Using Genetic Algorithm in the Multiprocessor Flow Shop to Minimize the Makespan

In this paper, we consider the k-stage multiprocessor flow shop scheduling problem. Our study aims to provide a good approximate solution to this specific problem with the makespan minimization (Cmax) as the objective function. Considering, the success of the genetic algorithms developed for scheduling problems, we apply this metaheuristic to tackle with this problem. We develop a genetic algorithm with a new crossover operator which is a combination between the SJOX crossover operator proposed by Ruiz and Maroto (2006) and the NXO crossover operator proposed by Oguz and Ercan (2005). The design of our genetic algorithm is different compared to the classical structure of the genetic algorithm especially in the encoding of solutions. For the calibration of our metaheuristic's parameters, we conduct several experimental designs. Our algorithm is tested with benchmark problems presented. The results show that the proposed genetic algorithm is an efficient approach for solving the multiprocessor flow shop problem