PSFGA: A Parallel Genetic Algorithm for Multiobjective Optimization Francisco de Toro University of Huelva (Spain) ftoro@uhu.es Julio Ortega; Javier Fernández, Antonio Díaz University of Granada (Spain) {julio,javier,afdiaz}@atc.ugr.es Abstract This paper presents the Parallel Single Front Genetic Algorithm (PSFGA), a parallel Pareto-based algorithm for multiobjective optimization problems based on an evolutionary procedure. In this procedure, a population of solutions is sorted with respect to the values of the objective functions and partitioned into subpopulations which are distributed among the processors. Each processor applies a sequential multiobjective genetic algorithm that we have devised (called Single Front Genetic Algorithm, SFGA) to its subpopulation. Experimental results are provided comparing PSFGA with previously proposed multiobjective evolutionary algorithms. 1. Introduction Most real-world engineering optimization problems are multiobjective in nature, since they normally have several (usually conflicting) objectives that must be satisfied at the same time. These problems are known as MOP (Multiobjective Optimization Problems) [Coello98] in contrast with SOP (Single-objective optimization problems). The notion of optimum has to be re-defined in this context and instead of aiming to find a single solution, a procedure for solving MOP should determine a set of good compromises or trade-off solutions, generally known as Pareto optimal solutions from which the decision maker will select one. These solutions are optimal in the wider sense that no other solution in the search space is superior when all objectives are considered. Pareto optimal solutions form the Pareto frontier in a k-dimensional objective space, where k is the number of the objectives in the optimization problem. Evolutionary Algorithms (EAs) have the potential to finding multiple Pareto optimal solutions in a single run and have been widely used in this area [Ishibuchi96] [Cunha97] [Valenzuela97] [Fonseca98b] [Parks98]. A good Multiobjective Optimization Evolutionary Algorithm (MOEA) should achieve the following goals: 1. The distance between the set of solutions found by the MOEA and the Pareto frontier should be minimized. 2. The solutions found by the MOEA should present a distribution that provides a good description of the Pareto frontier. 3. The spread of the solutions obtained should be maximized (for each objective a wide range of values should be covered by the set of solutions found). Parallel computing has been widely applied to EAs [Cantu97]. In the case of MOEAs, parallelism has been successfully applied to reduce the time needed to evaluate the objective functions in sequential EAs, but little insight has been gained into the performance of a parallel MOEA where the population is distributed among the processors. In that sense, the work of some authors i.e. [Quagliarella00] shows that sometimes there are no advantages with respect to the single population model. One of the reasons for this is that Pareto-dominance comparisons should be made considering the whole population , thus reducing the efficiency of the parallel procedure. In this paper, Section 2 introduces the MOPs, while Section 3 and Section 4 present some ideass about the application of evolutionary techniques, and their corresponding parallel strategies previously proposed for MOPs. Section 5 presents the EAs proposed in this paper to solve MOPs, namely: the multiobjective evolutionary algorithms SFGA and PSFGA. Finally, experimental results and concluding remarks are summarized in Sections 6 and 7 respectively. 2. Statement of the problem A multiobjective optimization problem (MOP) can be defined [Coello98] as one of finding a vector of decision variables which satisfies a set of constraints and optimizes a vector function whose elements represent the objectives. These functions form a mathematical description of performance criteria, and are usually in conflict with each other. The problem can be formally stated as finding the vector x* = [x 1 * ,x 2 * , ... , x n * ] which satisfies the m inequality constraints g i (x) ≥ 0 i=1,2,...,m (1) the p equality constraints h i (x) = 0 i=1,2,...,p (2) and optimizes the vector function Proceedings of the 10th Euromicro Workshop on Parallel, Distributed and Network-based Processing (EUROMICRO-PDP02) 1066-6192/02 $17.00 ' 2002 IEEE