A population diffusion algorithm for energy-efficient distributed flexible job shop scheduling problem

Production scheduling is a critical requirement in today’s production systems. The production scheduling problem focuses on the rational allocation of production resources, determining the processing order of production tasks and operations, satisfying production constraints arising from the production environment such as the number of machines and task duration, and achieving optimal production goals, such as completing all tasks in the fastest way possible. The Flexible Job Shop Scheduling (FJSP) problem is a classical production scheduling issue, an extension of the Job Shop Scheduling (JSP) problem. The JSP problem involves allocating a set of jobs to a set of machines, where each job consists of multiple operations that must adhere to a precedence order. Each machine can process only one operation at a time for each job, and the time required for each operation on the corresponding machine is predetermined. The challenge in the JSP problem is to determine an appropriate order for processing operations or assignments, based on the production objective. FJSP represents a more complex and flexible variant of this problem, where at least one operation of a task can be performed on a set of alternative machines. Given that FJSP problems are NP-hard, solutions tend to be complex, varied, and often have limited applicability. Many FJSP scenarios require targeted modeling. In this paper, I propose a modeling approach for the static scheduling problem of job shops, considering low flexibility and demonstrating its usability by comparing it with other scheduling approaches, such as those based on genetic algorithm modeling. The paper is organized as follows:The first part of this paper offers a brief introduction to the FJSP problem, including background, research motivation, and main contributions, the second part provides a literature review,including a brief review and introduction of recent solutions to the FJSP problem, the third part describes a specific modeling approach, the fourth part details the test experiments and results of the modeling approach and includes comparisons with some other approaches, the fifth part analyzes the results from the fourth part and discusses the advantages and disadvantages of the modeling approach relative to others, and the sixth part concludes with a summary of findings and recommendations.

Flexible Job Shop Scheduling (FJSS) problem has many real-world applications such as manufacturing and cloud computing, and thus is an important area of study. In real world, the environment is often dynamic, and unpredicted job orders can arrive in real time. Dynamic FJSS consists of challenges of both dynamic optimisation and the FJSS problem. In Dynamic FJSS, two kinds of decisions (so-called routing and sequencing decisions) are to be made in real time. Dispatching rules have been demonstrated to be effective for dynamic scheduling due to their low computational complexity and ability to make real-time decisions. However, it is time consuming and strenuous to design effective dispatching rules manually due to the complex interactions between job shop attributes. Genetic Programming Hyper-heuristic (GPHH) has shown success in automatically designing dispatching rules which are much better than the manually designed ones. Previous works only focused on standard job shop scheduling with only the sequencing decisions. For FJSS, the routing rule is set arbitrarily by intuition. In this paper, we explore the possibility of evolving both routing and sequencing rules together and propose a new GPHH algorithm with Cooperative Co-evolution. Our results show that co-evolving the two rules together can lead to much more promising results than evolving the sequencing rule only.

A linguistic-based meta-heuristic modeling and solution approach for solving the flexible job shop scheduling problem (FJSSP) is presented in this study. FJSSP is an extension of the classical job-shop scheduling problem. The problem definition is to assign each operation to a machine out of a set of capable machines (the routing problem) and to order the operations on the machines (the sequencing problem), such that predefined performance measures are optimized. In this research, the scope of the problem is widened by taking into account the alternative process plans for each part (process plan selection problem). Probabilistic selection of alternative process plans and machines are also considered. The FJSSP is presented as a grammar and the productions in the grammar are defined as controls (Baykasoglu, 2002). Using these controls and Giffler and Thompson's (1960) priority rule-based heuristic along with the multiple objective tabu search algorithm of Baykasoglu et al. (1999) FJSSP is solved. This novel approach simplifies the modeling process of the FJSSP and enables usage of existing job shop scheduling algorithms for its fast solution. Instead of scheduling job shops with inflexible algorithms that cannot take into account the flexibility which is available in the job shop, the present algorithm is developed which can take into account the flexibility during scheduling. Such an approach will considerably increase the responsiveness of the job shops.

In real scheduling problems, unexpected changes may occur frequently such as changes in task features. These changes cause deviation from primary scheduling. In this article, a heuristic model, inspired from Artificial Bee Colony algorithm, is proposed for a dynamic flexible job-shop scheduling (DFJSP) problem. This problem consists of n jobs that should be processed by m machines and the processing time of jobs deviates from estimated times. The objective is near-optimal scheduling after any change in tasks in order to minimise the maximal completion time (Makespan). In the proposed model, first, scheduling is done according to the estimated processing times and then re-scheduling is performed after determining the exact ones considering machine set-up. In order to evaluate the performance of the proposed model, some numerical experiments are designed in small, medium and large sizes in different levels of changes in processing times and statistical results illustrate the efficiency of the proposed algorithm.

Flexible job shop scheduling problem (FJSP) is an extended formulation of the classical job shop scheduling problem, endowing great significance in the modern manufacturing system. The FJSP defines an operation that can be processed by any machine from a given set, which is a strong constrained NP-hard problem and intractable to be solved. In this paper, three recent proposed meta-heuristic optimization algorithms have been employed in solving the FJSP aiming to minimize the makespan, including moth-flame optimization (MFO), teaching-learning-based optimization (TLBO) and Rao-2 algorithm. Two featured FJSP cases are carried out and compared to evaluate the effectiveness and efficiency of the three algorithms, also associated with other classical algorithm counterparts. Numerical studies results demonstrate that the three algorithms can achieve significant improvement for solving FJSP, and MFO method appears to be the most competitive solver for the given cases.

The Flexible Job Shop scheduling Problem (FJSP) is a generalization of the classical Job Shop scheduling Problem (JSP) allowing to process operations on one machine out of a set of alternative machines. The FJSP is an NP-hard problem consisting of two sub-problems, which are the machine assignment and the operation scheduling problems. In this paper, we propose how to solve the FJSP by metaheuristics based on clustering in a holonic multiagent model. Firstly, a Neighborhood-based Genetic Algorithm (NGA) is applied by a scheduler agent for a global exploration of the search space. Secondly, a local search technique is used by a set of cluster agents to guide the research in promising regions of the search space and to improve the quality of the NGA final population. To evaluate our approach, numerical tests are made based on three sets of well known benchmark instances from the literature of the FJSP, which are Kacem, Brandimarte, Hurink. The experimental results show the efficiency of our approach in comparison to other approaches.

Flexible job shop scheduling problem (FJSP) has been extensively investigated and objectives are often related to time. Energy-related objective should be considered fully in FJSP with the advent of green manufacturing. In this study, FJSP with the minimisation of workload balance and total energy consumption is considered and the conflicting between two objectives is analysed. A shuffled frog-leaping algorithm (SFLA) is proposed based on a three-string coding approach. Population and a non-dominated set are used to construct memeplexes according to tournament selection and the search process of each memeplex is done on its non-dominated member. Extensive experiments are conducted to test the search performance of SFLA and computational results show the conflicting between two objectives of FJSP and the promising advantages of SFLA on the considered FJSP.

This paper researches on the flexible job shop scheduling problem (FJSP) with new job insertion. FJSP with new job insertion includes two phases: initializing schedules and rescheduling after new job(s) insertion. Initializing schedules is the standard FJSP problem while rescheduling is an FJSP with different job start time and different machine start time. The objective is to minimize maximum machine workload. A recently developed algorithm, so called Jaya, is employed to solve the FJSP with new job insertion and a discrete version of Jaya is proposed. Extensive computational experiments are carried out on eight real instances from remanufacturing enterprise. The discrete Jaya is compared to several existing heuristics and ensemble of them for FJSP with new job insertion. The results and comparisons verify that the discrete Jaya algorithm is superior over the existing methods. In future work, we will future improve the performance of discrete Jaya and compare it to more existing intelligent algorithms in literature.

The Flexible Job Shop Scheduling Problem (FJSP) is an extension of the classical job shop scheduling problem, which is characterized by the fact that each process can be processed on multiple candidate machines, and needs to solve the two subproblems of machine allocation and process sequencing simultaneously. Since FJSP is an NP-hard problem, its complexity and multi-objective characteristics make the traditional exact methods inefficient. At the same time, the existing intelligent optimization algorithms are prone to falling into local optimums, which makes it difficult to balance global exploration and local exploitation capabilities. To this end, this study proposed a Levy flight-based Harmony Search algorithm (LHS), which effectively avoids premature convergence by dynamically and adaptively adjusting the Harmony Memory Considering Rate (HMCR), the probability of Pitch Adjusting Rate (PAR), and the arbitrary distance Bandwidth(BW), and by introducing a Levy flight mechanism to perturb the parameters to broaden the search space and enhance the diversity of the population. We validate the experiments using 8 × 8, 10 × 10, and 10 benchmark instances proposed by Brandimarte in the literature, and the experimental results show that the Harmony search algorithm based on Levy flight outperforms the other comparative algorithms in terms of the solution quality and the convergence speed, demonstrating the effectiveness of its solution for FJSP.

Traditional planning and scheduling techniques still hold important roles in modern smart scheduling systems. Realistic features present in modern manufacturing systems need to be incorporated into these techniques. Flexible job-shop scheduling problem (FJSP) is one of the most challenging combinatorial optimization problems. FJSP is an extension of the classical job shop scheduling problem where an operation can be processed by several different machines. In this paper, we consider the FJSP with parallel operations (EFJSP) and we propose and compare a discrete firefly algorithm (FA) and a genetic algorithm (GA) for the problem. Several FJSP and EFJSP instances were used to evaluate the performance of the proposed algorithms. Comparisons among our methods and state-of-the-art algorithms are also provided. The experimental results demonstrate that the FA and GA achieved improvements in terms of efficiency and efficacy. Solutions obtained by both algorithms are comparable to those obtained by algorithms with local search. In addition, based on our initial experiments, results show that the proposed discrete firefly algorithm is feasible, more effective and efficient than our proposed genetic algorithm for the considered problem.

Scheduling for the flexible job shop is very important in both fields of production management and combinatorial optimization. However, when we attempt to formulate job shop scheduling problems which closely describe and represent the real world problem, various factors involved are often imprecisely or ambiguously known to the analyst. Also, in the real situations, machines are not continuously available due to preventive maintenance activity. Besides, in the production system, there are many users and machines in various priorities. Often, user satisfactions, machine stability and schedule itself are in conflict. By considering the imprecise or fuzzy nature of the data in real world problem, job shop scheduling with uncertain processing time and machine available constraint is introduced. Under the fuzzy circumstance, we attempt to make a feasible solution for flexible job shop scheduling problem (FJSSP) based on a hybrid optimization approach with multi-objective which not only to minimize the makespan, but also maximize the user satisfaction and machine stability. In the experiment, we make the comparisons with some other algorithms, such as genetic algorithm, to demonstrate the hybrid approach is much better on efficient search and stability with three benchmark examples. Sensitivity analysis is conducted to study the impact, in term of total objective, when the proportion of machine stability is varied.

The fuzzy processing time occasionally exists in job shop scheduling problem of flexible manufacturing system. To deal with fuzzy processing time, fuzzy flexible job shop model was established in several papers and has attracted numerous researchers’ attention recently. In our research, an improved version of discrete particle swarm optimization (IDPSO) is designed to solve flexible job shop scheduling problem with fuzzy processing time (FJSPF). In IDPSO, heuristic initial methods based on triangular fuzzy number are developed, and a combination of six initial methods is applied to initialize machine assignment and random method is used to initialize operation sequence. Then, some simple and effective discrete operators are employed to update particle’s position and generate new particles. In order to guide the particles effectively, we extend global best position to a set with several global best positions. Finally, experiments are designed to investigate the impact of four parameters in IDPSO by Taguchi method, and IDPSO is tested on five instances and compared with some state-of-the-art algorithms. The experimental results show that the proposed algorithm can obtain better solutions for FJSPF and is more competitive than the compared algorithms.

Particle swarm optimization is a population-based stochastic algorithm designed to solve difficult optimization problems, such as the flexible job shop scheduling problem. This problem consists of scheduling a set of operations on a set of machines while minimizing a certain objective function. This paper presents a two-level particle swarm optimization algorithm for the flexible job shop scheduling problem. The upper level handles the operations-to-machines mapping, while the lower level handles the ordering of operations on machines. A lower bound-checking strategy on the optimal objective function value is used to reduce the number of visited solutions and the number of objective function evaluations. The algorithm is benchmarked against existing state-of-the-art algorithms for the flexible job shop scheduling problem on a significant number of diverse benchmark problems.

The flexible job shop scheduling problem (FJSP) holds significant importance in both theoretical research and practical applications. Given the complexity and diversity of FJSP, improving the generalization and quality of scheduling methods has become a hot topic of interest in both industry and academia. To address this, this paper proposes a Preference-Based Mask-PPO (PBMP) algorithm, which leverages the strengths of preference learning and invalid action masking to optimize FJSP solutions. First, a reward predictor based on preference learning is designed to model reward prediction by comparing random fragments, eliminating the need for complex reward function design. Second, a novel intelligent switching mechanism is introduced, where proximal policy optimization (PPO) is employed to enhance exploration during sampling, and masked proximal policy optimization (Mask-PPO) refines the action space during training, significantly improving efficiency and solution quality. Furthermore, the Pearson correlation coefficient (PCC) is used to evaluate the performance of the preference model. Finally, comparative experiments on FJSP benchmark instances of varying sizes demonstrate that PBMP outperforms traditional scheduling strategies such as dispatching rules, OR-Tools, and other deep reinforcement learning (DRL) algorithms, achieving superior scheduling policies and faster convergence. Even with increasing instance sizes, preference learning proves to be an effective reward mechanism in reinforcement learning for FJSP. The ablation study further highlights the advantages of each key component in the PBMP algorithm across performance metrics.

The classic job shop scheduling problem mainly focuses on one kind of manufacturing resources, such as machine tools, and etc. But the job shop scheduling in practical production activities always needs to consider the constraints of different manufacturing resources. In this paper, a double-resource flexible job shop scheduling problem (DFJSSP) is presented. Both machines and workers are considered in the process of job shop scheduling in this DFJSSP. And a genetic algorithm (GA) is used to solve this problem, in which a new well designed three-layer chromosome encoding method has been adopted and some effective crossover and mutation operators are designed. Finally, a case study is used to validate the method.