Solving a new multi-objective hybrid flexible flowshop problem with limited waiting times and machine-sequence-dependent set-up time constraints

This paper develops a new multi-objective hybrid flexible flowshop problem with some useful constraints including of the limited waiting times (LWT) between every two successive operations, unrelated parallel machines at least one stage, sequence- and machine-dependent set-up times and due dates of jobs. A mathematical model for this problem as a mixed-integer programming is provided to simultaneously minimise the total weighted tardiness and maximum completion times. We applied two metaheuristic methods based on the Pareto approach, multi-objective Particle swarm optimisation and strength Pareto evolutionary algorithm II, to solve our problem and achieve the non-dominated Pareto frontier. To assess the performances of the presented algorithms and compare their results, a set of test problems in small and large sizes are created and then executed on the algorithms. Owing to the sensitivity of the values of parameters in the metaheuristic algorithms, a response surface methodology (RSM) as a strength statistical tool adjusts the parameters of both algorithms separately for small- and large-sized problems. The computational evaluation demonstrated that multi-objective Particle swarm optimisation is an effective and appropriate algorithm for our investigated problem.