A Study on Stepwise Satisfaction Method of Constraints using Dividing Constraints

Abstract

Due to significant improvements in the performance of computers, Genetic Algorithms are actively applied to actual engineering problems. Most engineering problems are constrained optimization problems that are used to optimize objective functions under many constraints. The penalty method is well-known solution to such constrained optimization problems. However, the benchmarks of constrained optimization problems have only a small number of constraints. Thus, the effectiveness of the penalty method has not been investigated in numerous constrained problems. In many constrained optimization problems, penalty method has a risk whereby all constraints cannot be satisfied. This paper proposes the stepwise satisfaction method of constraints to satisfy conditions that involve many constraints. In the proposed method, the priority of constraints to be satisfied is defined based on the initial population and the objective functions are optimized after the satisfaction of all constraints. Furthermore, this paper studies the effects of classifying constraints into difficult and easy ones as well as combining the proposed method with the penalty method. In the experiment, the performance of the proposed method and the penalty method was compared in two problems with more than 50 constraints.