A discrete artificial bee colony algorithm for distributed hybrid flowshop scheduling problem with sequence-dependent setup times

With the development of global and decentralised economies, distributed production emerges in large manufacturing firms. A distributed production model exists with hybrid flowshops. As an extension of the hybrid flowshop scheduling problem (HFSP), the distributed hybrid flowshop scheduling problem (DHFSP) with sequence dependent setup times (SDST) is a new challenging project. The DHFSP involves three sub-problems: the first one is to allocate a factory for each job; the second one is to determine job sequence in each factory; the third one is to allocate a machine for each job at each stage. This paper presents a machine position-based mathematical model and a discrete artificial bee colony algorithm (DABC) for the DHFSP-SDST to optimise the makespan. The proposed DABC employs a two-level encoding to ensure an initiative scheduling. Decoding method combines with the earliest available machine and earliest completion time rule for feasible schedules. The proposed DABC also employ effective solutions update techniques: the hybrid neighbourhood operators, and many times of Critical Factory Swap to enhance exploitation. 780 benchmarks in total are generated. Extensive experiments are carried out to test the performance of the DABC. Computational results and statistical analyses validate that the DABC outperforms the best performing algorithm in the literature.