Improved multi-objective artificial bee colony algorithm for parallel machine lot-streaming scheduling problem with limited and unequal sub-lots

Job splitting is a full-time effective measure used to improve corporate competitiveness, especially when the lot size of jobs is considerably large. This work investigates a parallel machine lot-streaming scheduling problem, where unequal sub-lot is considered and the number of sub-lots is strictly limited by that of cutters. Focus on this problem, a mixed-integer linear programming model is formulated to minimize makespan and due time deviation simultaneously, to scrutinize the coupling relationship among decision variables, i.e., the number and size of sub-lots, the machine allocation, and the processing order of all sub-lots. Then, an improved multi-objective artificial bee colony algorithm (IMOABC) with two categories of improvements is developed to obtain high-quality Pareto front solutions. Specifically, a semi-random initialization is proposed to balance the workload as evenly as possible, which includes a half-normal distribution strategy for determining the number of utilized sub-lots, an equal-probability lot-splitting strategy for determining the size of each sub-lots, and a machine allocation strategy to synchronize the completion time of all machines. Besides, a multipoint preservative crossover is designed to enhance diversity in the employed bee phase, a sub-lot adjustment operator is proposed to implement objective-oriented local search in the onlooker bee phase, and an individual restart mechanism is adopted to avoid being trapped in local optimum in the scout bee phase. Extensive experiment results demonstrate that IMOABC significantly outperforms the other six state-of-the-art algorithms in terms of diversity and convergence.