An efficient bi-objective heuristic for scheduling of hybrid flow shops

Abstract

This paper considers the problem of scheduling n independent jobs in hybrid flow shop environment with sequence-dependent setup times to minimize the makespan and total tardiness. For the optimization problem, an algorithm namely; bi-objective heuristic (BOH) is proposed for searching Pareto-optimal frontier. The aim of the proposed algorithm is to generate a good approximation of the set of efficient solutions. The BOH procedure initiates by generating a seed sequence. Since the output results are strongly dependent on the initial solution and in order to increase the quality of output results algorithm, we have considered how the generation of seed sequence with random way and particular sequencing rules. Two methods named Euclidean distance and percent error have been proposed to compare non-dominated solution sets obtain of each seed sequence. It is perceived from these methods that the generation of seed sequence using earliest due date rule is more effective. Then, the performance of the proposed BOH is compared with a simulated annealing proposed in the literature and a VNS heuristic on a set of test problems. The data envelopment analysis is used to evaluate the performance of approximation methods. From the results obtained, it can be seen that the proposed algorithm is efficient and effective.