Genetic Algorithm Application for Permutation Flow Shop Scheduling Problems

In this paper, permutation flow shop scheduling problems (PFSS) are investigated with a genetic algorithm. PFSS problem is a special type of flow shop scheduling problem. In a PFSS problem, there are n jobs to be processed on m machines in series. Each job has to follow the same machine order and each machine must process jobs in the same job order. The most common performance criterion in the literature is the makespan for permutation scheduling problems. In this paper, a genetic algorithm is applied to minimize the makespan. Taillard's instances including 20, 50, and 100 jobs with 5, 10, and 20 machines are used to define the efficiency of the proposed GA by considering lower bounds or optimal makespan values of instances. Furthermore, a sensitivity analysis is made for the parameters of the proposed GA and the sensitivity analysis shows that crossover probability does not affect solution quality and elapsed time. Supplementary to the parameter tuning of the proposed GA, we compare our GA with an existing GA in the literature for PFSS problems and our experimental study reveals that our proposed and well-tuned GA outperforms the existing GA for PFSS problems when the objective is to minimize the makespan.