Scheduling hybrid flowshops with sequence dependent setup times to minimize makespan and maximum tardiness

Abstract

This article addresses the problem of scheduling hybrid flowshops where the setup times are sequence dependent to minimize makespan and maximum tardiness. To solve such an NP-hard problem, we introduce a novel simulated annealing (SA) with a new concept, called “Migration mechanism”, and a new operator, called “Giant leap”, to bolster the competitive performance of SA through striking a compromise between the lengths of neighborhood search structures. We hybridize the SA (HSA) with a simple local search to further equip our algorithm with a new strong tool to promote the quality of final solution of our proposed SA. We employ the Taguchi method as an optimization technique to extensively tune different parameters and operators of our algorithm. Taguchi orthogonal array analysis is specifically used to pick the best parameters for the optimum design process with the least number of experiments. We established a benchmark to draw an analogy between the performance of SA with other algorithms. Two basically different objective functions, minimization of makespan and maximum tardiness, are taken into consideration to evaluate the robustness and effectiveness of the proposed HSA. Furthermore, we explore the effects of the increase in the number of jobs on the performance of our algorithm to make sure it is effective in terms of both the acceptability of the solution quality and robustness. The excellence and strength of our HSA are concluded from all the results acquired in various circumstances.