Search Results (6)

To optimize the production scheduling of a flexible job shop, this paper, based on the NSGA-II algorithm, proposes an adaptive simulated annealing non-dominated sorting genetic algorithm II with enhanced elitism (ASA-NSGA-EE) that establishes a multi-objective flexible job shop scheduling model with the objective functions of minimizing the maximum completion time, processing cost, and carbon emissions generated from processing. The ASA-NSGA-EE algorithm adopts an adaptive crossover and mutation genetic strategy, which dynamically adjusts the crossover and mutation rates based on the evolutionary stage of the population, aiming to reduce the loss of optimal solutions. Additionally, it incorporates the simulated annealing algorithm to optimize the selection strategy by leveraging its cooling characteristics. Furthermore, it improves the elite strategy through incorporating elite selection criteria. Finally, by simulation experiments, the effectiveness of the improved NSGA-II algorithm is validated by comparing it with other algorithms. Full article

As the focus on environmental sustainability sharpens, the significance of low-carbon manufacturing and energy conservation continues to rise. While traditional flexible job shop scheduling strategies are primarily concerned with minimizing completion times, they often overlook the energy consumption of machines. To address this gap, this paper introduces a novel solution utilizing deep reinforcement learning. The study begins by defining the Low-carbon Flexible Job Shop Scheduling problem (LC-FJSP) and constructing a disjunctive graph model. A sophisticated representation, based on the Markov Decision Process (MDP), incorporates a low-carbon graph attention network featuring multi-head attention modules and graph pooling techniques, aimed at boosting the model’s generalization capabilities. Additionally, Bayesian optimization is employed to enhance the solution refinement process, and the method is benchmarked against conventional models. The empirical results indicate that our algorithm markedly enhances scheduling efficiency by 5% to 12% and reduces carbon emissions by 3% to 8%. This work not only contributes new insights and methods to the realm of low-carbon manufacturing and green production but also underscores its considerable theoretical and practical implications. Full article

With the rapid development of economic globalization and green manufacturing, traditional flexible job shop scheduling has evolved into the low-carbon heterogeneous distributed flexible job shop scheduling problem (LHDFJSP). Additionally, modern smart manufacturing processes encounter complex and diverse contingencies, necessitating the ability to address dynamic events in real-world production activities. To date, there are limited studies that comprehensively address the intricate factors associated with the LHDFJSP, including workshop heterogeneity, job insertions and transfers, and considerations of low-carbon objectives. This paper establishes a multi-objective mathematical model with the goal of minimizing the total weighted tardiness and total energy consumption. To effectively solve this problem, diverse composite scheduling rules are formulated, alongside the application of a deep reinforcement learning (DRL) framework, i.e., Rainbow deep-Q network (Rainbow DQN), to learn the optimal scheduling strategy at each decision point in a dynamic environment. To verify the effectiveness of the proposed method, this paper extends the standard dataset to adapt to the LHDFJSP. Evaluation results confirm the generalization and robustness of the presented Rainbow DQN-based method. Full article

Green and low carbon automated production has become a research hotspot. In this paper, the AGV transport resource constraint, machine layout and job setup time have been integrated into the background of a flexible job shop. From a whole life-cycle perspective, the AGV allocation strategy has been formulated by simulating multiple scenarios within the production system. Aimed at makespan, carbon footprint, and machine load, a green low-carbon flexible job shop scheduling model with multiple transport equipment (GFJSP-MT) has been constructed. To address this problem, a relevant case dataset was formed, and a heuristic strategy NSGA-II using a real number encoded embedded cycle to replace repeated individuals was proposed. Through longitudinal and horizontal comparisons, the effectiveness of the AGV allocation strategy has been verified and the optimum number of AGVs in the case determined. Finally the quality and diversity of the Pareto frontier solutions are compared and the scheduling scheme for each sub-objective are discussed. The results show that the model and algorithm constructed in this paper can effectively achieve the optimal scheduling of green flexible shop production. Full article

Low carbon manufacturing has received increasingly more attention in the context of global warming. The flexible job shop scheduling problem (FJSP) widely exists in various manufacturing processes. Researchers have always emphasized manufacturing efficiency and economic benefits while ignoring environmental impacts. In this paper, considering carbon emissions, a multi-objective flexible job shop scheduling problem (MO-FJSP) mathematical model with minimum completion time, carbon emission, and machine load is established. To solve this problem, we study six variants of the non-dominated sorting genetic algorithm-III (NSGA-III). We find that some variants have better search capability in the MO-FJSP decision space. When the solution set is close to the Pareto frontier, the development ability of the NSGA-III variant in the decision space shows a difference. According to the research, we combine Pareto dominance with indicator-based thought. By utilizing three existing crossover operators, a modified NSGA-III (co-evolutionary NSGA-III (NSGA-III-COE) incorporated with the multi-group co-evolution and the natural selection is proposed. By comparing with three NSGA-III variants and five multi-objective evolutionary algorithms (MOEAs) on 27 well-known FJSP benchmark instances, it is found that the NSGA-III-COE greatly improves the speed of convergence and the ability to jump out of local optimum while maintaining the diversity of the population. From the experimental results, it can be concluded that the NSGA-III-COE has significant advantages in solving the low carbon MO-FJSP. Full article

The flexible job shop scheduling problem (FJSP) is a difficult discrete combinatorial optimization problem, which has been widely studied due to its theoretical and practical significance. However, previous researchers mostly emphasized on the production efficiency criteria such as completion time, workload, flow time, etc. Recently, with considerations of sustainable development, low-carbon scheduling problems have received more and more attention. In this paper, a low-carbon FJSP model is proposed to minimize the sum of completion time cost and energy consumption cost in the workshop. A new bio-inspired metaheuristic algorithm called discrete whale optimization algorithm (DWOA) is developed to solve the problem efficiently. In the proposed DWOA, an innovative encoding mechanism is employed to represent two sub-problems: Machine assignment and job sequencing. Then, a hybrid variable neighborhood search method is adapted to generate a high quality and diverse population. According to the discrete characteristics of the problem, the modified updating approaches based on the crossover operator are applied to replace the original updating method in the exploration and exploitation phase. Simultaneously, in order to balance the ability of exploration and exploitation in the process of evolution, six adjustment curves of a are used to adjust the transition between exploration and exploitation of the algorithm. Finally, some well-known benchmark instances are tested to verify the effectiveness of the proposed algorithms for the low-carbon FJSP. Full article