Search Results (232)

The Mixed No-Idle Permutation Flow Shop Scheduling Problem (MNPFSSP) represents a specific case within regular flow scheduling problems. In this problem, some machines allow idle times between consecutive jobs or operations while other machines do not. Traditionally, the MNPFSSP has been addressed using the metaheuristics and exact methods. This work proposes an Evolutionary Strategy Based on the Generalized Mallows Model (ES-GMM) to solve the issue. Additionally, its advanced version, ES-GMMc, is developed, incorporating operating conditions to improve execution times without compromising solution quality. The proposed approaches are compared with algorithms previously used for the problem under study. Statistical tests of the experimental results show that the ES-GMMc achieved reductions in execution time, especially standing out in large instances, where the shortest computing times were obtained in 23 of 30 instances, without affecting the quality of the solutions. Full article

Cyber-physical systems need more intelligent decision-making methods. To address this issue with respect to incomplete process models and inefficient scheduling, we have previously proposed a new method called Petri-nets-adaptive ant colony optimization (PN-AACO). This method targets small-scale job shops with shared resource limits. These shops require symmetric job designs for resource sharing but have asymmetric job processing times. PN-AACO uses Petri net symmetry at edge nodes but faces a problem. Its marking–transition pheromone index mechanism causes state space explosion from Petri nets. This leads to a decrease in the computational speed of the algorithm in the face of an increase in scale or state, which results in a longer overall manufacturing process time that impacts productivity. Thus, we propose the improved PN-AACO (iPN-AACO). The improved method uses transition–transition pheromone recording to control pheromone amounts. It also adds pheromone-based initial selection and best-known-paths-based probability rules. Tests show this approach speeds up computations up to 92% in more-states models while keeping scheduling effective. Full article

With the development of Industry 4.0, discrete manufacturing systems are accelerating their transformation toward flexibility and intelligence to meet the market demand for various products and small-batch production. The flexible flow shop (FFS) paradigm enhances production flexibility, but existing studies often address FFS scheduling and automated guided vehicle (AGV) path planning separately, resulting in resource competition conflicts, such as equipment idle time and AGV congestion, which prolong the manufacturing cycle time and reduce system energy efficiency. To solve this problem, this study proposes an integrated production–transportation scheduling framework (FFSP-AGV). By using the adjacent sequence modeling idea, a mixed-integer linear programming (MILP) model is established, which takes into account the constraints of the production process and AGV transportation task conflicts with the aim of minimizing the makespan and improving overall operational efficiency. Systematic evaluations are carried out on multiple test instances of different scales using the CPLEX solver. The results show that, for small-scale instances (job count ≤10), the MILP model can generate optimal scheduling solutions within a practical computation time (several minutes). Moreover, it is found that there is a significant marginal diminishing effect between AGV quantity and makespan reduction. Once the number of AGVs exceeds 60% of the parallel equipment capacity, their incremental contribution to cycle time reduction becomes much smaller. However, the computational complexity of the model increases exponentially with the number of jobs, making it slightly impractical for large-scale problems (job count > 20). This research highlights the importance of integrated production–transportation scheduling for reducing manufacturing cycle time and reveals a threshold effect in AGV resource allocation, providing a theoretical basis for collaborative optimization in smart factories. Full article

In order to address the impact of equipment fault diagnosis and repair delays on production schedule execution in the dynamic scheduling of flexible job shops, this paper proposes a multi-resource, multi-objective dynamic scheduling optimization model, which aims to minimize delay time and completion time. It integrates the scheduling of the workpieces, machines, and maintenance personnel to improve the response efficiency of emergency equipment maintenance. To this end, a self-learning Ant Colony Algorithm based on deep reinforcement learning (ACODDQN) is designed in this paper. The algorithm searches the solution space by using the ACO, prioritizes the solutions by combining the non-dominated sorting strategies, and achieves the adaptive optimization of scheduling decisions by utilizing the organic integration of the pheromone update mechanism and the DDQN framework. Further, the generated solutions are locally adjusted via the feasible solution optimization strategy to ensure that the solutions satisfy all the constraints and ultimately generate a Pareto optimal solution set with high quality. Simulation results based on standard examples and real cases show that the ACODDQN algorithm exhibits significant optimization effects in several tests, which verifies its superiority and practical application potential in dynamic scheduling problems. Full article

The flexible job shop scheduling problem is relevant in many different areas. However, the usual deterministic approach sees its usefulness limited, as uncertainty plays a paramount role in real-world processes. Considering processing times in the form of fuzzy numbers is a computationally affordable way to model uncertainty that enhances the applicability of obtained solutions. Unfortunately, fuzzy processing times add an extra layer of complexity to otherwise straightforward operations. For example, in energy-aware environments, measuring the idle times of resources is of the utmost importance, but it goes from a trivial calculation in the deterministic setting to a critical modelling decision in fuzzy scenarios, where different approaches are possible. In this paper, we analyse the drawbacks of the existing translation of the deterministic approach to a fuzzy context and propose two alternative ways of computing the idle times in a schedule. We show that, unlike in the deterministic setting, the different definitions are not equivalent when fuzzy processing times are considered, and results are directly affected, depending on which one is used. We conclude that the new ways of computing idle times under uncertainty provide more reliable values and, hence, better schedules. Full article

Background: The job shop scheduling problem (JSSP) and its solution algorithms have been of enduring interest in both academia and industry for decades. In recent years, machine learning (ML) has been playing an increasingly important role in advancing existing solutions and building new heuristic solutions for the JSSP, aiming to find better solutions in shorter computation times. Methods: In this study, we built on top of a state-of-the-art deep reinforcement learning (DRL) agent, called Neural Local Search (NLS), which can efficiently and effectively control a large local neighborhood search on the JSSP. In particular, we developed a method for training the decision transformer (DT) algorithm on search trajectories taken by a trained NLS agent to further improve upon the learned decision-making sequences. Results: Our experiments showed that the DT successfully learns local search strategies that are different and, in many cases, more effective than those of the NLS agent itself. In terms of the tradeoff between solution quality and acceptable computational time needed for the search, the DT is particularly superior in application scenarios where longer computational times are acceptable. In this case, it makes up for the longer inference times required per search step, which are caused by the larger neural network architecture, through better quality decisions per step. Conclusions: Therefore, the DT achieves state-of-the-art results for solving the JSSP with ML-enhanced local search. Full article

In this paper, a dynamic energy-efficient hybrid flow shop (TDEHFSP) scheduling model is proposed, considering random arrivals of new jobs and transport by transfer vehicles. To simultaneously optimise the maximum completion time and the total energy consumption, a co-evolutionary approach (DDQCE) using a double deep Q-network (DDQN) is introduced, where global and local search tasks are assigned to different populations to optimise the use of computational resources. In addition, a multi-objective NEW heuristic strategy is implemented to generate an initial population with enhanced convergence and diversity. The DDQCE incorporates an energy-efficient strategy based on time interval ‘left shift’ and turn-on/off mechanisms, alongside a rescheduling model to manage dynamic disturbances. In addition, 36 test instances of varying sizes, simplified from the excavator boom manufacturing process, are designed for comparative experiments with traditional algorithms. The experimental results demonstrate that DDQCE achieves 40% more Pareto-optimal solutions compared to NSGA-II and MOEA/D while requiring 10% less computational time, confirming that this algorithm efficiently solves the TDEHFSP problem. Full article

Uncertainty in processing times is a key issue in distributed production; it severely affects scheduling accuracy. In this study, we investigate a dynamic distributed flexible job shop scheduling problem with variable processing times (DDFJSP-VPT), in which the processing time follows a normal distribution. First, the mathematical model is established by simultaneously considering the makespan, tardiness, and total factory load. Second, a chance-constrained approach is employed to predict uncertain processing times to generate a robust initial schedule. Then, a heuristic scheduling method which involves a left-shift strategy, an insertion-based local adjustment strategy, and a DMOGWO-based global rescheduling strategy is developed to dynamically adjust the scheduling plan in response to the context of uncertainty. Moreover, a hybrid initialization scheme, discrete crossover, and mutation operations are designed to generate a high-quality initial population and update the wolf pack, enabling GWO to effectively solve the distributed flexible job shop scheduling problem. Based on the parameter sensitivity study and a comparison with four algorithms, the algorithm’s stability and effectiveness in both static and dynamic environments are demonstrated. Finally, the experimental results show that our method can achieve much better performance than other rules-based reactive scheduling methods and the hybrid-shift strategy. The utility of the prediction strategy is also validated. Full article

The agricultural equipment market has the characteristics of rapid demand changes and high demand for machine models, etc., so multi-variety, small-batch, and customized production methods have become the mainstream of agricultural machinery enterprises. The flexible job shop scheduling problem (FJSP) in the context of agricultural machinery and equipment manufacturing is addressed, which involves multiple resources including machines, workers, and automated guided vehicles (AGVs). The aim is to optimize two objectives: makespan and the maximum continuous working hours of all workers. To tackle this complex problem, a Multi-Objective Discrete Grey Wolf Optimization (MODGWO) algorithm is proposed. The MODGWO algorithm integrates a hybrid initialization strategy and a multi-neighborhood local search to effectively balance the exploration and exploitation capabilities. An encoding/decoding method and a method for initializing a mixed population are introduced, which includes an operation sequence vector, machine selection vector, worker selection vector, and AGV selection vector. The solution-updating mechanism is also designed to be discrete. The performance of the MODGWO algorithm is evaluated through comprehensive experiments using an extended version of the classic Brandimarte test case by randomly adding worker and AGV information. The experimental results demonstrate that MODGWO achieves better performance in identifying high-quality solutions compared to other competitive algorithms, especially for medium- and large-scale cases. The proposed algorithm contributes to the research on flexible job shop scheduling under multi-resource constraints, providing a novel solution approach that comprehensively considers both workers and AGVs. The research findings have practical implications for improving production efficiency and balancing multiple objectives in agricultural machinery and equipment manufacturing enterprises. Full article

Flexible job-shop scheduling problems (FJSPs) represent one of the most complex combinatorial optimization challenges. Modern production systems and control processes demand rapid decision-making in scheduling. To address this challenge, we propose a quantum computing approach for solving FJSPs. We propose a quadratic unconstrained binary optimization (QUBO) model to minimize the makespan of FJSPs, with the scheduling scheme encoded in the ground state of the Hamiltonian operator. The model is solved using a coherent Ising machine (CIM). Numerical experiments are conducted to evaluate and validate the performance and effectiveness of the CIM. The results demonstrate that quantum computing holds significant potential for solving FJSPs more efficiently than traditional computational methods. Full article

The dual-resource constrained flexible job shop scheduling problem with variable sublots (DRCFJSP-VS) can be decomposed into four subproblems: the sublot splitting subproblem, the sublot sequencing subproblem, the machine assignment subproblem, and the worker assignment subproblem, which are difficult to solve efficiently using conventional methods. The introduction of variable-size batch splitting and the constraints of multiple levels and skills of workers further increase the complexity of the problem, making it difficult to solve efficiently using conventional methods. This paper proposes a mixed-integer linear programming (MILP) model to solve this complex problem and introduces a two-stage multi-objective evolutionary algorithm (TSMOEA). In the first stage of the algorithm, an improved multi-objective discrete difference evolutionary algorithm is used to optimize the dual-resource constrained flexible job shop scheduling problem; in the second stage, an adaptive simulated annealing algorithm is used to search for variable-size batch splitting strategies. To validate the feasibility of the model, the solution results are obtained using the CPLEX solver and compared with the results of TSMOEA. The performance of TSMOEA is compared with NSGA-II, PSO, DGWO, and WOA on improved instances. The results show that TSMOEA outperforms the other algorithms in both IGD and HV metrics, demonstrating its superior solution quality and robustness. Full article

This paper addresses the Flexible Job Shop Scheduling Problem (FJSP) with the objective of minimizing both earliness/tardiness (E/T) and intermediate storage time (IST). An extended S-graph framework that incorporates E/T and IST minimization while maintaining the structural advantages of the original S-graph approach is presented. The framework is further enhanced by integrating linear programming (LP) techniques to adjust machine assignments and operation timings dynamically. The following four methodological approaches are systematically analyzed: a standalone S-graph for E/T minimization, an S-graph for combined E/T and IST minimization, a hybrid S-graph with LP for E/T minimization, and a comprehensive hybrid approach addressing both E/T and IST. Computational experiments on benchmark problems demonstrate the efficacy of the proposed methods, with the standalone S-graph showing efficiency for smaller instances and the hybrid approaches offering improved solution quality for more complex scenarios. The research provides insights into the trade-offs between computational time and solution quality across different problem configurations and storage policies. This work contributes to the field of production scheduling by offering a versatile framework capable of addressing the multi-objective nature of modern manufacturing environments. Full article

This paper tackles the green permutation flow shop scheduling problem (GPFSP) with the goal of minimizing both the maximum completion time and energy consumption. It introduces a novel hybrid approach that combines end-to-end deep reinforcement learning with an improved genetic algorithm. Firstly, the PFSP is modeled using an end-to-end deep reinforcement learning (DRL) approach, named PFSP_NET, which is designed based on the characteristics of the PFSP, with the actor–critic algorithm employed to train the model. Once trained, this model can quickly and directly produce relatively high-quality solutions. Secondly, to further enhance the quality of the solutions, the outputs from PFSP_NET are used as the initial population for the improved genetic algorithm (IGA). Building upon the traditional genetic algorithm, the IGA utilizes three crossover operators, four mutation operators, and incorporates hamming distance, effectively preventing the algorithm from prematurely converging to local optimal solutions. Then, to optimize energy consumption, an energy-saving strategy is proposed that reasonably adjusts the job scheduling order by shifting jobs backward without increasing the maximum completion time. Finally, extensive experimental validation is conducted on the 120 test instances of the Taillard standard dataset. By comparing the proposed method with algorithms such as the standard genetic algorithm (SGA), elite genetic algorithm (EGA), hybrid genetic algorithm (HGA), discrete self-organizing migrating algorithm (DSOMA), discrete water wave optimization algorithm (DWWO), and hybrid monkey search algorithm (HMSA), the results demonstrate the effectiveness of the proposed method. Optimal solutions are achieved in 28 test instances, and the latest solutions are updated in instances Ta005 and Ta068 with values of 1235 and 5101, respectively. Additionally, experiments on 30 instances, including Taillard 20-10, Taillard 50-10, and Taillard 100-10, indicate that the proposed energy strategy can effectively reduce energy consumption. Full article

Economic performance in modern manufacturing enterprises is often influenced by random dynamic events, requiring real-time scheduling to manage multiple conflicting production objectives simultaneously. However, traditional scheduling methods often fall short due to their limited responsiveness in dynamic environments. To address this challenge, this paper proposes an innovative online rescheduling framework called the Dual-Level Integrated Deep Q-Network (DLIDQN). This framework is designed to solve the dynamic multi-objective flexible job shop scheduling problem (DMOFJSP), which is affected by six types of dynamic events: new job insertion, job operation modification, job deletion, machine addition, machine tool replacement, and machine breakdown. The optimization focuses on three key objectives: minimizing makespan, maximizing average machine utilization ($U_{ave}$), and minimizing average job tardiness rate ($T{R}_{ave}$). The DLIDQN framework leverages a hierarchical reinforcement learning approach and consists of two integrated IDQN-based agents. The high-level IDQN serves as the decision-maker during rescheduling, implementing dual-level decision-making by dynamically selecting optimization objectives based on the current system state and guiding the low-level IDQN’s actions. To meet diverse optimization requirements, two reward mechanisms are designed, focusing on job tardiness and machine utilization, respectively. The low-level IDQN acts as the executor, selecting the best scheduling rules to achieve the optimization goals determined by the high-level agent. To improve scheduling adaptability, nine composite scheduling rules are introduced, enabling the low-level IDQN to flexibly choose strategies for job sequencing and machine assignment, effectively addressing both sub-tasks to achieve optimal scheduling performance. Additionally, a local search algorithm is incorporated to further enhance efficiency by optimizing idle time between jobs. The numerical experimental results show that in 27 test scenarios, the DLIDQN framework consistently outperforms all proposed composite scheduling rules in terms of makespan, surpasses the widely used single scheduling rules in 26 instances, and always exceeds other reinforcement learning-based methods. Regarding the $U_{ave}$ metric, the framework demonstrates superiority in 21 instances over all composite scheduling rules and maintains a consistent advantage over single scheduling rules and other RL-based strategies. For the $T{R}_{ave}$ metric, DLIDQN outperforms composite and single scheduling rules in 20 instances and surpasses other RL-based methods in 25 instances. Specifically, compared to the baseline methods, our model achieves maximum performance improvements of approximately 37%, 34%, and 30% for the three objectives, respectively. These results validate the robustness and adaptability of the proposed framework in dynamic manufacturing environments and highlight its significant potential to enhance scheduling efficiency and economic benefits. Full article

The flexible job shop scheduling problem is a typical and complex combinatorial optimization problem. In recent years, the assembly problem in job shop scheduling problems has been widely studied. However, most of the studies ignore the learning effect of workers, which may lead to higher costs than necessary. This paper considers a flexible assembly job scheduling problem with learning effect (FAJSPLE) and proposes a hybrid multi-objective artificial bee colony (HMABC) algorithm to solve the problem. Firstly, a mixed integer linear programming model is developed where the maximum completion time (makespan), total energy consumption and total cost are optimized simultaneously. Secondly, a critical path-based mutation strategy was designed to dynamically adjust the level of workers according to the characteristics of the critical path. Finally, the local search capability is enhanced by combining the simulated annealing algorithm (SA), and four search operators with different neighborhood structures are designed. By comparative analysis on different scales instances, the proposed algorithm reduces 55.8 and 958.99 on average over the comparison algorithms for the GD and IGD metrics, respectively; for the C-metric, the proposed algorithm improves 0.036 on average over the comparison algorithms. Full article