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As regards distributed hybrid flow shop scheduling with sequence-dependent setup times (DHFSP-SDST), three novel mixed-integer linear programming (MILP) models and a constraint programming (CP) model are formulated for the same-factory and different-factory environments. The three novel MILP models are based on two different modeling ideas. The existing MILP model and the three proposed MILP models are compared in detail from several aspects, such as binary decision variables, continuous decision variables, constraints, solution performance and solution time. By solving the benchmarks in existing studies, the effectiveness and superiority of the proposed MILP and CP models are proved. Experimental results show that the MILP model of sequence-based modeling idea performs best, the MILP model of adjacent sequence-based modeling idea takes the second place and the existing MILP model of position-based modeling idea performs worst. The CP model is more efficient and effective than MILP models. In addition, compared with the existing meta-heuristic algorithms (e.g., DABC and IABC), the proposed MILP models prove the optimal solutions of 37 instances and improve 17 current best solutions. The CP model solves all the 45 instances to optimality and improves 19 current best solutions for benchmarks in the existing studies [ABSTRACT FROM AUTHOR]

Sustainable scheduling problems have been attracted great attention from researchers. For the flow shop scheduling problems, researches mainly focus on reducing economic costs, and the energy consumption has not yet been well studied up to date especially in the blocking flow shop scheduling problem. Thus, we construct a multi-objective optimization model of the blocking flow shop scheduling problem with makespan and energy consumption criteria. Then a discrete evolutionary multi-objective optimization (DEMO) algorithm is proposed. The three contributions of DEMO are as follows. First, a variable single-objective heuristic is proposed to initialize the population. Second, the self-adaptive exploitation evolution and self-adaptive exploration evolution operators are proposed respectively to obtain high quality solutions. Third, a penalty-based boundary interstation based on the local search, called by PBI-based-local search, is designed to further improve the exploitation capability of the algorithm. Simulation results show that DEMO outperforms the three state-of-the-art algorithms with respect to hypervolume, coverage rate and distance metrics. • A multi-objective model of BFS scheduling problem with makespan and energy consumption criteria is proposed. • A variant of single-heuristic is incorporated in population initialization. • Two self-adaptive exploitation and exploration evolution strategies are proposed respectively. • A PBI-based-local search is adopted to enhance the exploitation capability of the algorithm. • It contributes to enhance the capacity of the algorithm in convergence and spread. [ABSTRACT FROM AUTHOR]