An improved non-dominated sorting genetic algorithm II for distributed heterogeneous hybrid flow-shop scheduling with blocking constraints

Distributed manufacturing is a new trend to accommodate the economic globalization, which means multiple geographically-distributed factories can collaborate to meet urgent delivery requirements. However, such factories may vary due to layout adjustments and equipment aging, thus the production efficiency greatly depends on the allocation of orders. This scenario is frequently found in energy-intensive process industries, e.g., chemical and pharmaceutical and industries, where the lack of buffers usually results in extra non-blocking constraints and makes the production scheduling even harder. Therefore, this paper investigates a distributed heterogeneous hybrid blocking flow-shop scheduling problem (DHHBFSP) for minimizing the makespan and total energy consumption simultaneously, and proposes an improved non-dominated sorting genetic algorithm II (INSGA-II) to address the problem. First, two heuristic algorithms, i.e., bi-objective considered heuristic (BCH) and similarity heuristic (SH), are developed for the population initialization. Then, to speed-up the local search, a comparison method for non-dominated solutions is proposed to reserve more solutions that are likely to be further improved. Afterwards, a probabilistic model is developed to eliminate unnecessary operations during local search processes. Finally, the proposed INSGA-II is tested on benchmark instances and a real-world case for the validation. Numerical experiments suggest that the SH can generates high-quality solutions within a very short period of time, and the BCH has significantly improved average IGD and HV values for the initial population. Besides, the probabilistic model saves considerable computational time for the local search without compromising the solution quality. With the help of these strategies, the proposed INSGA-II improves average IGD and HV values by 68 % and 57 % for the basic NSGA-II respectively, and obtains better Pareto fronts compared to existing multi-objective algorithms on the majority of test instances. Moreover, the industrial case study shows that the proposed INSGA-II is capable of providing solid scheduling plans for a pharmaceutical enterprise with large-scale orders.