregated in a single objective func- tion, and, (II) only one solution can be detected per opti- mization run. The inherent difficulty to foreknow which aggregation of the objectives is appropriate in addition to the heavy computational cost of gradient–based techniques, necessitates the development of more efficient and rigor- ous methods. Evolutionary Algorithms (EAs) seem to be particularly suited to MO problems due to their ability to synchronously search for multiple Pareto optimal solu- tions and perform better global exploration of the search space [1, 2, 3]. Moreover, EAs are easily parallelized, thus, decreasing the computational load and the required execu- tion time. The parallel computation of many solutions may also result in a better representation of the possible out- comes, enhancing the performance of the EA [4]. Particle Swarm Optimization (PSO) is a swarm in- telligence method that roughly models the social behavior of swarms [5]. PSO is characterized by its simplicity and straightforward applicability, and it has proved to be effi- cient on a plethora of problems in science and engineer- ing. Several studies have been recently performed with PSO on MO problems, and new variants of the method, which are more suitable for such problems, have been de- veloped [6, 7, 8, 9]. Vector Evaluated Particle Swarm Optimization (VEPSO) is a multi–swarm variant of PSO, which is inspired by the Vector Evaluated Genetic Algorithm (VEGA) [3, 8]. In VEPSO, each swarm is evaluated using only one of the objective functions of the problem under consideration, and the information it possesses for this objective function is communicated to the other swarms through the exchange of their best experience. In this paper, a study of the performance of VEPSO, using more than two swarms, as well as a parallel imple- mentation of this approach, is presented. The efficiency of the algorithm, as well as the advantages of the parallel im- plementation are investigated and the results are reported and compared with the corresponding results of the VEGA approach. The rest of the paper is organized as follows; in Section 2 the basic MO concepts are described, and, in Section 3, the PSO and the VEPSO algorithms are briefly presented and, also, a description of the parallel implemen- tation is provided. Experimental results are reported in Sec- tion 4, followed by conclusions in Section 5. 2 Basic Concepts of Multiobjective Opti- mization Let be an –dimensional search space and (1) be objective functions defined over . Assuming, be inequality constraints, the MO problem can be stated as finding a vector