System Reliability Optimization with Fuzzy Goals Using Genetic Algorithm

Abstract

Goal programming is one of the powerful methods for multiobjective decision making and is one of the excellent models for multiobjective decision making problem in many real-world problems. But in real-world problems such as the optimal design problems of system reliability, these problems are formulated by mixed integer programming model with nonlinear objective functions, real variables, and integer variables. There are many cases that the goal establishment of these objectives is difficult and imprecise. In this paper, we attempt to apply genetic algorithms, which have received a great deal of attention about their ability as optimization techniques for combinatorial problems and have been used to solve multiobjective decision making problems, to the reliability optimization problem formulated by fuzzy nonlinear mixed integer programming problem. Nonlinear mixed integer programming problem having fuzziness is difficult to solve directly. Fuzzy nonlinear mixed integer programming problem with multiple objectives is harder to manipulate. Therefore we employ the fuzzy goal programming technique to transform the system reliability optimization problem depicted by the fuzzy nonlinear mixed integer programming problem into the nonlinear mixed integer programming problem. We use the genetic algorithm to slove the nonlinear mixed integer programming problem without any transformation for nonlinear problem into a linear model or other methods. Also, we introduce the steepest descent method in order to make the proposed genetic algorithm better. Finally, we try to get some numerical experiments which have multiobjective, and imprecise nonlinear mixed integer information, using fuzzy goal programming and genetic algorithm.