Dynamical Artificial Bee Colony for Energy-Efficient Unrelated Parallel Machine Scheduling with Additional Resources and Maintenance

Unrelated parallel machine scheduling problem (UPMSP) is a typical scheduling one and UPMSP with various real- life constraints such as additional resources has been widely studied; however, UPMSP with additional resources, maintenance, and energy-related objectives is seldom investigated. The Artificial Bee Colony (ABC) algorithm has been successfully applied to various production scheduling problems and demonstrates potential search advantages in solving UPMSP with additional resources, among other factors. In this study, an energy-efficient UPMSP with additional resources and maintenance is considered. A dynamical artificial bee colony (DABC) algorithm is presented to minimize makespan and total energy consumption simultaneously. Three heuristics are applied to produce the initial population. Employed bee swarm and onlooker bee swarm are constructed. Computing resources are shifted from the dominated solutions to non-dominated solutions in each swarm when the given condition is met. Dynamical employed bee phase is implemented by computing resource shifting and solution migration. Computing resource shifting and feedback are used to construct dynamical onlooker bee phase. Computational experiments are conducted on 300 instances from the literature and three comparative algorithms and ABC are compared after parameter settings of all algorithms are given. The computational results demonstrate that the new strategies of DABC are effective and that DABC has promising advantages in solving the considered UPMSP.