Distributed Job Shop Scheduling Research Articles

A hybrid genetic tabu search algorithm for distributed job-shop scheduling problems

The distributed job-shop scheduling problem (DJSP) is an extension of the traditional job-shop scheduling problem, which are composed of two sub-problems, assigning jobs to suitable factories and deciding the operation sequence on machines. To evaluate the performance of algorithms for solving DJSP, several famous benchmark instances have been proposed, and most of these instances have not been solved so far. This paper proposes a hybrid genetic tabu search algorithm (HGTSA) for solving DJSP. The proposed HGTSA combines the global search ability of the genetic algorithm (GA) and the local search ability of the tabu search (TS) well. In GA part, a crossover operation and a mutation operation are devised based on the critical factory. The two operations can effectively improve the discreteness of the population. In TS part, a tabu search procedure is performed on the critical factory. The procedure can effectively enhance the local search ability of HGTSA. For evaluating the performance of HGTSA, it has been compared with five classical algorithms on 240 benchmark instances. The computational results show the efficiency and effectiveness of HGTSA for solving DJSP. In particular, the proposed HGTSA updates the upper bounds for 235 out of these difficult instances.

Deep reinforcement learning for dynamic distributed job shop scheduling problem with transfers

Dynamic events and transportation constraints would significantly affect the full utilization of resources and the reduction of production costs in distributed job shops. Therefore, in this paper, a deep reinforcement learning algorithm (DRL)-based real-time scheduling method is developed to minimize the mean tardiness of the dynamic distributed job shop scheduling problem with transfers (DDJSPT) considering random job arrivals. Firstly, the proposed DDJSPT is modeled as a Markov decision process (MDP). Then, ten problem-oriented state features covering four aspects of factories, machines, jobs, and operations are elaborately extracted from the dynamic distributed job shop. After that, eleven composite rules considering the uniqueness of DDJSPT are constructed as a pool of actions to intelligently prioritize unfinished jobs and allocate the selected job to an appropriate factory. Moreover, a justified reward function adapted from the objective is designed for better convergence of DRLs. Subsequently, five DRLs are employed to address the DDJSPT, encompassing deep Q-network (DQN), double DQN (DDQN), dueling DQN (DlDQN), trust region policy optimization (TRPO), and proximal policy optimization (PPO). Finally, grounded in numerical comparison experiments under 243 production configurations of the DDJSPT, the effectiveness and generalization of DRL-based scheduling methods are credibly verified and confirmed.

A cooperative hierarchical deep reinforcement learning based multi-agent method for distributed job shop scheduling problem with random job arrivals

Distributed manufacturing can reduce the production cost through the cooperation among factories, and it has been an important trend in the industrial field. For the enterprises with daily delivered production tasks, the random job arrivals are regular. Thus, the Distributed Job-shop Scheduling Problem (DJSP) with random job arrivals is studied, and it is a typical case from the equipment manufacturing industry. The DJSP involves two coupled decision-making processes, job assigning and job sequencing, and the distributed and uncertain production environment requires the scheduling method to be more responsive and adaptive. Thus, a Deep Reinforcement Learning (DRL) based multi-agent method is explored, and it is composed of the assigning agent and the sequencing agent. Two Markov Decision Processes (MDPs) are formulated for the two agents respectively. In the MDP for the assigning agent, fourteen factory-and-job related features are extracted as the state features, seven composite assigning rules are designed as the candidate actions, and the reward depends on the total processing time of different factories. In the MDP of the sequencing agent, five machine-and-job related features are set as the state features, six sequencing rules make up the action space, and the change of the factory makespan is the reward. Besides, to enhance the learning ability of the agents, a Deep Q-Network (DQN) framework with variable threshold probability in the training stage is designed, which can balance the exploitation and exploration in the model training. The proposed multi-agent method’s effectiveness is proved by the independent utility test and the comparison test that are based on 1350 production instances, and its practical value in the actual production is implied by the case study from an automotive engine manufacturing company.

A novel priority dispatch rule generation method based on graph neural network and reinforcement learning for distributed job-shop scheduling

With the development of a global economy, distributed manufacturing becomes common in the industrial field. The Distributed Job-shop Scheduling Problem (DJSP), which is widespread in real-life production, is a hotspot in the academic field. The existing Priority Dispatch Rules (PDRs), which are used to assign a value to each waiting job according to some method and select the job with minimum or maximum “value” for next processing, are all relatively simple but lack self-learning ability, while the metaheuristics are all complex and with fixed evolutionary trajectory and cannot change with the manufacturing environment. This paper proposes a novel PDR generation method based on Graph Neural Network (GNN) and Reinforcement Learning (RL), which can self-learn and self-evolute by interacting with the scheduling environment. To combine DJSP with GNN closely, a new solution representation based on disjunctive graph is designed. DJSP is formulated as a Markov decision process, and the problem features and inner connections among the vertices of the disjunctive graph are fully explored by the GNN. An Actor-Critic RL method is applied to automatically train the network parameters to optimize the policy, so that it can be used to schedule the best action at each step. Comprehensive experiments on 240 test instances are conducted to evaluate the performance of the proposed method, and the results indicate that the proposed method shows greater effectiveness, generalizability and stability than other 8 classical PDRs, 5 metaheuristics and 3 RL-based methods.

Distributed shop scheduling: A comprehensive review on classifications, models and algorithms.

In the intelligent manufacturing environment, modern industry is developing at a faster pace, and there is an urgent need for reasonable production scheduling to ensure an organized production order and a dependable production guarantee for enterprises. Additionally, production cooperation between enterprises and different branches of enterprises is increasingly common, and distributed manufacturing has become a prevalent production model. In light of these developments, this paper presents the research background and current state of distributed shop scheduling. It summarizes relevant research on issues that align with the new manufacturing model, explores hot topics and concerns and focuses on the classification of distributed parallel machine scheduling, distributed flow shop scheduling, distributed job shop scheduling and distributed assembly shop scheduling. The paper investigates these scheduling problems in terms of single-objective and multi-objective optimization, as well as processing constraints. It also summarizes the relevant optimization algorithms and their limitations. It also provides an overview of research methods and objects, highlighting the development of solution methods and research trends for new problems. Finally, the paper analyzes future research directions in this field.

A discrete spotted hyena optimizer for solving distributed job shop scheduling problems

Scheduling is an important decision-making process for manufacturing companies. Shop scheduling is a subsection of scheduling related to manufacturing shops. The job shop scheduling problem (JSP) aims to minimize the makespan of a product value of the production process. This issue is related to optimizing the sequence of the jobs on appropriate machines. With globalization, manufacturing shops are scattered around the world. The distributed job shop scheduling problem (DJSP) tries to solve the optimizing sequence on these scattered facilities. DJSP is more complex than JSP. DJSP is solved by exact and heuristic solvers. Exact solvers more time-consuming processes for huge problems. In this work, a discrete version of the spotted hyena optimizer (DSHO) is proposed for solving DJSP. A workload-based facility order mechanism and a greedy heuristic approach are combined with the DSHO algorithm. 80 distributed job shop scheduling problems (DJSP) are solved by DSHO. For evaluating the performance of the DSHO, numerical results of the 480 (2 facilities to 7 facilities) large instances that are derived from well-known JSP benchmarks are compared with four different discrete meta-heuristic algorithms. The experimental results are shown that DSHO is a pioneer solver for DJSP.

Solving energy-efficient distributed job shop scheduling via multi-objective evolutionary algorithm with decomposition

Abstract The energy-efficient distributed job shop scheduling problem (EEDJSP) is studied in this paper with the criteria of minimizing both makespan and energy consumption. A mathematical model is presented and an effective modified multi-objective evolutionary algorithm with decomposition (MMOEA/D) is proposed. First, the encoding scheme and decoding scheme are designed based on the characteristics of the EEDJSP. Second, several initialization rules are fused together to produce a diverse population with certain diversity. Third, a collaborative search is proposed to exchange the information between individuals for exploring good solutions. Fourth, three problem-specific local intensification heuristics are designed. Moreover, an adaptive selection strategy is proposed to adjust the utilization of local search operators dynamically. Besides, an energy adjustment strategy is designed for further improvement. We carry out extensive numerical tests with the benchmarking instances. The effectiveness of local intensification as well as energy adjustment strategy is verified via the statistical comparisons. It also shows that the MMOEA/D outperforms other algorithms.

Distributed Job Shop Scheduling using Consensus Alternating Direction Method of Multipliers

Distributed Job Shop Scheduling using Consensus Alternating Direction Method of Multipliers

Deep reinforcement learning-based dynamic scheduling in smart manufacturing

Scheduling problems are a classic type of optimization problems in the manufacturing domain, such as job shop scheduling, flexible job shop scheduling, and distributed job shop scheduling problems. Especially, the dynamic task scheduling problem is closer to the requirements of real manufacturing systems than the static scheduling problem. In recent years, with the deeper application of the Internet of Things, big data, and cloud platform technologies, manufacturing systems have evolved from job shops to networked, collaborative and intelligent manufacturing systems. Smart manufacturing scheduling has some characteristics compared with job shop scheduling not only because of the larger number of tasks and services, but also because of the dynamic state of services and uncertainties. In this paper, we analyze the smart manufacturing service scheduling problem and give its mathematical description. Then a deep reinforcement learning-based method is proposed to minimize the maximum completion time of all tasks. In the system framework of the proposed method, the agent, environment, as well as the interaction between them, are designed. The queue times of all candidate services are considered as the system state, and the maximum queue time at the current moment is considered as the target value. Besides, we use two networks the prediction network and the target network to learn the prediction value and the target value, respectively. Two case studies are used to show the efficiency of the considered problem and the proposed method.

A review of job shop scheduling problems in multi-factories

The distributed job shop scheduling problem (DJSP) deals with the assignment of jobs to factories geographically distributed and with determining a good operation schedule of each factory. It is one of the well-known NP-hard combinatorial optimisation problem to solve optimally. In the last two decades, the problem has captured the interest of a number of researchers and therefore various methods have been employed to study this problem. In this paper, we first present an overview of pioneer studies conducted on solving distributed job shop scheduling problems and a classification of the employed techniques is given. Then, depth analysis of the outcome of existing literature is presented.

An Effective Multi-Objective Artificial Bee Colony Algorithm for Energy Efficient Distributed Job Shop Scheduling

Distributed Job Shop Scheduling Problem (DJSSP) is a generalization of the classic job shop scheduling problem (JSSP), characterized by simultaneously assigning jobs to different factories/workshops and determining their processing sequence. Due to energy efficient and productivity significantly affect the profits of enterprises, two criteria (i.e., makespan and total energy consumption) are used to evaluate the DJSSP. In this paper, a mixed integer programming model is developed, and a multi-objective artificial bee colony algorithm (MOABC) is proposed to evaluate the trade-off between the two objectives. In the MOABC, a solution encoding is represented by three parts: a factory assignment vector, a job permutation vector and a machine speed selection matrix. Meanwhile, a solution decoding is designed to present the scheduling scheme. A numerical experiment is designed to verify the effectiveness of the proposed MOABC. The experimental result demonstrates that the proposed MOABC can generate better Pareto solutions than NSGA-II and SPEA2 for the DJSSP.

A novel dynamic assignment rule for the distributed job shop scheduling problem using a hybrid ant-based algorithm

Distributed scheduling problems are among the most investigated research topics in the fields of Operational Research, and represents one of the greatest challenges faced by industrialists and researchers today. The Distributed Job shop Scheduling Problem (DJSP) deals with the assignment of jobs to factories and with determining the sequence of operations on each machine in distributed manufacturing environments. The objective is to minimize the global makespan over all the factories. Since the problem is NP-hard to solve, one option to cope with this intractability is to use an approximation algorithm that guarantees near-optimal solutions quickly. Ant based algorithm has proved to be very effective and efficient in numerous scheduling problems, such as permutation flow shop scheduling, flexible job shop scheduling problems and network scheduling, etc. This paper proposes a hybrid ant colony algorithm combined with local search to solve the Distributed Job shop Scheduling Problem. A novel dynamic assignment rule of jobs to factories is also proposed. Furthermore, the Taguchi method for robust design is adopted for finding the optimum combination of parameters of the ant-based algorithm. To validate the performance of the proposed algorithm, intensive experiments are carried out on 480 large instances derived from well-known classical job-shop scheduling benchmarks. Also, we show that our algorithm can process up to 10 factories. The results prove the efficiency of the proposed algorithm in comparison with others.

Agent-based fuzzy constraint-directed negotiation mechanism for distributed job shop scheduling

This paper presents an agent-based fuzzy constraint-directed negotiation (AFCN) mechanism to solve distributed job shop scheduling problems (JSSPs). The scheduling problem is modelled as a set of fuzzy constraint satisfaction problems (FCSPs), interlinked by inter-agent constraints. Each FCSP represents the perspective of the participants and is governed by autonomous agents. The novelty of the proposed AFCN is to bring the concept of a fuzzy membership function to represent the imprecise preferences of task start time for job and resource agents. This added information sharing is crucial for the effectiveness of distributed coordination. It not only can speed up the convergence, but also enforce a global consistency through iterative exchange of offers and counter-offers. The AFCN mechanism can also flexibly adopt different negotiation strategies, such as competitive, win–win, and collaborative strategies, for different production environments. The experimental results demonstrate that the proposed model can provide not only high-quality and cost-effective job shop scheduling (i.e., comparable to that of centralized methods) but also superior performance in terms of the makespan and average flow time compared with other negotiation models for agent-based manufacturing scheduling. As a result, the proposed AFCN mechanism is flexible and useful for distributed manufacturing scheduling with unforeseen disturbances.

An improved model and novel simulated annealing for distributed job shop problems

To benefit from globalization, the single-facility scheduling problem is extended to a distributed multi-facility level. This paper tackles both the mathematical modeling and solution techniques for the problem of distributed job shop scheduling. The problem is first mathematically formulated by a mixed integer linear programming model. This model supersedes the best available model in the literature in terms of both size and computational complexities. Moreover, novel simulated annealing algorithms are developed. These algorithms propose an advanced move operators matching the special encoding scheme used. The developed near-optimal search method has been enhanced by combining it with a local search method and adding advanced features to it such as the introduced restart phase. Also, we have hybridized the developed metaheuristic further with a greedy algorithm. Using the Taguchi method, the algorithm is finely tuned. Numerical experiments are conducted to evaluate the performance of the algorithms against an available genetic and a greedy algorithm. The results show that the proposed algorithm outperforms both algorithms.

Modeling and heuristics for scheduling of distributed job shops

This paper deals with the problem of distributed job shop scheduling in which the classical single-facility job shop is extended to the multi-facility one. The mathematical formulation of the problem is comprehensively discussed. Two different mixed integer linear programming models in form of sequence and position based variables are proposed. Using commercial software of CPLEX, the small sized problems are optimally solved. To solve large sized problems, besides adapting three well-known heuristics, three greedy heuristics are developed. The basic idea behind the developed heuristics is to iteratively insert operations (one at each iteration) into a sequence to build up a complete permutation of operations. The permutation scheme, although having several advantages, suffers from redundancy which is having many different permutations representing the same schedule. The issue is analyzed to recognize the redundant permutation. That improves efficiency of heuristics. Comprehensive experiments are conducted to evaluate the performance of the two models and the six heuristics. The results show sequence based model and greedy heuristics equipped with redundancy exclusion are effective for the problem.

A job shop distributed scheduling based on Lagrangian relaxation to minimise total completion time

This paper considers a distributed job shop scheduling problem where autonomous sub-production systems share common machines with each other. Each sub-production system is responsible for the scheduling of a set of jobs to minimise the total completion time on shared machines. A sub-production system has ultimate responsibility on maintaining private information such as objective function, processing time and routings on shared machines. Also sub-production systems must cooperate each other in order to achieve a global goal while sharing minimum of private information. In this research, we propose a distributed cooperation method in which sub-production systems and shared machines interact with one another to find a compromised solution between a locally optimised solution and a system-wide solution. We tested the proposed method for small, medium and large size of job shop scheduling problems and compared to a global optimal solutions. The proposed method shows promising results in terms of solution qualities and computational times.

Exploring local search in winner determination problem

In Combinatorial Auctions, multiple goods (items) are available for auction simultaneously, and bidders bid for combinations of goods called bundles. In the single unit combinatorial auction problem, there is only single unit of each item present and the items are considered to be indivisible. This forms the supply side constraint resulting in a need by the seller to decide on which bundles to allocate for maximizing the revenue. Determining these winning bundles is an NP-complete problem and is known by the name of Winner Determination Problem (WDP) in literature. Combinatorial auction mechanism has a wide range of practical applications such as allocation of railroads, auction of adjacent pieces of real estate, auction of airport landing slots, distributed job shop scheduling etc. The optimal heuristic search algorithms like CASS and CABOB proposed for solving the WDP take a lot of CPU time for solving large problem instances. Though these algorithms give optimal solutions, they would be useful only in scenarios where time is not at all a constraint, and the bidding is a one time affair. This poses a limitation in conducting combinatorial auctions with multiple rounds of bidding and hence hinders the widespread use of combinatorial auctions on the patterns of traditional English auction and internet auctions. Thus faster solution of WDP holds the key to widespread use and popularity of combinatorial auctions. This paper attempts to address the above issue, and proposes a simple local search technique LSWDP (Local Search for Winner Determination Problem) that runs very fast and provides solutions quite close to optimal for a number of applications. It also outputs optimal solutions in many instances taking only a fraction of the CPU time taken by CASS. In addition LSWDP was found to outperform the anytime algorithm CASS given a time cutoff. This paper also presents an enhancement called LSCN (Local Search using Complimentary Neighborhood) that provides still better solutions in terms of close to optimal behavior and achieves a much better strike rate in hitting optimal solutions. LSCN runs slower than LSWDP but still takes only a fraction of the CPU time taken by CASS thus encouraging the use of local search for combinatorial auctions. Finally, an extension to multi-partition search has been proposed and analyzed.

Exploring new patterns and mechanisms for advanced information technology and systems in the internet-era: introduction to the WITS’05 special issue

This special issue includes four articles that were presented in the 15th Workshop on Information Technology and Systems (WITS’05), held in December 10–11, 2005, Las Vegas, Nevada. Since its first meeting in 1991 in MIT, WITS has become a premier annual forum for discussion and interaction among scholars with research interests in the cutting edge issues of information technology and systems. WITS’05 addressed many important research issues as the corporate world evolves toward service-oriented computing that can support business on demand, enabled by the emergence of web services, agent technologies, wireless computing, e-commerce standards, P2P technologies, the business web, among other technologies. The four selected articles have been extended substantially and went through two rounds of reviews. Collectively, these four articles explore new patterns and mechanisms that extend the new boundaries of information technologies and systems. It is our pleasure to make these four fine articles available to the community through the journal of Information Technology and Management. We thank all authors and reviewers for their diligent work that made this special issue possible. Next, we give a brief overview of the four papers in terms of their main discoveries and important contributions. The first article, ‘‘Combining probability models and Web mining models: A framework for proper name transliteration’’ by Zhou, Huang, and Chen combines probability models and web mining models to develop a framework for proper name transliteration. The authors argue that web pages are created today in almost every popular language. However, language boundaries prevent information sharing and discovery across countries. Their paper studies transliteration (referred to that proper names are translated phonetically) issue on the Web. Previous transliteration models can be categorized into four approaches: a rule-based approach, a machine learning approach, a statistical approach, and a web mining approach. This paper proposes a generic proper name transliteration framework which improves the traditional statistical approach by incorporating an enhanced Hidden Markov Model and a web mining model. Evaluation of the proposed framework is very promising as it boosted the performance by 79.05%. Singh and Sen in their article ‘‘Exploring local search in winner determination problem,’’ report their research in developing a new combinatorial auction mechanism for a wide range of practical applications such as allocation of railroads, auction of adjacent pieces of real estate, auction of airport landing slots, and distributed job shop scheduling. Determining the winning bundles in combinatorial auctions is an NP-complete problem. The inefficiency problem in existing approaches to combinatorial auction poses a limitation in conducting combinatorial auctions with multiple rounds of bidding and hinders the widespread use of combinatorial auctions on the Internet. This paper proposes a local search algorithm for combinatorial auctions, which takes only fraction of the CPU time taken by T. Han College of Business, University of Nevada, NV, Las Vegas 89154, USA

Distributed constrained heuristic search

A model of decentralized problem solving, called distributed constrained heuristic search (DCHS), that provides both structure and focus in individual agent search spaces to optimize decisions in the global space, is presented. The model achieves this by integrating decentralized constraint satisfaction and heuristic search. It is a formalism suitable for describing a large set of distributed artificial intelligence problems. The notion of textures that allow agents to operate in an asynchronous concurrent manner is introduced. The use of textures coupled with distributed asynchronous backjumping, a type of distributed dependency-directed backtracking that the authors have developed, enables agents to instantiate variables in such a way as to substantially reduce backtracking. The approach has been tested experimentally in the domain of decentralized job-shop scheduling. A formulation of distributed job-shop scheduling as a DCHS and experimental results are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Exponentially distributed jobshop scheduling problems.

Consider n jobs and two machines (M1,M2). A job consists of a chain of operations requiring alternately one of the machines. For each job, the number of operations comprised in it, and the machine that the first operation requires, are given. Processing times of the operations requiring machine Ml(l=1,2) are independent random variables, identical -exponentially distributed with mean 1/λMl Preemptions are allowed. We prove that the longest - expected -remaining - processing time policy minimizes stochastically the schedule length. Surprisingly, it turns out that the shortest - expected - remaining - processing -time policy does not minimize the expected sum of completion times.