Metaheuristics optimization approaches for two-stage reentrant flexible flow shop with blocking constraint

• This problem is formed as FFS|2-stage,rcrc,block|Cmax.
• First report consideration both reentrant and blocking constraints.
• The proposed HGA and HPSO algorithms are very efficient.

This paper addresses a problem of the two-stage reentrant flexible flow shop (RFFS) with blocking constraint (FFS|2-stage,rcrc,block|Cmax). The objective is to find the optimal sequences in order to minimize the makespan. In this study, the hybridization of GA (HGA: hybrid genetic algorithm) with adaptive auto-tuning based on fuzzy logic controller and the hybridization of PSO (HPSO: hybrid particle swarm optimization) with Cauchy distribution were developed to solve the problem. The encoding and decoding routines that appropriate for blocking constraint and Relax-Blocking algorithm for improving chromosome and particle were suggested. Experimental results reveal that the HPSO and HGA algorithms give better solutions than the classical metaheuristics, GA and PSO, for all test problems respectively. Additionally, the relative improvement (RI) of the makespan solutions obtained by the proposed algorithms with respect to those of the current practice is performed in order to measure the quality of the makespan solutions generated by the proposed algorithms. The RI results show that the HGA and HPSO algorithms can improve the makespan solution by averages of 15.51% and 15.60%, respectively. We found that the performance of the HGA is not significantly competitive as compared to the HPSO but its computational times are significantly higher than those of the HPSO.