Genetic Algorithm-based Fuzzy Nonlinear Programming

Abstract

A type of model of fuzzy quadratic programming problems (FQP) is proposed. It describes the fuzzy objective and resource constraints with different types of membership functions according to different types of fuzzy objective and fuzzy resource constraints in actual production problems. An inexact approach is developed to solve this type of model of quadratic programming problems with fuzzy objective and resource constraints. Instead of finding an exact optimal solution, we use a genetic algorithm (GA) with mutation along the weighted gradient direction to find a family of solutions with acceptable membership degrees. Then by means of the human-computer interaction, the solutions are preferred by the decision maker (DM). As an extension, a non-symmetric model for a type of fuzzy nonlinear programming problem with penalty coefficients (FNLP-PC) is proposed. Based on a fuzzy optimal solution set and optimal decision set, a satisfying solution method and a crisp optimal solution method with GA for FNLP-PC are developed. Finally, the analysis of simulation results of an example in actual production problems is also given.