Imperialist Competitive Algorithm with Three Empires for Energy-Efficient Parallel Batch Processing Machine Scheduling with Preventive Maintenance

Batch processing machines (BPMs) are extensively present in high energy-consuming manufacturing processes such as casting, and they show some symmetries on adjacent batches and jobs within each batch. Preventive maintenance (PM) is very important for the stable running and energy saving of BPMs; however, PM in a parallel BPM shop is seldom studied. In this study, the energy-efficient parallel BPM scheduling problem with PM is considered and an imperialist competitive algorithm with three empires (TEICA) is presented to minimize makespan and total energy consumption. To obtain high-quality solutions, the number of empires is not used as a parameter and fixed at 3, a new way is applied to construct three initial empires, each of which has a new structure like two imperialists, a new assimilation is given, and an adaptive imperialist competition is implemented based on historical competition data. A number of computational experiments are conducted on 108 instances. The computational results show that the new strategies of TEICA are effective; TEICA can provide better results than all comparative methods on more than 90% instances of the considered BPM scheduling problem, and TEICA may be an effective way to solve other BPM scheduling problem.