A hybrid algorithm for the multi-stage flow shop group scheduling with sequence-dependent setup and transportation times

This study investigates the multi-stage flow shop group scheduling problem with job transportation times between machines and sequence-dependent setup times between groups. The objective is to minimize the makespan (F-m vertical bar fmls, S-plk, t(ijk), prmu vertical bar C-max). It is known that this problem is NP-hard and generalizes the typical multi-stage group scheduling problems. In this paper, a coding scheme is proposed to simultaneously determine both the sequence of jobs in each group and the sequence of groups. By reasonably combining particle swarm optimization (PSO) and genetic algorithms (GA), a fast and easily implemented hybrid algorithm (HA) is developed for solving the considered problem. The effectiveness and efficiency of the proposed HA are demonstrated and compared with those of standard PSO and GA by numerical results of various test instances with group numbers up to 20. In addition, three different lower bounds are developed to evaluate the solution quality of HA. Numerical results indicate that the proposed HA is a viable and effective approach for the studied multi-stage flow shop group scheduling problem. (C) 2015 Elsevier B.V. All rights reserved.