A hybrid genetic algorithm for the hybrid flow shop scheduling problem with machine blocking and sequence-dependent setup times

This study contributes to the hybrid flow shop due to a lack of consideration of characteristics existing in real-world problems. Prior studies are neglecting identical machines, explicit and sequence-dependent setup times, and machine blocking. We propose a hybrid genetic algorithm to solve the problem. Furthermore, we also propose a mixed-integer linear programming formulation. We note a predominance of the mathematical model for small instances, with five jobs and three machines because of how fast there is convergence. The objective function adopted is to minimize the makespan, and relative deviation is used as a performance criterion. Our proposal incorporates two metaheuristics in this process: a genetic algorithm to generate sequences (the flow shop subproblem) and a GRASP to allocate the jobs in the machines (the parallel machines subproblem). The extensive computational experience carried out shows that the proposed hybrid genetic algorithm is a promising procedure to solve large-sized instances.