Bi-objective parallel machines scheduling with sequence-dependent setup times using hybrid metaheuristics and weighted min-max technique

In the literature of multi-objective problem, there are different algorithms to solve different optimization problems. This paper presents a min-max multi-objective procedure for a dual-objective, namely make span, and sum of the earliness and tardiness of jobs in due window machine scheduling problems, simultaneously. In formulation of min-max method when this method is combined with the weighting method, the decision maker can have the flexibility of mixed use of weights and distance parameter to yield a set of Pareto-efficient solutions. This research extends the new hybrid metaheuristic (HMH) to solve parallel machines scheduling problems with sequence-dependent setup time that comprises three components: an initial population generation method based on an ant colony optimization (ACO), a simulated annealing (SA) as an evolutionary algorithm employs certain probability to avoid becoming trapped in a local optimum, and a variable neighborhood search (VNS) which involves three local search procedures to improve the population. In addition, two VNS-based HMHs, which are a combination of two methods, SA/VNS and ACO/VNS, are also proposed to solve the addressed scheduling problems. A design of experiments approach is employed to calibrate the parameters. The non-dominated sets obtained from HMH and two best existing bi-criteria scheduling algorithms are compared in terms of various indices and the computational results show that the proposed algorithm is capable of producing a number of high-quality Pareto optimal scheduling plans. Aside, an extensive computational experience is carried out to analyze the different parameters of the algorithm.