Flexible Job Shop Scheduling Research Articles

A multidimensional probabilistic model based evolutionary algorithm for the energy-efficient distributed flexible job-shop scheduling problem

With escalating environmental effects, the spotlight on low-carbon manufacturing has garnered significant attention. The rise of distributed production has emerged as a prominent trend in response to the imperatives of economic globalization. This article focuses on addressing the energy-efficient distributed flexible job-shop scheduling problem (EE_DFJSP), with the aim of minimizing both makespan and total energy consumption (TEC) simultaneously. The production process contains four pivotal phases: 1) job assignment in distributed factories; 2) machine selection within factories; 3) operation allocation on flexible machines; and 4) machine speed adjustment for processing. Given the problem's multi-phase and strong coupling characteristics, it is imperative to develop a promising evolutionary algorithm (EA) for EE_DFJSP. To tackle this challenge, we propose a multidimensional probabilistic model-based EA (MPMEA) paradigm. First, problem-specific encoding and decoding schemes are developed based on the solution features of EE_DFJSP. Second, a hybrid initialization strategy incorporating four heuristic rules is devised to yield an initial population with diversity. Third, an effective union probabilistic model (UPM) is formulated to learn promising patterns from superior solutions, and an efficient sampling strategy is designed to produce high-quality offspring individuals. To achieve a balance between global exploration and local exploitation, problem-specific multiple neighborhood operators are proposed to perform an in-depth local search. Furthermore, a two-stage energy-saving speed adjustment strategy is designed for the superior solutions obtained through local search. Finally, computational comparisons and simulation studies are conducted to validate the effectiveness and superiority of the MPMEA in effectively addressing EE_DFJSP.

Many-objective flexible job-shop scheduling based on a loose non-dominated sorting genetic algorithm

ABSTRACT To address the challenges of solving the many-objective flexible job-shop scheduling problem, this study proposes a loose non-dominated sorting genetic algorithm III (LNSGA-III), an enhancement of the non-dominated sorting genetic algorithm III (NSGA-III). First, a loose dominance principle is proposed to overcome the shortcomings of low selection pressure and slow convergence under the Pareto dominance principle. Next, a novel crossover operator without repair, named improved order crossover, is presented to fully preserve the characteristics of exchanged operations and enhance the exploration capability of the algorithm. Experimental studies involve testing algorithms on some typical scheduling instances with six simultaneously optimized objectives. The primary metric for algorithm comparison is the hypervolume, with additional investigation for statistical significance. Other metrics, including coverage, convergence and diversity, are also used for comparison. The experimental results demonstrate the effectiveness of the proposed enhancements, showcasing the significant superiority of the algorithm over some state-of-the-art alternatives.

Two-level balancing multi-objective algorithm for trapezoidal type-2 fuzzy flexible job shop problems

Uncertainty remains a critical issue in realistic applications in many fields. However, there is little literature considering trapezoidal interval type-2 fuzzy set (TIT2FS) in scheduling problems. To fill this gap, we propose a two-level balancing multi-objective optimization algorithm for a distributed flexible job shop scheduling problem (DFJSP), wherein two typical constraints are considered: the TIT2FS processing time and the transportation resource limitation. Two objectives are to be minimized: the TIT2FS fuzzy makespan and energy consumption. A two-level evolution mechanism is employed. The first level comprises two populations to optimize the two respective objectives, while the second level is composed of two populations to perform the convergence and diversity balancing tasks. Next, an efficient problem-specific initialization method with several heuristics is presented. Subsequently, different types of mutation and crossover operators are proposed under the consideration of problem knowledge. To further improve the performance of exploration and exploitation abilities, we present a balancing enhanced local search method. Finally, we performed detailed comparisons with four efficient algorithms. The results show that the two-level optimization algorithm was efficient in both convergence and diversity abilities, indicating that our algorithm can efficiently achieve a balance between these abilities.

A reinforcement learning enhanced memetic algorithm for multi-objective flexible job shop scheduling toward Industry 5.0

Flexible job shop scheduling problem (FJSP) with worker flexibility has gained significant attention in the upcoming Industry 5.0 era because of its computational complexity and its importance in production processes. It is normally assumed that each machine is typically operated by one worker at any time; therefore, shop-floor managers need to decide on the most efficient assignments for machines and workers. However, the processing time is variable and uncertain due to the fluctuating production environment caused by unsteady operating conditions of machines and learning effect of workers. Meanwhile, they also need to balance the worker workload while meeting production efficiency. Thus a dual resource-constrained FJSP with worker’s learning effect and fuzzy processing time (F-DRCFJSP-WL) is investigated to simultaneously minimise makespan, total machine workloads and maximum worker workload. Subsequently, the reinforcement learning enhanced multi-objective memetic algorithm based on decomposition (RL-MOMA/D) is proposed for solving F-DRCFJSP-WL. For RL-MOMA/D, the Q-learning is incorporated into memetic algorithm to perform variable neighbourhood search and further strengthen the exploitation capability for the algorithm. Finally, comprehensive experiments on extensive test instances and a case study of aircraft overhaul shop-floor are conducted to demonstrate effectiveness and superiority of the proposed method.

Dynamic flexible scheduling with transportation constraints by multi-agent reinforcement learning

Reinforcement learning-based methods have addressed production scheduling problems with flexible processing constraints. However, delayed rewards arise due to the dynamic arrival of jobs and transportation constraints between two successive operations. The flow time of operations can only be determined after processing due to the possibility that the solution for job sequencing may change if new operations are inserted in dynamic environments. Job sequencing is often overlooked in single-agent-based scheduling methods. The lack of information sharing between multiple agents necessitates that researchers manually design reward functions to fit the relationship between optimization objectives and rewards, thereby reducing the accuracy of the learned policies. Thus, this paper proposes a multi-agent-based scheduling optimization framework that facilitates collaboration between the agents of both machines and jobs to address dynamic flexible job-shop scheduling problems (DFJSP) with transportation time constraints. Then, this paper formulates the Partial Observation Markov Decision Process and constructs a reward-sharing mechanism to tackle the delayed reward issue and facilitate policy learning. Finally, we develop an improved multi-agent dueling double deep Q network algorithm to optimize scheduling policy during long-term training. The results show that, compared with the state-of-the-art methods, the proposed method efficiently shortens the weighted flow time under the trained and unseen scenarios. Additionally, the case study results demonstrate its efficiency and responsiveness. It indicates that the proposed method efficiently addresses production scheduling problems with complex constraints, including the insertion of jobs, transportation time constraints, and flexible processing routes.

Fast Pareto set approximation for multi-objective flexible job shop scheduling via parallel preference-conditioned graph reinforcement learning

The Multi-Objective Flexible Job Shop Scheduling Problem (MOFJSP) is a complex challenge in manufacturing, requiring balancing multiple, often conflicting objectives. Traditional methods, such as Multi-Objective Evolutionary Algorithms (MOEA), can be time-consuming and unsuitable for real-time applications. This paper introduces a novel Graph Reinforcement Learning (GRL) approach, named Preference-Conditioned GRL, which efficiently approximates the Pareto set for MOFJSP in a parallelized manner. By decomposing the MOFJSP into distinct sub-problems based on preferences and leveraging a parallel multi-objective training algorithm, our method efficiently produces high-quality Pareto sets, significantly outperforming MOEA methods in both solution quality and speed, especially for large-scale problems. Extensive experiments demonstrate the superiority of our approach, with remarkable results on large instances, showcasing its potential for real-time scheduling in dynamic manufacturing environments. Notably, for large instances (50 × 20), our approach outperforms MOEA baselines with remarkably shorter computation time (less than 1% of that of MOEA baselines). The robust generalization performance across various instances also highlights the practical value of our method for decision-makers seeking optimized production resource utilization.

Low-Carbon Flexible Job Shop Scheduling Problem Based on Deep Reinforcement Learning

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.

Matheuristic and learning-oriented multi-objective artificial bee colony algorithm for energy-aware flexible assembly job shop scheduling problem

With the increase of mass customization, flexible job shop scheduling problem considering assembly stage has widely existed in many manufacturing industries, such as die-casting mould factories. This problem is to find a reasonable machine assignment and operation sequence both in fabrication and assembly stages and simultaneously maximize production efficiency. In reality, energy shortages and environmental pollution have given an impetus to the development of energy-aware production scheduling problems. In this study, we address an energy-aware flexible assembly job shop scheduling problem (EFAJSP) with the objectives of minimizing flow time and energy consumption and first develop a mixed-integer linear programming (MILP) model to solve EFAJSP problem. Then, the model-specific characteristics are extracted and applied to a matheuristic decoding method for exploring the Pareto optimal solution. Due to the complexity of EFAJSP problem, a matheuristic and learning-oriented multi-objective artificial bee colony algorithm (MLABC), which combines the advantages of mathematical programming, reinforcement learning and meta-heuristic algorithm, is proposed. In addition, an initialization, destruction/construction operator and population update operator are proposed and work together to improve the exploration and exploitation performance of the proposed MLABC. Finally, numerical experimental results demonstrate the effectiveness of the proposed MILP model and the superiority of the MLABC over other algorithms in the literature.

Textile Flexible Job-Shop Scheduling Based on a Modified Ant Colony Optimization Algorithm

To improve the workshop production efficiency of textile enterprises and balance the total operating time of all machines in each operation, this paper proposes a modified algorithm based on the combination of the ant colony optimization (ACO) algorithm and production products, which we call the product ant colony optimization (PACO) algorithm. The local pheromone update rule in the ACO algorithm is modified through the close relationship between textile machinery and production products in the textile workshop; the pheromone is then introduced into production products based on the constraints of the textile machine. A heuristic function is designed to improve the utilization rate of textile machines to increase the heuristic value of machines that are less frequently used in the algorithm iteration process. In addition, this paper combines the convergence speed and the global search ability of the algorithm with a designed variable pheromone evaporate parameter. The comparison among the initially designed PACO algorithm, the separately modified PACO algorithm, and the integratively modified PACO algorithm demonstrates that the proposed enhancement effectively addresses scheduling issues in textile flexible workshops and various workshops with similar constraint conditions.

Research on Multi-Objective Flexible Job Shop Scheduling Problem with Setup and Handling Based on an Improved Shuffled Frog Leaping Algorithm

Flexible job shop scheduling problem (FJSP), widely prevalent in many intelligent manufacturing industries, is one of the most classic problems of production scheduling and combinatorial optimization. In actual manufacturing enterprises, the setup of machines and the handling of jobs have an important impact on the scheduling plan. Furthermore, there is a trend for a cluster of machines with similar functionalities to form a work center. Considering the above constraints, a new order-driven multi-equipment work center FJSP model with setup and handling including multiple objectives encompassing the minimization of the makespan, the number of machine shutdowns, and the number of handling batches is established. An improved shuffled frog leading algorithm is designed to solve it through the optimization of the initial solution population, the improvement of evolutionary operations, and the incorporation of Pareto sorting. The algorithm also combines the speed calculation method in the gravity search algorithm to enhance the stability of the solution search. Some standard FJSP data benchmarks have been selected to evaluate the effectiveness of the algorithm, and the experimental results confirm the satisfactory performance of the proposed algorithm. Finally, a problem example is designed to demonstrate the algorithm’s capability to generate an excellent scheduling plan.

Automatic Design of Energy-Efficient Dispatching Rules for Multi-Objective Dynamic Flexible Job Shop Scheduling Based on Dual Feature Weight Sets

Considering the requirements of the actual production scheduling process, the utilization of the genetic programming hyper-heuristic (GPHH) approach to automatically design dispatching rules (DRs) has recently emerged as a popular optimization approach. However, the decision objects and decision environments for routing and sequencing decisions are different in the dynamic flexible job shop scheduling problem (DFJSSP), leading to different required feature information. Traditional algorithms that allow these two types of scheduling decisions to share one common feature set are not conducive to the further optimization of the evolved DRs, but instead introduce redundant and unnecessary search attempts for algorithm optimization. To address this, some related studies have focused on customizing the feature sets for both routing and sequencing decisions through feature selection when solving single-objective problems. While being effective in reducing the search space, the selected feature sets also diminish the diversity of the obtained DRs, ultimately impacting the optimization performance. Consequently, this paper proposes an improved GPHH with dual feature weight sets for the multi-objective energy-efficient DFJSSP, which includes two novel feature weight measures and one novel hybrid population adjustment strategy. Instead of selecting suitable features, the proposed algorithm assigns appropriate weights to the features based on their multi-objective contribution, which could provide directional guidance to the GPHH while ensuring the search space. Experimental results demonstrate that, compared to existing studies, the proposed algorithm can significantly enhance the optimization performance and interpretability of energy-efficient DRs.

Flexible job shop scheduling via deep reinforcement learning with meta-path-based heterogeneous graph neural network

The flexible job shop scheduling problem (FJSP) is an important production scheduling problem in intelligent manufacturing. How to model the complex FJSP more accurately and improve the efficiency and generalization of scheduling policies is an urgent challenge to be solved. Therefore, a new end-to-end deep reinforcement learning (DRL) method combined with the meta-path-based heterogeneous graph neural network (MHGNN) is proposed to effectively solve FJSP. The task of solving FJSP is decomposed into two subtasks of operation selection and machine allocation. This dual-task FJSP is represented by introducing a heterogeneous graph and modeled as the dual Markov decision process (DMDP). A MHGNN is proposed to embed the global scheduling states of the dual-task FJSP. A heterogeneous graph neural network (GNN) framework is designed for the dual-task FJSP to efficiently encode the operation nodes and machine nodes, where the extracted embedded feature information is used to represent the operation selection policy and the machine allocation policy. Two policy networks are designed to efficiently predict the operation selection policy and the machine allocation policy, and a soft double-actors critic algorithm is proposed to train these two policy networks, where the trained policies can be used to efficiently solve FJSP instances of different scales. The experiments on three public benchmarks show that the proposed method outperforms the well-known heuristic scheduling rules and some advanced methods for solving FJSP. In particular, when solving large-scale FJSPs, the proposed method performs more prominently in terms of solution quality and solution time.

A hybrid estimation of distribution algorithm for solving assembly flexible job shop scheduling in a distributed environment

This paper proposes a novel distributed assembly flexible job shop scheduling problem (DAFJSP), which involves three stages: production stage, assembly stage, and delivery stage. The production stage is accomplished in a few flexible job shops, the assembly stage is accomplished in a few single-machine factories, and the delivery stage is to deliver the obtained products to the corresponding customers. To address the problem, a hybrid estimation of distribution algorithm based on differential evolution operator and variable neighborhood search (HEDA-DEV) is proposed with the goal of minimizing the total cost and tardiness. Firstly, a new multidimensional coding method is designed based on the features of the DAFJSP. Secondly, two mutation operators and the similarity coefficient based on the probability matrix are put forward to implement the dynamic mutation. Thirdly, five types of neighborhood structures satisfying cooperative search strategies are employed to adequately improve the local exploitation ability. Finally, the comparison experiment results suggest that the proposed HEDA-DEV has competitive performance compared to the selected efficient algorithms. Moreover, a real case study is used to demonstrate that HEDA-DEV is an effective method for solving DAFJSP.

A Double Deep Q-Network framework for a flexible job shop scheduling problem with dynamic job arrivals and urgent job insertions

In the semiconductor manufacturing industry, the Dynamic Flexible Job Shop Scheduling Problem is regarded as one of the most complex and significant scheduling problems. Existing studies consider the dynamic arrival of jobs, however, the insertion of urgent jobs such as testing chips poses a challenge to the production model, and there is an urgent need for new scheduling methods to improve the dynamic response and self-adjustment of the shop floor. In this work, deep reinforcement learning is utilized to address the dynamic flexible job shop scheduling problem and facilitate near-real-time shop floor decision-making. We extracted eight state features, including machine utilization, operation completion rate, etc., to reflect real-time shop floor production data. After examining machine availability time, the machine's earliest available time is redefined and incorporated into the design of compound scheduling rules. Eight compound scheduling rules have been developed for job selection and machine allocation. By using the state features as inputs to the Double Deep Q-Network, it is possible to acquire the state action values (Q-values) of each compound scheduling rule, and the intelligent agent can learn a reasonable optimization strategy through training. Simulation studies show that the proposed Double Deep Q-Network algorithm outperforms other heuristics and well-known scheduling rules by generating excellent solutions quickly. In most scenarios, the Double Deep Q-Network algorithm outperforms the Deep Q-Network, Q-Learning, and State-Action-Reward-State-Action (SARSA) frameworks. Moreover, the intelligent agent has good generalization ability in terms of optimization for similar objectives.

A discrete event simulator to implement deep reinforcement learning for the dynamic flexible job shop scheduling problem

The job shop scheduling problem, which involves the routing and sequencing of jobs in a job shop context, is a relevant subject in industrial engineering. Approaches based on Deep Reinforcement Learning (DRL) are very promising for dealing with the variability of real working conditions due to dynamic events such as the arrival of new jobs and machine failures. Discrete Event Simulation (DES) is essential for training and testing DRL approaches, which are based on the interaction of an intelligent agent and the production system. Nonetheless, there are numerous papers in the literature in which DRL techniques, developed to solve the Dynamic Flexible Job Shop Problem (DFJSP), have been implemented and evaluated in the absence of a simulation environment. In the paper, the limitations of these techniques are highlighted, and a numerical experiment that demonstrates their ineffectiveness is presented. Furthermore, in order to provide the scientific community with a simulation tool designed to be used in conjunction with DRL techniques, an agent-based discrete event simulator is also presented.

A novel method-based reinforcement learning with deep temporal difference network for flexible double shop scheduling problem

This paper studies the flexible double shop scheduling problem (FDSSP) that considers simultaneously job shop and assembly shop. It brings about the problem of scheduling association of the related tasks. To this end, a reinforcement learning algorithm with a deep temporal difference network is proposed to minimize the makespan. Firstly, the FDSSP is defined as the mathematical model of the flexible job-shop scheduling problem joined to the assembly constraint level. It is translated into a Markov decision process that directly selects behavioral strategies according to historical machining state data. Secondly, the proposed ten generic state features are input into the deep neural network model to fit the state value function. Similarly, eight simple constructive heuristics are used as candidate actions for scheduling decisions. From the greedy mechanism, optimally combined actions of all machines are obtained for each decision step. Finally, a deep temporal difference reinforcement learning framework is established, and a large number of comparative experiments are designed to analyze the basic performance of this algorithm. The results showed that the proposed algorithm was better than most other methods, which contributed to solving the practical production problem of the manufacturing industry.

An improved MOEA/D for multi-objective flexible job shop scheduling by considering efficiency and cost

To achieve cost reduction and efficiency improvement in the production process of the aerospace industry, this study establishes a mathematical model for the multi-objective flexible job shop scheduling problem (MOFJSP). The model comprehensively considers four optimisation objectives: completion time, tool number, machine load, and machine energy consumption. For solving the MOFJSP, an improved MOEA/D (IMOEA/D) algorithm is proposed. To improve the quality of solutions, the algorithm introduces another global update strategy in addition to the original substitution operation. The population is initialised using four allocation rules, and the neighbourhood is dynamically updated based on the degree of population evolution. The simulation results on a single instance indicate that the simulation time of IMOEA/D has decreased by 10.5% and machine energy consumption has reduced by 9.5%. Moreover, when compared to various classic multi-objective algorithms on 25 benchmark instances, the IMOEA/D algorithm achieved optimal results in 19 instances for inverted generational distance comparisons, 15 instances for hypervolume comparisons and nearly all instances for set coverage comparisons. The results reveal that the proposed IMOEA/D is effective and competitive in solving MOFJSP.

Solving multi-objective green flexible job shop scheduling problem by an improved chimp optimization algorithm

As environmental contamination becomes more and more severe, enterprises need to consider optimizing environmental criteria while optimizing production criteria. In this study, a multi-objective green flexible job shop scheduling problem (MO_GFJSP) is established with two objective functions: the makespan and the carbon emission. To effectively solve the MO_GFJSP, an improved chimp optimization algorithm (IChOA) is designed. The proposed IChOA has four main innovative aspects: 1) the fast non-dominated sorting (FDS) method is introduced to compare the individuals with multiple objectives and strengthen the solution accuracy. 2) a dynamic convergence factor (DCF) is introduced to strengthen the capabilities of exploration and exploitation. 3) the position weight (PW) is used in the individual position updating to enhance the search efficiency. 4) the variable neighborhood search (VNS) is developed to strengthen the capacity to escape the local optimum. By executing abundant experiments using 20 benchmark instances, it was demonstrated that the developed IChOA is efficient to solve the MO_GFJSP and effective for reducing carbon emission in the flexible job shop.

An effective deep actor-critic reinforcement learning method for solving the flexible job shop scheduling problem

An effective deep actor-critic reinforcement learning method for solving the flexible job shop scheduling problem

Dynamic scheduling mechanism for intelligent workshop with deep reinforcement learning method based on multi-agent system architecture

With the development and changes of industry and market demand, the personalized customization production mode with small batch and multiple batches has gradually become a new production mode. This makes production environment become more complex and dynamic. However, traditional production workshops cannot effectively adapt to this environment. Combining with new technologies, transforming traditional workshops into intelligent workshop to cope with new production mode become an urgent problem. Therefore, this paper proposes a multi-agent manufacturing system based on IoT for intelligent workshop. Meanwhile, this paper takes flexible job shop scheduling problem (FJSP) as a specific production scenario and establishes relevant mathematics model. To build the agent in intelligent workshop, this paper proposes a data-based with combination of virtual and physical agent (DB-VPA) which has information layer, software layer and physical layer. Then, based on the manufacturing system, this paper designs a dynamic scheduling mechanism with deep reinforcement learning (DRL) for intelligent workshop. This method contains three aspects: (1) Modeling production process based on Markov decision process (MDP). (2) Designing communication mechanism for DB-VPAs. (3) Designing scheduling model combining with improved genetic programming and proximal policy optimization (IGP-PPO) which is a DRL method. Finally, relevant experiments are executed in a prototype experiment platform. The experiments indicate that the proposed method has superiority and generality in solving scheduling problem with dynamic events.