A Genetic Algorithm for Solving Nonlinear Optimization Problem with Max-Archimedean Bipolar Fuzzy Relation Equations

Abstract

This paper discusses a nonlinear optimization problem with the system of max-Archimedean bipolar fuzzy relation equations as constraints. Some results related to the structure of the solution set of max-Archimedean bipolar fuzzy relation equations are proved. Using these results, a genetic algorithm is proposed to solve the problem for obtaining optimal or converging solutions. The effectiveness of the algorithm is also compared with other methods found in the literature. The previous methods require conversion of the problem into 0-1 mixed integer optimization problem solvable by some nonlinear optimization solvers and thereby, the computational work may increase with the size of the problem. Some test problems are developed to evaluate the performance of the proposed algorithm.