Bi-Objective, Dynamic, Multiprocessor Open-Shop Scheduling: A Hybrid Scatter Search–Tabu Search Approach

This paper presents a novel, multi-objective scatter search algorithm (MOSS) for a bi-objective, dynamic, multiprocessor open-shop scheduling problem (Bi-DMOSP). The considered objectives are the minimization of the maximum completion time (makespan) and the minimization of the mean weighted flow time. Both are particularly important for improving machines’ utilization and customer satisfaction level in maintenance and healthcare diagnostic systems, in which the studied Bi-DMOSP is mostly encountered. Since the studied problem is NP-hard for both objectives, fast algorithms are needed to fulfill the requirements of real-life circumstances. Previous attempts have included the development of an exact algorithm and two metaheuristic approaches based on the non-dominated sorting genetic algorithm (NSGA-II) and the multi-objective gray wolf optimizer (MOGWO). The exact algorithm is limited to small-sized instances; meanwhile, NSGA-II was found to produce better results compared to MOGWO in both small- and large-sized test instances. The proposed MOSS in this paper attempts to provide more efficient non-dominated solutions for the studied Bi-DMOSP. This is achievable via its hybridization with a novel, bi-objective tabu search approach that utilizes a set of efficient neighborhood search functions. Parameter tuning experiments are conducted first using a subset of small-sized benchmark instances for which the optimal Pareto front solutions are known. Then, detailed computational experiments on small- and large-sized instances are conducted. Comparisons with the previously developed NSGA-II metaheuristic demonstrate the superiority of the proposed MOSS approach for small-sized instances. For large-sized instances, it proves its capability of producing competitive results for instances with low and medium density.