Model and method based on GA for nonlinear programming problems with fuzzy objective and resources

As the extension of our previous paper for solving nonlinear programming problems, this paper focuses on a symmetric model for a kind of fuzzy nonlinear programming problems (FO/RNP) by way of a special Genetic Algorithm (GA) with mutation along the weighted gradient direction. It uses an r-power type of membership function to formulate a kind of fuzzy objective and two kinds of fuzzy resource constraints which are commonly used in actual production problems. The solution to FO/RNP may be transformed into the solution to three kinds of model according to different kinds of criteria preferred by the decision maker (DM). This paper develops an inexact approach to solve this type of model of nonlinear programming problems. Instead of finding an exact optimal solution, this approach uses a 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 preferred by the (DM) under different criteria can be achieved. The overall procedure for FO/RNP is also developed in this paper, it may supply a preliminary framework for practical application of the FO/RNP model.