Solving nonlinear optimization problems subjected to fuzzy relation equation constraints with max–average composition using a modified genetic algorithm

In this paper a nonlinear objective optimization model subject to a system of fuzzy relation equations with max–average composition are presented. When the set of solutions of fuzzy relation equations is not empty, it is in general a non-convex set and so the conventional nonlinear programming methods are not ideal for solving such a problem. In order to solve this problem, a modified genetic algorithm is reviewed and some of its components are changed to solve the problem. The construction of test problems is also developed to evaluate the performance of the proposed algorithm.