New multi-objective method to solve reentrant hybrid flow shop scheduling problem

This paper focuses on the multi-objective resolution of a reentrant hybrid flow shop scheduling problem (RHFS). In our case the two objectives are: the maximization of the utilization rate of the bottleneck and the minimization of the maximum completion time. This problem is solved with a new multi-objective genetic algorithm called L-NSGA which uses the Lorenz dominance relationship. The results of L-NSGA are compared with NSGA2, SPEA2 and an exact method. A stochastic model of the system is proposed and used with a discrete event simulation module. A test protocol is applied to compare the four methods on various configurations of the problem. The comparison is established using two standard multi-objective metrics. The Lorenz dominance relationship provides a stronger selection than the Pareto dominance and gives better results than the latter. The computational tests show that L-NSGA provides better solutions than NSGA2 and SPEA2; moreover, its solutions are closer to the optimal front. The efficiency of our method is verified in an industrial field-experiment.