COEVOLUTIONARY GENETIC ALGORITHMS FOR NONCONVEX NONLINEAR PROGRAMMING PROBLEMS: REVISED GENOCOP III

Abstract

In this paper, we focus on general nonconvex nonlinear programming problems and consider an applicability of genetic algorithms. For such problems, Michalewicz et al. 1995 recently proposed the coevolutionary genetic algorithm, called GENOCOP III, by introducing the concepts of search points and reference points which, respectively, satisfy the linear constraints and all of the constraints. Unfortunately, however, in GENOCOP III, since an initial population is randomly generated, it is quite difficult to generate reference points. Furthermore, a new search point is randomly generated on the line segment between a search point and a reference point and effectiveness and speed of search may be quite low. Realizing such difficulties, in this paper we propose the revised GENOCOP III by introducing a method for generating a reference point by minimizing the sum of squares of violated nonlinear constraints and a bisection method for generating a new search point on the line segment between a search point and a reference point. Through a lot of numerical experiments, both feasibility and effectiveness of the proposed method are demonstrated.