Pareto-based continuous evolutionary algorithms for multiobjective optimization

In an attempt to solve multiobjective optimization problems, many traditional methods scalarize an objective vector into a single objective by a weight vector. In these cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands a user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. In this paper, Pareto-based Continuous Evolutionary Algorithms for Multiobjective Optimization problems having continuous search space are introduced. These algorithms are based on Continuous Evolutionary Algorithms, which were developed by the authors to solve single-objective optimization problems with a continuous function and continuous search space efficiently. For multiobjective optimization, a progressive reproduction operator and a niche-formation method for fitness sharing and a storing process for elitism are implemented in the algorithm. The operator and the niche formulation allow the solution set to be distributed widely over the Paretooptimal tradeoff surface. Finally, the validity of this method has been demonstrated through some numerical examples.