A Novel Genetic Algorithm for a Flow Shop Scheduling Problem with Fuzzy Processing Time

Abstract

Various procedures, methods, constraints and objectives are studied in a flow shop problem during the past decades. In order to adapt the problem to the reality form, its parameters are considered as a fuzzy model. In this problem, we consider the processing time as the trapezoidal fuzzy numbers. The purpose of this problem is to find an optimum sequence in a way that the makespan or the completing time of jobs to be minimized. In order to solve this problem, in this paper, the Random-Elitist Genetic Algorithm (REGA) is presented in this regard. Observing the performance and the efficiency of this algorithm, we code it by the VBA and compare with the other results. We first test the performance of different crossover operators for our algorithm. Next, using a specific example, we examine the performance of our algorithm. The results indicated that due to very good searching; this algorithm has the good performance in finding the optimal solution and reaching the optimum solution in a very short time.