A multi-objective genetic algorithm (MOGA) for hybrid flow shop scheduling problem with assembly operation

Scheduling for a two-stage production system is one of the most common problems in production management. In this production system, a number of products are produced and each product is assembled from a set of parts. The parts are produced in the first stage that is a fabrication stage and then they are assembled in the second stage that usually is an assembly stage. In this article, the first stage assumed as a hybrid flow shop with identical parallel machines and the second stage will be an assembling work station. Two objective functions are considered that are minimizing the makespan and minimizing the sum of earliness and tardiness of products. At first, the problem is defined and its mathematical model is presented. Since the considered problem is NP-hard, the multi-objective genetic algorithm (MOGA) is used to solve this problem in two phases. In the first phase the sequence of the products assembly is determined and in the second phase, the parts of each product are scheduled to be fabricated. In each iteration of the proposed algorithm, the new population is selected based on the non-dominance rule and fitness value. To validate the performance of the proposed algorithm, in terms of solution quality and diversity level, various test problems are designed and the reliability of the proposed algorithm is compared with two prominent multi-objective genetic algorithms, i.e. WBGA, and NSGA-II. The computational results show that the performance of the proposed algorithms is good in both efficiency and effectiveness criteria. In small-sized problems, the number of non-dominance solution come out from the two algorithms N-WBGA (the proposed algorithm) and NSGA-II is approximately equal. Also, more than 90% solution of algorithms N-WBGA and NSGA-II are identical to the Pareto-optimal result. Also in medium problems, two algorithms N-WBGA and NSGA-II have approximately an equal performance and both of them are better than WBGA. But in large-sized problems, N-WBGA presents the best results in all indicators.