The optimal solution for several different degrees of feasibility for fuzzy linear and non-linear programming problems

Abstract

This paper proposes a novel meta-heuristic based algorithm which provides the optimal solution for several different degrees of feasibility for fuzzy linear and nonlinear programming problems. The proposed method has got the ability for solving those problems in which all coefficients of the objective function and constraints are represented by LR fuzzy numbers with linear and/or non-linear membership function. To solve the fuzzy problems, this paper provides a new hybrid genetic algorithm accompanied by a new proposed method of simulating fuzzy coefficients which 1) eliminates the need of applying defuzzification methods and/or expected interval methods, and 2) allows dealing with different types of fuzzy numbers, properly. In order to show the performance of the proposed method, it is compared with “M. Jimenez, M. Arenas, A. Bilbao and M.V. Rodriguez, Linear programming with fuzzy parameters: An interactive method resolution, European Journal of Operational Research 177 (2007), 1599–1609.”. Computational results reveal that the proposed method is superior to the Jimenez et al. [13] method from the viewpoint of feasibility and optimality.