Flexible Job Shop Scheduling Problem Research Articles

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.

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.

Towards Sustainable Production: An Adaptive Intelligent Optimization Genetic Algorithm for Solid Wood Panel Manufacturing

Optimizing production processes to conserve resources and reduce waste has become crucial in pursuing sustainable manufacturing practices. The solid wood panel industry, marked by substantial raw materials and energy consumption, stands at the forefront of addressing this challenge. This research delves into production scheduling and equipment utilization inefficiencies, offering innovative solutions for the solid wood panel processing line aimed at achieving environmental sustainability and operational efficiency. The study is articulated through two main segments: (1) an exhaustive analysis and the development of a simulation system for the solid wood panel processing line, delineating all production elements and operational logic, furnished with a user-friendly simulation interface, and (2) a comprehensive evaluation and enhancement of various scheduling algorithms specific to the Flexible Job-Shop Scheduling Problem (FJSP) encountered in solid wood panel workshops. A significant leap forward is made with the introduction of the Adaptive Intelligent Optimization Genetic Algorithm (AIOGA), an evolved version of the standard Genetic Algorithm (GA) engineered for optimal scheduling within the solid wood panel processing line. AIOGA incorporates advanced features such as encoding strategy, population initialization, objective function setting, selection strategy, crossover operation, and mutation operation, demonstrating the methodological depth of the study. We applied AIOGA in a designed FJSP, and AIOGA substantially reduced the maximum completion time to 90 min. It evidenced an improvement of 39.60% over the conventional GA, enhancing the equilibrium of the equipment workload across the system. This research presents a multifaceted strategy to address the scheduling complications inherent in solid wood panel production and highlights the extensive applicability of adaptive intelligent optimization in diverse industrial settings. This study establishes a new paradigm in manufacturing optimization, underlining the valuable integration of sustainability and efficiency in production methodologies.

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.

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.

A matheuristic-based multi-objective evolutionary algorithm for flexible assembly jobs shop scheduling problem in cellular manufacture

The flexible assembly job shop scheduling problem (FAJSP) and its extensions have received increased attention. However, multi-objective FAJSP in cellular manufacture (FAJSP-CM), a real-world extension of FAJSP with important applications in the mass customization of complex products, is barely considered in most previous studies. Hence, this study first addresses the multi-objective FAJSP-CM problem via a mixed-integer linear programming model (MILP). Then, a matheuristic-based multi-objective evolutionary algorithm (MMOEA), with a matheuristic decoding method, knowledge-guided initialization and learning-based local intensification method, is presented to efficiently tackle the FAJSP-CM problem in polynomial-time. The matheuristic decoding method, which hybrids a decomposition linear programming model (D-LP) that can quickly and optimally allocate the execution times of all operations, to search for the optimal solution in a specific space. The knowledge-guided initialization is extended to get a high-quality and great-diversity initial population for accelerated convergence. Meanwhile, the learning-based local intensification method is developed to adaptively coordinate five problem-specific local search operators to enhance the exploitation ability of the MMOEA algorithm. Finally, comprehensive experiments based on 720 instances are conducted to evaluate the proposed MILP model and MMOEA algorithm. The results of the first experiments illustrate the MILP model can obtain the Pareto solutions of small-scale instances. The remaining experiments demonstrate that the proposed MMOEA algorithm outperforms its competitors by 0.21 and 0.72 in hypervolume ratio and coverage indictors, along with approximately a 25 % improvement in success rate.

Deep reinforcement learning for adaptive flexible job shop scheduling: coping with variability and uncertainty

ABSTRACT The frequently evolving manufacturing system necessitates real-time large-scale data analytics, surpassing the capabilities of classical systems or human skills, necessitating knowledge development and self-adaptive control. Unpredictable real-time events in smart factories cause changes in the effectiveness of planned schedules or tasks; even slight interruptions can accumulate to make the preplanned schedule unoptimized, if not impossible. To meet the required production efficiency, typical dynamic scenarios on the shop floor, such as failures, random job arrivals, and machine setup, must be addressed quickly. Hence, this study proposes a novel Triple Deep Q Network (TDQN) approach for learning high-quality dispatching rules for addressing the Flexible Job Shop Scheduling Problem (FJSSP) in uncertainty. For the dispatching rule-based FJSSP, the Markov Decision Process (MDP) to choose a suitable operation-machine (O-M) pair is formulated to allow operation selection and resource assignment resolutions to be made simultaneously. The performance of the TDQN method is investigated against the Double Deep Q Network (DDQN) and Deep Q Network (DQN) approach and found to be more stable. Moreover, among the 29 different shopfloor configuration settings, TDQN performed better in 62.07% of the overall instances, while DDQN and DQN performed better in only 31.03% and 6.9% of instances, respectively.

A Reinforcement Learning Approach for Flexible Job Shop Scheduling Problem With Crane Transportation and Setup Times.

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.

Multi-policy deep reinforcement learning for multi-objective multiplicity flexible job shop scheduling

This study considers the simultaneous minimization of makespan and total tardiness for the multi-objective multiplicity flexible job shop scheduling problem (MOMFJSP). A deep reinforcement learning framework employing a multi-policy proximal policy optimization algorithm (MPPPO) is developed to solve MOMFJSP. The MOMFJSP is treated as a Markov decision process, allowing an intelligent agent to make sequential decisions based on the current production status. This framework involves multiple policy networks with different objective weight vectors. Using MPPPO, these networks are optimized simultaneously to obtain a set of high-quality Pareto-optimal policies. Moreover, a fluid model is introduced to extract state features and devise composite dispatching rules as discrete actions. A multi-policy co-evolution mechanism (MPCEM) is proposed to facilitate collaborative evolution among policy networks, supported by a reward mechanism that considers the objective weights. A training algorithm based on MPPPO is designed for learning across multiple policy networks. The effectiveness and superiority of the proposed method are confirmed through comparisons with composite dispatching rules and other scheduling methods.

Dynamic Intelligent Scheduling in Low-Carbon Heterogeneous Distributed Flexible Job Shops with Job Insertions and Transfers.

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.

Dynamic Events in the Flexible Job-Shop Scheduling Problem: Rescheduling with a Hybrid Metaheuristic Algorithm

In the real world of manufacturing systems, production planning is crucial for organizing and optimizing various manufacturing process components. The objective of this paper is to present a methodology for both static scheduling and dynamic scheduling. In the proposed method, a hybrid algorithm is utilized to optimize the static flexible job-shop scheduling problem (FJSP) and dynamic flexible job-shop scheduling problem (DFJSP). This algorithm integrates the genetic algorithm (GA) as a global optimization technique with a simulated annealing (SA) algorithm serving as a local search optimization approach to accelerate convergence and prevent getting stuck in local minima. Additionally, variable neighborhood search (VNS) is utilized for efficient neighborhood search within this hybrid algorithm framework. For the FJSP, the proposed hybrid algorithm is simulated on a 40-benchmark dataset to evaluate its performance. Comparisons among the proposed hybrid algorithm and other algorithms are provided to show the effectiveness of the proposed algorithm, ensuring that the proposed hybrid algorithm can efficiently solve the FJSP, with 38 out of 40 instances demonstrating better results. The primary objective of this study is to perform dynamic scheduling on two datasets, including both single-purpose machine and multi-purpose machine datasets, using the proposed hybrid algorithm with a rescheduling strategy. By observing the results of the DFJSP, dynamic events such as a single machine breakdown, a single job arrival, multiple machine breakdowns, and multiple job arrivals demonstrate that the proposed hybrid algorithm with the rescheduling strategy achieves significant improvement and the proposed method obtains the best new solution, resulting in a significant decrease in makespan.

An improved memetic algorithm for multi-objective resource-constrained flexible job shop inverse scheduling problem: An application for machining workshop

Resource-constrained flexible job shop scheduling problems are commonly encountered in some manufacturing industries, and have been widely studied in recent years. However, traditional resource constrained flexible job shop scheduling problem rarely consider the uncertainties in actual manufacturing systems, which may make the original schedule become suboptimal or even unfeasible. Therefore, a resource constrained flexible job shop inverse scheduling problem (RCFJISP) is proposed in this paper, which aims to cope with uncertain events by simultaneously adjusting the machine, worker and process parameters of the original schedule. A multi-objective optimization model is constructed to minimize the makespan, worker cost, machine energy consumption and deviation index. Furthermore, an improved memetic algorithm (IMA) is developed for solving the proposed problem. In IMA, a novel double-layer encoding mechanism is designed to enhance the capacity in exploring new solution’s domains. Three initialization strategies utilizing original scheduling information are designed to improve the quality of initial solutions. An adaptive mutation strategy and a local search mechanism are designed to enhance exploration and exploitation ability of the algorithm. And a crowding operator is proposed to reflect the diversity of the population effectively. In computational experiments, 28 extended benchmarks are constructed, and the effectiveness of the proposed strategy and algorithm is verified by comparing IMA with its 4 variants and other 4 widely used algorithms. Finally, two inverse scheduling problems of a real-world hydraulic cylinder machining workshop under two uncertain situations are studied. The results demonstrate that IMA can effectively solve the actual inverse scheduling problem. With a slight adjustment to the original scheduling, it can reduce the makespan by 11.5%, the worker cost by 8.1% and the machine energy consumption by 27.9% on average.

Research on the performance of harmony search with local search algorithms for solving flexible job-shop scheduling problem

Combining the harmony search algorithm (HS) with the local search algorithm (LS) can prevent the HS from falling into a local optimum. However, how LS affects the performance of HS has not yet been studied systematically. Therefore, in this paper, it is first proposed to combine four frequently used LS with HS to obtain several search algorithms (HSLSs). Then, by taking the flexible job-shop scheduling problem (FJSP) as an example and considering decoding times, study how the parameters of HSLSs affect their performance, where the performance is evaluated by the difference rate based on the decoding times. The simulation results mainly show that (I) as the harmony memory size (HMS) gradually increases, the performance of HSLSs first increases rapidly and then tends to remain unchanged, and HMS is not the larger the better; (II) as harmony memory considering rate increases, the performance continues to improve, while the performance of pitch adjusting rate on HSLSs goes to the opposite; Finally, more benchmark instances are also used to verify the effectiveness of the proposed algorithms. The results of this paper have a certain guiding significance on how to choose LS and other parameters to improve HS for solving FJSP.