In this study, a flexible job shop scheduling problem with time-of-use electricity price constraint is considered. The problem includes machine processing speed, setup time, idle time, and the transportation time between machines. Both maximum completion time and total electricity price are optimized simultaneously. A hybrid multi-objective optimization algorithm of estimation of distribution algorithm and deep Q-network is proposed to solve this. The processing sequence, machine assignment, and processing speed assignment are all described using a three-dimensional solution representation. Two knowledge-based initialization strategies are designed for better performance. In the estimation of distribution algorithm component, three probability matrices corresponding to solution representation are provided. In the deep Q-network component, 34 state features are selected to describe the scheduling situation, while nine knowledge-based actions are defined to refine the scheduling solution, and the reward based on the two objectives is designed. As the knowledge for initialization and optimization strategies, five properties of the considered problem are proposed. The proposed mixed integer linear programming model of the problem is validated by exact solver CPLEX. The results of the numerical testing on wide-range scale instances show that the proposed hybrid algorithm is efficient and effective at solving the integrated flexible job shop scheduling problem.

A permutation flow-shop scheduling problem (PFSP) has been studied for a long time due to its significance in real-life applications. This work proposes an improved artificial bee colony (ABC) algorithm with $Q$ -learning, named QABC, for solving it with minimizing the maximum completion time (makespan). First, the Nawaz–Enscore–Ham (NEH) heuristic is employed to initialize the population of ABC. Second, a set of problem-specific and knowledge-based neighborhood structures are designed in the employ bee phase. $Q$ -learning is employed to favorably choose the premium neighborhood structures. Next, an all-round search strategy is proposed to further enhance the quality of individuals in the onlooker bee phase. Moreover, an insert-based method is applied to avoid local optima. Finally, QABC is used to solve 151 well-known benchmark instances. Its performance is verified by comparing it with the state-of-the-art algorithms. Experimental and statistical results demonstrate its superiority over its peers in solving the concerned problems.

Flexible job shop scheduling problem (FJSP) has attracted research interests as it can significantly improve the energy, cost, and time efficiency of production. As one type of reinforcement learning, deep Q-network (DQN) has been applied to solve numerous realistic optimization problems. In this study, a DQN model is proposed to solve a multiobjective FJSP with crane transportation and setup times (FJSP-CS). Two objectives, i.e., makespan and total energy consumption, are optimized simultaneously based on weighting approach. To better reflect the problem realities, eight different crane transportation stages and three typical machine states including processing, setup, and standby are investigated. Considering the complexity of FJSP-CS, an identification rule is designed to organize the crane transportation in solution decoding. As for the DQN model, 12 state features and seven actions are designed to describe the features in the scheduling process. A novel structure is applied in the DQN topology, saving the calculation resources and improving the performance. In DQN training, double deep Q-network technique and soft target weight update strategy are used. In addition, three reported improvement strategies are adopted to enhance the solution qualities by adjusting scheduling assignments. Extensive computational tests and comparisons demonstrate the effectiveness and advantages of the proposed method in solving FJSP-CS, where the DQN can choose appropriate dispatching rules at various scheduling situations.

In this article, we propose a hybrid artificial bee colony (ABC) algorithm to solve a parallel batching distributed flow-shop problem (DFSP) with deteriorating jobs. In the considered problem, there are two stages as follows: 1) in the first stage, a DFSP is studied and 2) after the first stage has been completed, each job is transferred and assembled in the second stage, where the parallel batching constraint is investigated. In the two stages, the deteriorating job constraint is considered. In the proposed algorithm, first, two types of problem-specific heuristics are proposed, namely, the batch assignment and the right-shifting heuristics, which can substantially improve the makespan. Next, the encoding and decoding approaches are developed according to the problem constraints and objectives. Five types of local search operators are designed for the distributed flow shop and parallel batching stages. In addition, a novel scout bee heuristic that considers the useful information that is collected by the global and local best solutions is investigated, which can enhance searching performance. Finally, based on several well-known benchmarks and realistic industrial instances and via comprehensive computational comparison and statistical analysis, the highly effective performance of the proposed algorithm is favorably compared against several algorithms in terms of both solution quality and population diversity.