Application of Group Based Sorting Method to Multiple-Constrained Optimization Problems

1. Abstract The purpose of this study is to develop a practicable method for multiple-constrained optimization problems. In real-world optimization problems, the complexity of design space depends on their formulation. Thus, in order to search useful solutions within feasible computational time, the simplicity of applications is necessary for the technique of constraint satisfaction. The proposed method of this paper attempts to treat multi-constraint conditions with simple rules by sorting in the order of satisfactory degree to each constraint. In this method, a criterion to satisfy each constraint can be defined respectively. Then, solution candidates are divided into groups based on their violated constraint conditions. In a group, candidates are compared by the criterion appropriate to corresponding constraints. In addition, the relation among constraints is represented as the comparison of groups. Therefore, the optimization method can obtain practicable solutions efficiently with the simple formulation of constraint conditions. Furthermore, it is expected that the proposed technique is useful for the evaluation of multi-attributes. In this paper, by applying to Genetic Algorithm and Particle Swarm Optimization in several problems, numerical examples are presented to demonstrate the practical utility of the proposed method. 2.