A Two-Layer Reinforcement Learning-Integrated Genetic Algorithm for Flexible Job Shop Scheduling Considering Transportation Constraints

This paper undertakes an innovative review and organization of the relevant issues of the FJSP in the genetic algorithm to provide some systematic way of organizing its issues and provide useful insights in this method of the genetic algorithm Flexible Job-shop Scheduling Problem (FJSP) is a type of scheduling problem with a wide range of application backgrounds. In recent years, genetic algorithms have become one of the most popular algorithms for solving FJSP problems and have attracted widespread attention. In this paper, a comprehensive review of chromosome coding methods of the genetic algorithm for solving the FJSP and three standards are used to compare the advantages and disadvantages of each coding method. The results show that MSOS-I coding is a better chromosomal encoding method for solving FJSP problems, whose chromosome structure is simple, feasibility and larger storage. The main contribution of this paper is to fill the literature gap, because No such comprehensive review of the FJSP in the GA prevails in the existing literature. This comprehensive review will be useful for scholars and practical applications of the FJSP and the genetic algorithm for artificial intelligence and machine learning implementations and applications.

An Efficient Two-Stage Genetic Algorithm for Flexible Job-Shop Scheduling

Flexible job-shop scheduling problem (FJSP) is an extended job-shop scheduling problem. FJSP allows an operation to be processed by several different machines. FJSP with overlapping in operations means that each operation is divided into several sublots. Sublots are processed and transferred separately without waiting for the entire operation to be processed. In previous research, a mathematical model was developed and a genetic algorithm proposed to solve this problem. In this study, we try to improve the procedure of previous research to achieve better results. The proposed improvements were tested on some benchmark problems and compared with the results obtained by previous research.

The flexible job shop scheduling problem (FJSP) is an extension of the classical job shop scheduling problem (JSP) which allows an operation to be processed by any machine from a given set of machines. FJSP is NP-hard and presents two major difficulties. The first is to assign each operation to a machine out of a set of capable machines; and the second deals with sequencing the assigned operations on the machines. However, it is quite difficult to obtain an optimal solution to this problem in medium and large size problems with traditional optimization approaches. In this paper, a memetic algorithm (MA) for flexible job shop scheduling with overlapping operations is proposed that solves the FJSP to minimize makespan. We also proposed a heuristic that uses the critical path method (CPM) in order to improve the results of MA and reduce the objective function. The experimental results of MA and CPM show that our approach is capable of achieving the optimal solution for small size problems and near-optimal solutions for medium and large size problems in a reasonable time.

The flexible job shop scheduling problem (FJSSP) is an extension of the classical job shop scheduling problem (JSSP). The classical JSSP determines the job sequence for each machine. In contrast, FJSSP decides not only the job sequence but also the machine assignment for jobs; thus, it is a combinatorial optimization problem of a larger scale. To efficiently solve an FJSSP, which is non-deterministic polynomial-time hard, we require a heuristic method. In previous studies, the FJSSP has been solved by neighborhood algorithms, which employ various metaheuristic methods. Some approaches constrain the neighborhood operation from jobs on a critical path and simultaneously change the machine assignment and job sequence. However, a method that can independently change machine assignment and job sequence may improve the efficiency of FJSSP because the solution of JSSP already exists. In this study, we investigate the effect of continuing to change job sequence and machine assignment, and job sequence and machine assignment change are iterated using a local search method. In numerical experiments, the effects of the frequency of job sequence change and machine assignment change on the performance of the solution are investigated. Finally, we find the best machine assignment and job sequence change method for FJSSP.

Flexible job-shop scheduling problem (FJSP) is extension of job-shop scheduling problem which allows an operation to be performed by any machine among a set of available machines. In many FJSP, it is assumed that a lot which contains a batch of identical items is transferred from one machine to the next only when all items in the lot have completed their processing. In this paper, FJSP with overlapping in operations is handled. According to this approach, sublots are transferred from one machine to the next for processing without waiting for the entire lot to be processed at the predecessor machine. The study is carried out in two steps. In the first step, a new mathematical model is developed for the considered problem and compared to other model in the literature in terms of computational efficiency. However, it is quite difficult to achieve an optimal solution for real size problems with mathematical modelling approach because of its NP-hard structure. Thus, in the second step, a genetic algorithm is proposed to solve this problem. An effective chromosome representation is used and in generation of initial population, a new search methodology is developed. At the same time, efficient decoding methodology is adopted considering only active schedule in order to reduce the search space. The proposed algorithm was tested on benchmark problems taken from literature of different scales. Obtained results were compared with the results obtained by other algorithms. Computational studies show that our algorithm surpasses other known algorithms for the same problem, and gives results comparable with the best algorithm known so far.

A flexible casting job shop scheduling problem (FCJSP) with batch processing machines is proposed based on the analysis of the flexible job shop scheduling problem (FJSP) and the study of the expendable casting process. Considering the makespan under the influence of the energy consumption, the authors apply the time execution window to the FCJSP model in conjunction with the characteristics of casting production. A hybrid particle swarm optimisation algorithm (HPSO) is developed to solve the FCJSP. The HPSO employs a block integration decoding rule to address scheduling integration. Particle swarm optimisation is used for global search, employing both discrete and continuous search strategies. Furthermore, the local search employs tabu search with neighbourhood operations based on knowledge‐driven techniques. Simulation experiments demonstrate the feasibility of the proposed optimisation model. In the end, the HPSO algorithm has been successfully applied to the real expendable casting scheduling. The results demonstrate that it is more efficient and robust than previously reported algorithms.

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

Flexible job shop scheduling (FJSS) problems which are parts of real life applications are the extended case of classical job shop scheduling (JSS) problems. There are no parallel machines at JSS problems. FJSS Problems arise when works need to be done on parallel machines in the workshop. In FJSS problems, jobs have different routes and each job is consisted of at least one operation. These operations are processed by any of the machine sets which are parallel to each other. In literature; the number of studies on FJSS problems are more limited than the one on JSS problems. In this paper, recent studies in the literature on the topic of FJSS problems are reviewed. The findings and recommendations on the solution of this kind of problems by using meta-heuristic methods are presented.

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.

An effective backtracking search algorithm for multi-objective flexible job shop scheduling considering new job arrivals and energy consumption

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.

This paper presents a flexible job shop scheduling problem with fuzzy processing time. An efficient decomposition-integration genetic algorithm (DIGA) is developed for the problem to minimise the maximum fuzzy completion time. DIGA uses a two-string representation, an effective decoding method and a main population. In each generation, DIGA decomposes the chromosomes of the main population into a job sequencing part and a machine assigning part and independently evolves the populations of these parts. Some instances are designed and DIGA is tested and compared with other algorithms. Computational results show the effectiveness of DIGA.

Green manufacturing has become a new production mode for the development and operation of modern and future manufacturing industries. The flexible job shop scheduling problem (FJSP), as one of the key core problems in the field of green manufacturing process planning, has become a hot topic and a difficult issue in manufacturing production research. In this paper, an improved multi-objective wolf pack algorithm (MOWPA) is proposed for solving a multi-objective flexible job shop scheduling problem with transportation constraints. Firstly, a multi-objective flexible job shop scheduling model with transportation constraints is established, which takes the maximum completion time and total energy consumption as the optimization objectives. Secondly, an improved wolf pack algorithm is proposed, which designs individual codes from two levels of process and machine. The precedence operation crossover (POX) operation is used to improve the intelligent behavior of wolves, and the optimal Pareto solution set is obtained by introducing non-dominated congestion ranking. Thirdly, the Pareto solution set is selected using the gray relational decision analysis method and analytic hierarchy process to obtain the optimal scheduling scheme. Finally, the proposed algorithm is compared with other algorithms through a variety of standard examples. The analysis results show that the improved multi-objective wolf pack algorithm is superior to other algorithms in terms of solving speed and convergence performance of the Pareto solution, which shows that the proposed algorithm has advantages when solving FJSPs.

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.