Hassan Dana Mazraeh - School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
Ali Abbasi Molai - School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran

This paper studies the nonlinear optimization problems subject to bipolar max-min fuzzy relation equation constraints. The feasible solution set of the problems is non-convex, in a general case. Therefore, conventional nonlinear optimization methods cannot be ideal for resolution of such problems. Hence, a Genetic Algorithm (GA) is proposed to find their optimal solution. This algorithm uses the structure of the feasible domain of the problems and lower and upper bound of the feasible solution set to choose the initial population. The GA employs two different crossover operations: ۱- N-points crossover and ۲- Arithmetic crossover. We run the GA with two crossover operations for some test problems and compare their results and performance to each other. Also, their results are compared with the results of other authors' works.

Bipolar fuzzy relation equations, Max-min composition, Nonlinear optimization, Genetic Algorithm