Multi-objective Flexible Job-shop Scheduling Problem Research Articles

Energy-saving scheduling strategy for variable-speed flexible job-shop problem considering operation-dependent energy consumption

The rapid growth of industrial production signifies its CO2 footprint and climate impact, highlighting the demand for efficient and energy-saving production scheduling. Generally, a single production job comprises multiple operations on various machines. Existing studies estimate job energy consumption from a broader perspective, often disregarding the detailed scheduling of operations. This simplification may result in inaccurate evaluations of energy consumption and savings, as energy consumption can differ significantly among operations, with each requiring specific levels of energy on various machines. Proposing a new scheduling framework to replace the classical strategy is challenging yet necessary due to these variations. This study aims to investigate the multiobjective flexible job-shop scheduling problem by considering operation-dependent energy consumption and to improve the accuracy and thoroughness of the energy-consumption evaluation framework. First, a core metamodel for energy assessment is established and a mathematical model is introduced to minimize the manufacturing span and total energy consumption. Subsequently, a dynamic diffusion weight adjustment for a multiobjective evolutionary algorithm based on decomposition (MOEA/D-DDWA) is proposed. Operation-dependent energy consumption and processing quality are discussed, and a superior unified energy-saving strategy is designed to facilitate the selection of the processing-speed range, balancing energy consumption and saving. Finally, numerical experiments are conducted based on datasets of various scales, demonstrating that the core metamodel for energy assessment can achieve significant energy savings. Compared with other classical multiobjective optimization algorithms, the MOEA/D-DDWA is more energy efficient.

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.

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.

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.

Research on Flexible Job Shop Scheduling Problem with Handling and Setup Time Based on Improved Discrete Particle Swarm Algorithm

With the gradual emergence of customized manufacturing, intelligent manufacturing systems have experienced widespread adoption, leading to a surge in research interests in the associated problem of intelligent scheduling. In this paper, we study the flexible job shop scheduling problem (FJSP) with setup time, handling time, and processing time in a multi-equipment work center production environment oriented toward smart manufacturing and make-to-order requirements. A mathematical model with the optimization objectives of minimizing the maximum completion time, the total number of machine adjustments, the total number of workpieces handled and the total load of the machine is constructed, and an improved discrete particle swarm algorithm based on Pareto optimization and a nonlinear adaptive inertia weighting strategy is proposed to solve the model. By integrating the model characteristics and algorithm features, a hybrid initialization method is designed to generate a higher-quality initialized population. Next, three cross-variance operators are used to implement particle position updates to maintain information sharing among particles. Then, the performance effectiveness of this algorithm is verified by testing and analyzing 15 FJSP test instances. Finally, the feasibility and effectiveness of the designed algorithm for solving multi-objective FJSPs are verified by designing an FJSP test example that includes processing time, setup time and handling time.

Energy-efficient scheduling for a flexible job shop problem considering rework processes and new job arrival

Sustainable production is not limited to environmental concerns only; It also provides economic benefits for businesses. Businesses that adopt sustainability principles can gain advantages in matters such as cost savings, competitive advantage, risk management, legal compliance and corporate reputation. Therefore, sustainability is no longer an option but a strategic imperative for businesses. For this reason, studies on energy-sensitive scheduling have started to increase recently. Another important factor in sustainable manufacturing is the reduction of scrap. Rework operations are required to reduce scrap. In this study, the multi-objective flexible job shop scheduling problem (MO-FJSP) that considers energy efficiency is discussed. The created model aims to minimize the energy consumption, total machine workload and makespan. In this study, new job arrivals are considered as dynamic events. Another dynamic event added to the model is the addition of rework processes between operations to reduce the scrap rate when a scrap decision is made during the production stages. The enhanced NSGA II algorithm was applied to solve this problem. The enhanced NSGA II algorithm was applied to test instances and its performance was compared using some of the multi-objective performance indicators. These experimental results prove the effectiveness of the proposed solution method.

A Study of Deep Learning Neural Network Algorithms and Genetic Algorithms for FJSP

Flexible job-shop scheduling problem (FJSP) is a new research hotspot in the field of production scheduling. To solve the multiobjective FJSP problem, the production of flexible job shop can run normally and quickly. This research takes into account various characteristics of FJSP problems, such as the need to ensure the continuity and stability of processing, the existence of multiple objectives in the whole process, and the constant complexity of changes. It starts with deep learning neural networks and genetic algorithms. Long short-term memory (LSTM) and convolutional neural networks (CNN) are combined in deep learning neural networks. The new improved algorithm is based on the combination of deep learning neural networks LSTM and CNN with genetic algorithm (GA), namely, CNN-LSTM-GA algorithm. Simulation results showed that the accuracy of the CNN-LSTM-GA algorithm was between 85.2% and 95.3% in the test set. In the verification set, the minimum accuracy of the CNN-LSTM-GA algorithm was 84.6%, both of which were higher than the maximum accuracy of the other two algorithms. In the FJSP simulation experiment, the AUC value of the CNN-LSTM-GA algorithm was 0.92. After 40 iterations, the F1 value of the CNN-LSTM-GA algorithm remained above 0.8, which was significantly higher than the other two algorithms. CNN-LSTM-GA is superior to the other two algorithms in terms of prediction accuracy and overall performance of FJSP. It is more suitable for solving the discrete manufacturing job scheduling problem with FJSP characteristics. This study significantly raises the utilisation rate of the assembly shop’s equipment, optimises the scheduling of FJSP, and fully utilises each processing device’s versatile characteristics, which are quite useful for the production processes of domestic vehicle manufacturing companies.

Multiobjective Optimization for FJSP Under Immediate Predecessor Constraints Based OFA and Pythagorean Fuzzy Set

In the flexible job shop scheduling problem (FJSP), immediate predecessor operations have an explicit impact on the scheduling results, and are often ignored. To analyze the influence of immediate predecessor operations on machine tool manufacturing workshops, four forms of immediate predecessor operations with the consideration of uncertain transportation and preparation time are defined. Then, the four forms of immediate predecessor operations are integrated into the FJSP, and a multiobjective FJSP is constructed. An improved optimal foraging algorithm (OFA) and Pythagorean fuzzy set (PFS) are combined to establish a multiobjective optimization algorithm, named PFSOFA. This algorithm is then used to solve the multiobjective FJSP. In PFSOFA, the Pareto fronts are mapped into PFSs. The Pythagorean fuzzy numbers (PFNs) in a PFS are transformed into right triangles, and the distances between the PFNs and the reference PFNs are defined as the distances between their right triangle centroids. Then, all distances of a PFS are integrated by the distance prospect function to obtain a distance prospect value. This value is then used to lead the iteration of PFSOFA. Through extensive experiments, including a real factory application case, the performance of PFSOFA is verified to be better than four classical multiobjective optimization algorithms for solving the multiobjective FJSP constructed in this paper. And for the factory case, PFSOFA also obtained the better schemes.

The Optimization of Multi-objective FJSP Based on the Hybrid Algorithm

The flexible job-shop scheduling problem (FJSP) is a critical model in manufacturing systems that assigns operations from different jobs to various machines. However, optimizing multiple targets during the production scheduling process is always necessary. While the non-dominated sorting genetic algorithm (NSGA-II) is an effective method to solve the multi-objective FJSP, it can have the main drawbacks of converging too early and falling into local optimization. To address these issues, this research proposes a hybrid algorithm that combines NSGA-II and multi-objective simulated annealing using a pareto-domination based acceptance criterion (PDMOSA). The PDMOSA has a powerful search performance that can overcome the limitations of NSGA-II. The hybrid algorithm also includes original modification methods such as a deletion criterion, duplicated solution deletion, and new individual adding. Additionally, a plug-in decoding method is introduced. The proposed hybrid algorithm is compared with several improved ways based on NSGA-II in various experiments. The results demonstrate that the performance of the hybrid algorithm is better than the others in multi-objective FJSP.

Application of hybrid artificial bee colony algorithm based on load balancing in aerospace composite material manufacturing

The manufacturing of composite materials for the aerospace industry represents a cornerstone of future development in this advanced field. In this study, a mathematical model of flexible job-shop scheduling problem (FJSP) was established by extracting the key manufacturing information from an aerospace composite manufacturing workshop. Intelligent algorithms can effectively solve FJSP. However, when applied to a multi-objective FJSP (MOFJSP), they suffer from drawbacks such as blind search and low efficiency. Therefore, this study proposes a new artificial bee colony algorithm and implements it as part of a hybrid method (referred to as the HMABC) to solve MOFJSP. The method involves three steps: (1) A multiple-rule initial population is constructed to minimize randomness and improve quality. (2) A greedy decoding method is used to decode each individual to further narrow the search range to replace the conventional decoding method. (3) By considering the machine load index (which has often been neglected), the concept of machine load rate is proposed, and three heuristic strategies are designed (with the influences ranging from small to high) to diverge the solution in all directions instead of just a direction. The performance of the proposed method is compared with those of existing algorithms using a classical FJSP test example, and the effectiveness and efficiency of HMABC is verified. Finally, the method is applied to an actual aerospace composite manufacturing system to realize the scheduling of actual production activities.

A Two-Stage Multi-Objective Genetic Algorithm for a Flexible Job Shop Scheduling Problem with Lot Streaming

The work in this paper is motivated by a recently published article in which the authors developed an efficient two-stage genetic algorithm for a comprehensive model of a flexible job-shop scheduling problem (FJSP). In this paper, we extend the application of the algorithm to solve a lot streaming problem in FJSP while at the same time expanding the model to incorporate multiple objectives. The objective function terms included in our current work are the minimization of the (1) makespan, (2) maximum sublot flowtime, (3) total sublot flow time, (4) maximum job flowtime, (5) total job flow time, (6) maximum sublot finish-time separation, (7) total sublot finish-time separation, (8) maximum machine load, (9) total machine load, and (10) maximum machine load difference. Numerical examples are presented to illustrate the greater need for multi-objective optimization in larger problems, the interaction of the various objective function terms, and their relevance in providing better solution quality. The ability of the two-stage genetic algorithm to jointly optimize all the objective function terms is also investigated. The results show that the algorithm can generate initial solutions that are highly improved in all of the objective function terms. It also outperforms the regular genetic algorithm in convergence speed and final solution quality in solving the multi-objective FJSP lot streaming. We also demonstrate that high-performance parallel computation can further improve the performance of the two-stage genetic algorithm. Nevertheless, the sequential two-stage genetic algorithm with a single CPU outperforms the parallel regular genetic algorithm that uses many CPUs, asserting the superiority of the two-stage genetic algorithm in solving the proposed multi-objective FJSP lot streaming.

A reinforcement learning based RMOEA/D for bi-objective fuzzy flexible job shop scheduling

The flexible job shop scheduling problem (FJSP) is significant for realistic manufacturing. However, the job processing time usually is uncertain and changeable during manufacturing. This paper presents a multi-objective FJSP with fuzzy processing time (MOFFJSP) for optimizing the makespan and total machine workload as objectives. To solve the MOFFJSP, a MOEA/D based on reinforcement learning named RMOEA/D is proposed. RMOEA/D can be featured as: (i) an initial strategy with three rules is used to get a high-quality initial population; (ii) a parameter adaption strategy based on Q-learning is proposed to guide the population choose the best parameter to increase diversity; (iii) a variable neighborhood search based on reinforcement learning is designed to lead the solution to choose the right local search method; and (iv) an elite archive is used to improve the usage rate of the abandoned historical solution. RMOEA/D is compared with five well-known realted methods, i.e., MOEA/D, NSGA-II, MOEA/D-M2M, NSGA-III and IAIS on three benchmark suites. The results show that RMOEA/D outperforms these five state-of-art algorithms.

Multi-objective flexible job-shop scheduling problem researching based on improved adaptive NSGA-II

To solve the scheduling problem of products manufacturing in the military electronic equipment enterprises, a multi-objective flexible job-shop scheduling model was established with the objective of minimum the make span, production costs and equipment load. According to the characteristics of flexible job-shop scheduling problem, an adaptive NSGA-II algorithm was proposed in this paper, which could change the probabilities of crossover and mutation operation at different stages of genetic processes. To improve the diversity of population, the algorithm performed independent crossover and mutation operations on the working processes and equipment. Besides, a population independent elite retention strategy was adopted to avoid the loss of optimum solutions. At last, the feasibility and validity of the improved adaptive NSGA-II are verified by a flexible job-shop example.

An Effective Hybrid Multiobjective Flexible Job Shop Scheduling Problem Based on Improved Genetic Algorithm

Multiobjective Flexible Job Shop Scheduling Problem (MO-FJSP) is a scheduling problem used in manufacturing sectors to use energy efficiently and thriftily. The scheduling problem aims to increase productivity and reduce energy consumption via a mathematical model. With this paper, an effective genetic algorithm is proposed for MO-FJSP based on maximum completion time, total machine load, and bottleneck machine load. The solution method utilizes a hybrid multiobjective genetic algorithm. A combination of global selection and fast selection is used for initialization and obtaining a uniformly distributed initial population. The cross-variance operator is adaptively improved to enhance the searching in the population. Following that an elite retention mechanism is designed to address the possible limitations of the elite strategy in maintaining population diversity. As a result, an improved harmonic search algorithm is introduced to improve the quality of individuals in the elite pool. The proposed hybrid method is implemented in MATLAB R2018a. Tests were conducted using the benchmark Kacem test set, the BR data data set, and with the actual production cases. The algorithm succeeded in achieving 13 nondominated solutions in the initial 20 runs. Moreover, the method obtains the optimal value criterion for the solution accuracy factor. As a whole, results of the evaluation testify that the proposed method can be used to solve the MO-FJSP with high accuracy and fast convergence. The method also provides feasible and effective scheduling solutions for the decision-makers in actual production. Based on the promising results obtained, it is deduced that the method has a wide applicability range particularly in manufacturing sector.

A multi-objective flexible job-shop cell scheduling problem with sequence-dependent family setup times and intercellular transportation by improved NSGA-II

With the development of Industry 4.0 and requirement of smart factory, cellular manufacturing system (CMS) has been widely concerned in recent years, which may leads to reducing production cost and wip inventory due to its flexibility production with groups. Intercellular transportation consumption, sequence-dependent setup times, and batch issue in CMS are taken into consideration simultaneously in this paper. Afterwards, a multi-objective flexible job-shop cell scheduling problem (FJSCP) optimization model is established to minimize makespan, total energy consumption, and total costs. Additionally, an improved non-dominated sorting genetic algorithm is adopted to solve the problem. Meanwhile, for improving local search ability, hybrid variable neighborhood (HVNS) is adopted in selection, crossover, and mutation operations to further improve algorithm performance. Finally, the validity of proposed algorithm is demonstrated by datasets of benchmark scheduling instances from literature. The statistical result illustrates that improved method has a better or an equivalent performance when compared with some heuristic algorithms with similar types of instances. Besides, it is also compared with one type scalarization method, the proposed algorithm exhibits better performance based on hypervolume analysis under different instances.

A non-dominated ensemble fitness ranking algorithm for multi-objective flexible job-shop scheduling problem considering worker flexibility and green factors

The worker flexibility and green production related factors are two key aspects that widely exit in real-life production and seriously affect the production efficiency and ecological environment, while both of them are usually neglected in the existing scheduling studies. In this paper, a multi-objective flexible job-shop scheduling problem considering worker flexibility and green factors (MO-FJSPG) is explored with the criteria of minimizing makespan, labor cost and green production related factors. A non-linear integer programming model is constructed for MO-FJSPG and a new non-dominated ensemble fitness ranking algorithm (NEFRL) is proposed to solve this problem. In the NEFRL, a specific three-layer representation method is proposed; a non-dominated ensemble fitness ranking method is developed to rank and select solutions for the next generation; a local search method based on critical path is designed to strengthen the exploitation ability of the algorithm and used to optimize the non-dominated solutions further in each iteration. Finally, 31 instances are constructed and the effectiveness of NEFRL is verified by comparing with other multi-objective algorithms.

A decomposition-based artificial bee colony algorithm for the multi-objective flexible jobshop scheduling problem

Competition among companies leads to a race in order to improve the management system of their production with respect to the delivery time. In the last few decades, the optimization of production scheduling has attracted the interest of numerous researchers. This article deals with the Flexible Jobshop Scheduling Problem (FJSP) as one of the most challenging combinatorial optimization problems. FJSP is an extension of the classical jobshop scheduling problem, in which an operation can be processed by several different machines. This article presents a new decomposition based artificial bee colony algorithm for the multi-objective FJSP. The proposed algorithm is tested and compared to other algorithms from the literature on benchmarks of the multi-objective FJSP and its superior performance and robust results have been proved.

Modified Multi-Crossover Operator NSGA-III for Solving Low Carbon Flexible Job Shop Scheduling Problem

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.

An improved non-dominated sorting biogeography-based optimization algorithm for the (hybrid) multi-objective flexible job-shop scheduling problem

With the continuous advancement of intelligent manufacturing and industry 4.0, production scheduling has become a significant problem that most enterprises must deal with. Thereinto, (hybrid) multi-objective flexible job-shop scheduling problem, widely existing in the real-life manufacturing systems, is one of the NP-hard problems in various scheduling problems. Consequently, in this paper, an improved non-dominated sorting biogeography-based optimization (INSBBO) algorithm has been proposed to solve the problem. First of all, to overcome the pressure scarcity of individual selection in the Pareto dominance principle, especially in the late iteration of the algorithm, a novel V-dominance principle based on the volume enclosed by the normalized objective function values has been developed to enhance the convergence speed. Then, a hybrid variable neighborhood search (HVNS) structure is designed as a local search algorithm to amend the local search ability. Thereafter, for avoiding the loss of the partial (sub-)optimal solutions in the iteration, an elite storage strategy (ESS) is constructed to store the (sub-)optimal solutions. Additionally, we modify the internal habitat suitability index (HSI), migration and mutation operators of the NSBBO algorithm to further improve its performance. To evaluate the effectiveness of the above improved operations and the robustness of parameter setting, we compare the performances of each modified operation and critical parameter combination through multiple independent running the typical scheduling instance from the literature. The statistical results exhibit that each amended operation has a significant influence on the performance of INSBBO and its key parameter configuration is robust. Meanwhile, INSBBO has a better or similar performance among other state-of-the-art intelligent algorithms by comparing three classical benchmark scheduling datasets.

An improved artificial bee colony algorithm for solving multi-objective low-carbon flexible job shop scheduling problem

Based on the analysis of multi-objective flexible job-shop scheduling problem (FJSP), a multi-objective low-carbon job-shop scheduling problem(MLFJSP) with variable processing speed constraint is proposed in this paper. The optimization objectives of MLFJSP include minimizing the makespan, total carbon emission and machine loading. Meanwhile, an improved artificial bee colony algorithm (IABC) is designed to solve the MLFJSP. The improvement of algorithm mainly includes: (1) an effective three-dimensions encoding/decoding mechanism and a mixed initialization strategy are designed to generate a better initial population; (2) special crossover operators and mutation operators were designed to increase the diversity of the population in the employed bee phase; (3)an efficient dynamic neighbor search (DNS) is applied to enhance local search capabilities in the onlooker bee phase; (4) the new food sources generation strategy was proposed to reduce the blindness in the scout bee phase. Finally, this paper carried out a series of comparative experimental studies, including the comparison before and after algorithm improvement, and the comparison between the improved algorithm with MOPSO, MODE and NSGA-II. The results demonstrate that the IABC can achieve a better performance for solving the MLFJSP.