A modified imperialist competitive algorithm for solving nonlinear programming problems subject to mixed fuzzy relation equations

The mixed fuzzy relation programming with a nonlinear objective function and two operators of max-product and max-min composition is studied in this paper. Its feasible domain structure is investigated and some simplification procedures are presented to reduce the dimension of the original problem. We intend to modify the assimilation and revolution operators of the imperialist competitive algorithm in order to prevent the generation of infeasible solutions. The modified imperialist competitive algorithm (MICA) is compared with a real-value genetic algorithm to solve the original problem. Several test problems are presented to compare its performance with respect to the performance of the genetic algorithm. Their results show the superiority of the proposed algorithm over the genetic algorithm.