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.

The hybrid flow shop scheduling problem (HFSP) is an extension of the classic flow shop scheduling problem and widely exists in real industrial production systems. In real production, sequence-dependent setup times (SDST) are very important and cannot be neglected. Therefore, this study focuses HFSP with SDST (HFSP-SDST) to minimize the makespan. To solve this problem, a mixed-integer linear programming (MILP) model to obtain the optimal solutions for small-scale instances is proposed. Given the NP-hard characteristics of HFSP-SDST, an improved artificial bee colony (IABC) algorithm is developed to efficiently solve large-sized instances. In IABC, permutation encoding is used and a hybrid representation that combines forward decoding and backward decoding methods is designed. To search for the solution space that is not included in the encoding and decoding, a problem-specific local search strategy is developed to enlarge the solution space. Experiments are conducted to evaluate the effectiveness of the MILP model and IABC. The results indicate that the proposed MILP model can find the optimal solutions for small-scale instances. The proposed IABC performs much better than the existing algorithms and improves 61 current best solutions of benchmark instances.

This paper addresses the permutation flowshop scheduling problem with peak power consumption constraints (PFSPP). The real-time power consumption of the PFSPP cannot exceed a given peak power at any time. First, a mathematical model is established to describe the concerned problem. The sequence of operations is taken as a solution and the characteristics of solutions are analyzed. Based on the problem characteristics, eight heuristics are proposed, including balanced machine-job decoding method, balanced machine-job insert method, balanced job-machine insert method, balanced machine-job group insert method, balanced job-machine group insert method, greedy algorithm, beam search algorithm, and improved beam search algorithm. Similarly, the canonical artificial bee colony algorithm and iterated local search algorithm are modified based on the problem characteristics to solve the PFSPP. A large number of experiments are carried out to evaluate the performance of new proposed heuristics and metaheuristics. The results and discussion show that the proposed heuristics and metaheuristics perform well in solving the PFSPP.