Abstract:To address the energy-efficient hybrid flow shop scheduling problem that incorporates sequence-dependent setup time and transportation time constraints, a multi-population discrete artificial bee colony (MPDABC) algorithm is introduced. First, a two-layer encoding strategy is employed to represent a feasible scheduling solution, encompassing job sequencing and machine speed. During decoding, traditional rules are refined to accommodate time constraints arising from machine setup and job transportation. Next, a tournament mechanism partitions the population into multiple subpopulations. Four neighborhood structures are designed to facilitate detailed searches within each subpopulation during the employed bee phase. In the onlooker bee phase, individuals from each subpopulation select subsequent targets based on interaction factors, fostering inter-subpopulation information exchange. To prevent the algorithm from getting trapped in local optima during the scout bee phase, a simulated annealing mechanism is applied. Finally, the MPDABC is evaluated through simulation experiments alongside three other multi-objective algorithms on 24 instances. Comparison results demonstrate the superior search performance and effectiveness of the proposed MPDABC.