Multi-objective artificial bee colony algorithm for energy-efficient scheduling of unrelated parallel batch processing machines with flexible preventive maintenance

The parallel batch-processing machine scheduling problem is widely present in industries such as manufacturing, service, and healthcare, and becomes more complex when incorporating flexible preventive maintenance (FPM). This paper presents a mixed-integer programming (MIP) model and a multi-objective artificial bee colony (MOABC) algorithm to tackle the unrelated parallel batch-processing machine scheduling problem with flexible preventive maintenance (UPBPM-FPM). The objective is to simultaneously minimize the makespan, earliness and tardiness, and total energy consumption, providing a comprehensive solution to optimize both scheduling efficiency and energy use while incorporating preventive maintenance considerations. The MOABC algorithm integrates three key innovations: (1) a novel processing power-feature information (PP-FI) heuristic to generate high-quality initial solutions, (2) a hybrid selection strategy combining the hypervolume index and roulette wheel approach to improve diversity and convergence, and (3) a set of random and goal-oriented neighborhood search methods to enhance Pareto frontier. Experimental results demonstrate that the MOABC algorithm outperforms three classical algorithms, NSGA-III, ABC, and PSO, in terms of convergence, diversity, and robustness of the Pareto solutions. This study provides a robust framework for energy-efficient scheduling in complex manufacturing environments.