A hybrid genetic algorithm for non-permutation flow shop scheduling problems with unavailability constraints

This article deals with the non-permutation flow shop scheduling problems with non-availability intervals. Specifically, two kinds of unavailability constraints are investigated and the jobs are non-resumable in both cases. In the first case, the non-availability intervals are periodically fixed and known in advance. In the second case, the intervals are flexible and the machines’ continuous working time cannot exceed a maximum allowed time. Two mixed binary integer programming models are provided for deriving the optimal schedules, respectively. The problems of minimising makespan in such flow shops are proved Non-deterministic Polynomial-time hard in strong sense. Then a hybrid incremental genetic algorithm (HIGA) that combines an incremental evolution strategy framework, a local refinement and a population diversity supervision scheme is proposed to solve the large-sized problems efficiently. The numerical experiments under different problem parameters’ settings indicate that the HIGA can achieve quite satisfactory performance compared with genetic algorithm and a constructive heuristic based on Nawaz, Enscore, Ham.