University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415220180429RESOLUTION OF NONLINEAR OPTIMIZATION PROBLEMS SUBJECT TO BIPOLAR MAX-MIN FUZZY RELATION EQUATION CONSTRAINTS USING GENETIC ALGORITHM109131376210.22111/ijfs.2018.3762ENHassan DanaMazraehSchool of Mathematics and Computer Sciences, Damghan
University, Damghan, IranAli AbbasiMolaiSchool of Mathematics and Computer Sciences, Damghan University, Damghan, IranJournal Article20161208This 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: 1- N-points crossover and 2- 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.http://ijfs.usb.ac.ir/article_3762_2154eb21dc0b0710dca0c101b1419ad8.pdf