Evolutionary multiobjective optimization for the multi-machine flow shop scheduling problem under blocking

Recently, the flow shop scheduling problem under blocking has gained broad attention in academic fields. Various papers have been devoted to investigate this issue and have been mostly restricted to the treatment of single objective at a time. Nevertheless, in practice the scheduling decisions often involve simultaneous consideration of multiple objectives (usually contradicting) to give more realistic solutions to the decision maker. In this study, we deal with a bi-objective blocking permutation flow shop scheduling problem where the makespan and total completion time are considered as objective functions. Both measures lead to an NP-hard problem. Our interest is to propose for the first time a Genetic Algorithm based on NSGA-II for searching locally Pareto-optimal frontier for the problem under consideration. The individuals in the algorithm are represented as discrete job permutations. Some specific versions of the NEH heuristic are used to generate the initial population. Non-dominated solutions and differences among parents are taken advantage of when designing the selection operator. The efficiency of the proposed algorithm, based on various metrics, is compared against the multiobjective evolutionary algorithm SPEA-II.