Distributed Flow Shop Research Articles

A reinforcement learning hyper-heuristic algorithm for the distributed flowshops scheduling problem under consideration of emergency order insertion

Large enterprises are composed of several subproduction centers. The production plan is changed based on the procedure of the manufacturing system. The distributed flowshop scheduling problem under consideration of emergence order insertion is challenging as the assignment of the product, and the scheduling of the process are coupled with each other. A general distributed flow shop scheduling problem regarding emergency order insertion (DFSP_EOI) is addressed under rescheduling circumstances in this paper. The Q-learning hyper-heuristic algorithm with dynamic insertion rule (QLHH_DIR) is proposed to solve the DFSP_EOI. Eight low-level heuristics (LLHs) for static job assignment. A dynamic insertion rule based on the state of each production center is designed for emergency order insertion. The Q-learning mechanism at high-level space selects appropriate LLH through learning the experience from the optimization process. The computational simulation is carried out, and the results confirm that the proposed algorithm is superior to the competitors in solving the distributed flow shop rescheduling problem. The results of the 720 problem instances show that the proposed algorithm is highly efficient in rescheduling problems.

The paradoxes, accelerations and heuristics for a constrained distributed flowshop group scheduling problem

In this paper, we tackle a previously unexplored challenge in contemporary manufacturing: constrained distributed flowshop group scheduling problem (CDFGSP). Different from the traditional distributed flowshop group scheduling problem (DFGSP), CDFGSP introduces a unique perspective: some job families are bounded by particular production specifications and share a common deadline, while the remaining job families are not subject to such limits. This real-world constraint complicates the problem, and often results in infeasible solutions when using existing algorithms. To address the problem, a mathematical model for CDFGSP with the objective of minimizing makespan is first established. Then, we uncover three counterintuitive paradoxes resulting in invalid searches, summarize two new bound theories to exclude infeasible insertions and provide two accelerations for evaluating constraints and computing optimization objectives. Integrating the above problem properties, we propose four composite heuristics, each of which combines an improved Nawaz, Enscore and Ham (NEH) heuristic and a cooperative local search. Finally, thoroughly computed results prove that the mathematical model and acceleration mechanism are effective. Our two top heuristics demonstrate decent improvements over the best comparative algorithm from related research. Specifically, the rating metric is lowered by 2.09% for the best heuristic and by 1.38% for the second-best heuristic.

Memetic discrete differential evolution with domain knowledge for blocking scheduling distributed flow shop with lot-streaming constraints

This article addresses the blocking distributed flow shop scheduling problem with lot-streaming (BDFSPL) with the objective of minimizing the maximum completion time, or makespan. In many realistic conditions, a job is divided into multiple continuous processed sublots. This pattern achieves operation overlap on consecutive machines and decreases the completion time of the whole job. Moreover, there are no buffers between machines, potentially causing finished sublots to be blocked on the current machine until the downstream machine is available. This is the first study to consider distributed production, blocking constraints, and lot-streaming together. To address this problem, we formulate a mathematical model for BDFSPL and propose a memetic discrete differential evolution (MDDE) algorithm. First, the MDDE algorithm partitions the entire population into three subpopulations based on solution quality, and each subpopulation evolves independently through adaptive scale and parameter adjustment. Second, four discrete mathematical operators are proposed to generate new individuals, and based on these operators, discrete mutation, crossover, and selection operations of MDDE are designed. Additionally, a crucial path-based local search strategy, informed by the domain knowledge of the best individual, is embedded into MDDE to enhance the exploitation capacity. To validate MDDE’s effectiveness, comprehensive experiments with several related algorithms on extensive testing instances are carried out, and the parameters of the MDDE algorithm are calibrated by employing a design of experiments. The comparison results demonstrate the effectiveness and efficiency of the proposed MDDE algorithm for the BDFSPL.

Modeling and Scheduling a Constrained Flowshop in Distributed Manufacturing Environments

This paper addresses a constrained distributed flowshop scheduling problem (CDFSP) that widely exists in modern manufacturing industry but has not been investigated before. Different from the distributed flowshop scheduling problem (DFSP) in the literature, CDFSP considers that all jobs are grouped for processing efficiently, and part of the groups subject to production requirements have a common deadline while the others do not have such a constraint. This constraint not only increases the complexity of the problem but also makes many solutions generated by the existing algorithms infeasible. Therefore, in this paper, a mathematical model is first established for the CDFSP with makespan criterion. After that, we explore the problem-specific knowledge to exclude infeasible solutions, and provide an acceleration method to evaluate feasible solutions in the insertion neighborhood. By automatically selecting parameters to match different search stages, a self-adaptive cooperative iterated greedy algorithm is designed where re-insertion and re-destruction mechanisms are integrated to address the infeasible solutions caused by a paradox and greedy mechanism. A cooperative mechanism is proposed to strengthen the coordination between family scheduling and job scheduling. Finally, the comprehensive experiments verify the effectiveness of the proposed algorithmic components and self-adaptive mechanism, and demonstrate the significant superiority of the proposed algorithm over five state-of-the-art metaheuristics.

Sustainable Scheduling of Distributed Flow Shop Group: A Collaborative Multi-Objective Evolutionary Algorithm Driven by Indicators

Sustainable Scheduling of Distributed Flow Shop Group: A Collaborative Multi-Objective Evolutionary Algorithm Driven by Indicators

Multi-Objective Q-Learning-Based Brain Storm Optimization for Integrated Distributed Flow Shop and Distribution Scheduling Problems

In recent years, integrated production and distribution scheduling (IPDS) has become an important subject in supply chain management. However, IPDS considering distributed manufacturing environments is rarely researched. Moreover, reinforcement learning is seldom combined with metaheuristics to deal with IPDS problems. In this work, an integrated distributed flow shop and distribution scheduling problem is studied, and a mathematical model is provided. Owing to the problem’s NP-hard nature, a multi-objective Q-learning-based brain storm optimization is designed to minimize makespan and total weighted earliness and tardiness. In the presented approach, a double-string representation method is utilized, and a dynamic clustering method is developed in the clustering phase. In the generating phase, a global search strategy, a local search strategy, and a simulated annealing strategy are introduced. A Q-learning process is performed to dynamically choose the generation strategy. It consists of four actions defined as the combinations of these strategies, four states described by convergence and uniformity metrics, a reward function, and an improved ε-greedy method. In the selecting phase, a newly defined selection method is adopted. To assess the effectiveness of the proposed approach, a comparison pool consisting of four prevalent metaheuristics and a CPLEX optimizer is applied to conduct numerical experiments and statistical tests. The results suggest that the designed approach outperforms its competitors in acquiring promising solutions when handling the considered problem.

A variant of the NSGA II for the speed scaling distributed flow shop scheduling problem with total tardiness minimisation

In this study, an energy-efficient distributed flow shop scheduling (DFSS) problem with total tardiness minimisation and machine-sequence dependent setup times is addressed. A mixed integer linear programming (MILP) model is proposed for the problem. A variant of the NSGA II algorithm is suggested for the solution of large scale problems. The proposed algorithm is compared with the state-of-the-art NSGA II, SPEA II, and multiobjective iterated local search algorithm. The computational results show that the proposed algorithm is efficient and effective for the problem. This is the first study to propose a heuristic algorithm for the distributed flow shop scheduling problem with total tardiness minimisation, speed scaling and setups.

An effective two-stage iterated greedy algorithm for distributed flowshop group scheduling problem with setup time

The distributed flow shop group scheduling problem (DFGSP) has wide industrial applications. Due to the strong coupling of DFGSP, three issues should be solved, such as assigning groups to factories, arranging the sequence of groups in each factory and scheduling the sequence of jobs in each group. Meanwhile, the calculation for the objective has a high time complexity. To solve the above problems, we first build a mixed-integer linear programming model of DFGSP and verify its correctness by using the Gurobi solver. By exploring the implicit characteristics of the problem, two rapid evaluation methods based on group insertion and job insertion are designed to accelerate the evaluation of the objective. Then, an effective two-stage iterated greedy algorithm (tIGA) is proposed to solve the above three coupled subproblem. In the proposed tIGA, two intra-factory and inter-factory cooperative neighborhood search strategies and two intra-group and inter-group enhanced search strategies are proposed, respectively, to improve the search breadth and depth. The results of comprehensive statistical experiments on 810 test instances show that the proposed algorithm significantly outperforms the compared ones in terms of objective values and relative percentage increase values, and demonstrates the effectiveness of the proposed tIGA.

A knowledge-driven cooperative scatter search algorithm with reinforcement learning for the distributed blocking flow shop scheduling problem

The distributed flow shop scheduling problem has become one of the key problems related to the high efficiency impacted factor in the manufacturing industry due to its typical scenarios in real-world industrial applications. In this paper, a knowledge-driven cooperative scatter search (KCSS) is proposed to address the distributed blocking flow shop scheduling problem (DBFSP) to minimize the makespan. The scatter search (SS) is adopted as the basic optimization framework in KCSS. The neighborhood perturbation operator and the Q-learning algorithm are combined to select the appropriate perturbation operator in the search process. Firstly, considering the complexity of distributed scenarios, five search operators are used to construct a disturbance strategy pool. Secondly, the Q-learning algorithm dynamically chooses disturbance strategies to enhance exploration ability and search efficiency. Afterward, a local search method based on neighborhood reconstruction is proposed to perturb the currently found optimal solution to strengthen the ability of KCSS to develop in local areas. In addition, the path relinking mechanism is introduced into the subset combination method to guarantee the diversity of solutions in the optimization process. Finally, the performance of the KCSS algorithm is verified on the benchmark set, and the experimental results demonstrate the robustness and effectiveness of the KCSS algorithm. In addition, 518 of the best-known solutions out of 720 benchmark instances are updated.

Solving Biobjective Distributed Flow-Shop Scheduling Problems With Lot-Streaming Using an Improved Jaya Algorithm.

A distributed flow-shop scheduling problem with lot-streaming that considers completion time and total energy consumption is addressed. It requires to optimally assign jobs to multiple distributed factories and, at the same time, sequence them. A biobjective mathematic model is first developed to describe the considered problem. Then, an improved Jaya algorithm is proposed to solve it. The Nawaz-Enscore-Ham (NEH) initializing rule, a job-factory assignment strategy, the improved strategies for makespan and energy efficiency are designed based on the problem's characteristic to improve the Jaya's performance. Finally, experiments are carried out on 120 instances of 12 scales. The performance of the improved strategies is verified. Comparisons and discussions show that the Jaya algorithm improved by the designed strategies is highly competitive for solving the considered problem with makespan and total energy consumption criteria.

Multi-Objective brain storm optimization for integrated scheduling of distributed flow shop and distribution with maximal processing quality and minimal total weighted earliness and tardiness

At present, integrated production and distribution scheduling problems have obtained amounts of concern due to their essential roles in enhancing the supply chain performance. Along with the economic globalization, many manufacturing enterprises adopt distributed production structures to reduce operation costs and improve service quality. Besides, processing quality becomes a fundamental standard for manufacturing enterprises to keep their competitiveness. In the distributed production and distribution process, the jobs are first produced on machines in different factories at the production stage, and then shipped to their associated customers using vehicles at the distribution stage. To realize an overall optimization of these two stages, this work investigates a multi-objective integrated distributed flow shop and distribution scheduling problem to reach maximal processing quality and minimal total weighted earliness and tardiness. To define it mathematically, a mixed integer programming model is established. Given the problem’s NP-hard nature, a multi-objective brain storm optimization algorithm is addressed to settle it. Through performing numerical experiments and statistical tests on some test instances, the effectiveness of the developed method is demonstrated..

Mixed-Integer Programming vs. Constraint Programming for Shop Scheduling Problems: New Results and Outlook

Constraint programming (CP) has been recently in the spotlight after new CP-based procedures have been incorporated into state-of-the-art solvers, most notably the CP Optimizer from IBM. Classical CP solvers were only capable of guaranteeing the optimality of a solution, but they could not provide bounds for the integer feasible solutions found if interrupted prematurely due to, say, time limits. New versions, however, provide bounds and optimality guarantees, effectively making CP a viable alternative to more traditional mixed-integer programming (MIP) models and solvers. We capitalize on these developments and conduct a computational evaluation of MIP and CP models on 12 select scheduling problems. 1 We carefully chose these 12 problems to represent a wide variety of scheduling problems that occur in different service and manufacturing settings. We also consider basic and well-studied simplified problems. These scheduling settings range from pure sequencing (e.g., flow shop and open shop) or joint assignment-sequencing (e.g., distributed flow shop and hybrid flow shop) to pure assignment (i.e., parallel machine) scheduling problems. We present MIP and CP models for each variant of these problems and evaluate their performance over 17 relevant and standard benchmarks that we identified in the literature. The computational campaign encompasses almost 6,623 experiments and evaluates the MIP and CP models along five dimensions of problem characteristics, objective function, decision variables, input parameters, and quality of bounds. We establish the areas in which each one of these models performs well and recognize their conceivable reasons. The obtained results indicate that CP sets new limits concerning the maximum problem size that can be solved using off-the-shelf exact techniques. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.1287 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0326 ) at ( http://dx.doi.org/10.5281/zenodo.7541223 ).

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.

An effective two-stage iterated greedy algorithm to minimize total tardiness for the distributed flowshop group scheduling problem

This paper aims to minimize the total tardiness for a distributed flowshop group scheduling problem with sequence-dependent setup time, which is an extension of the traditional distributed flowshop scheduling problem and has significant applications in the practical manufacturing environment. A mathematical model is set up and an effective two-stage iterated greedy (TIG) algorithm with an elaborately designed two-stage structure is presented to address the considered problem. A heuristic method combining a problem-specific dispatching rule and a simplified tie-breaking method is designed to generate an initial solution. A novel reconstruction mechanism is developed to explore the most valuable search space to save the evaluation efforts. To validate the effectiveness of the proposed TIG, comprehensive computational and statistical experiments are conducted. Experimental results show that the proposed TIG outperforms the six state-of-the-art algorithms from the closely related literature by a considerable margin in terms of the relative deviation index values at the same maximum elapsed CPU time.

Distributed Co-Evolutionary Memetic Algorithm for Distributed Hybrid Differentiation Flowshop Scheduling Problem

This article deals with a practical distributed hybrid differentiation flowshop scheduling problem (DHDFSP) for the first time, where manufacturing products to minimize makespan criterion goes through three consecutive stages: 1) job fabrication in first-stage distributed flowshop factories; 2) job-to-product assembly based on specified assembly plan on a second-stage single machine; and 3) product differentiation according to customization on one of the third-stage dedicated machines. Considering the characteristics of multistage and diversified processing technologies of the problem, building new powerful evolutionary algorithm (EA) for DHDFSP is expected. To achieve this, we propose a general EA framework called distributed co-evolutionary memetic algorithm (DCMA). It includes four basic modules: 1) dual population (POP)-based global exploration; 2) elite archive (EAR)-oriented local exploitation; 3) elite knowledge transfer (EKT) among POPs and EAR; and 4) adaptive POP restart. EKT is a general model for information fusion among search agents due to its problem independence. In execution, four modules cooperate with each other and search agents co-evolve in a distributed way. This DCMA evolutionary framework provides some guidance in algorithm construction of different optimization problems. Furthermore, we design each module based on problem knowledge and follow the DCMA framework to propose a specific DCMA metaheuristic for coping with DHDFSP. Computational experiments validate the effectiveness of the DCMA evolutionary framework and its special designs, and show that the proposed DCMA metaheuristic outperforms the compared algorithms.

An Effective Cooperative Co-Evolutionary Algorithm for Distributed Flowshop Group Scheduling Problems.

This article addresses a novel scheduling problem, a distributed flowshop group scheduling problem, which has important applications in modern manufacturing systems. The problem considers how to arrange a variety of jobs subject to group constraints at a number of identical manufacturing cellulars, each one with a flowshop structure, with the objective of minimizing makespan. We explore the problem-specific knowledge and present a mixed-integer linear programming model, a counterintuitive paradox, and two suites of accelerations to save computational efforts. Due to the complexity of the problem, we consider a decomposition strategy and propose a cooperative co-evolutionary algorithm (CCEA) with a novel collaboration model and a reinitialization scheme. A comprehensive and thorough computational and statistical campaign is carried out. The results show that the proposed collaboration model and reinitialization scheme are very effective. The proposed CCEA outperforms a number of metaheuristics adapted from closely related scheduling problems in the literature by a significantly considerable margin.

An iterated greedy algorithm for distributed blocking flow shop with setup times and maintenance operations to minimize makespan

Nowadays, distributed scheduling problem is a reality in many companies. Over the last years, an increasingly attention has been given by distributed flow shop scheduling problems and the addition of constraints to the problem. This article introduces the distributed blocking flow shop scheduling problem with sequence-dependent setup times and maintenance operations to minimize makespan. A mixed-integer linear programming (MILP) is developed to mathematically describe the problem and heuristic procedures are proposed to incorporate maintenance operations to job scheduling. An Iterated Greedy with Variable Search Neighborhood (VNS), named IG_NM, is proposed to solve small and large instances with sizes of 4,800 and 13,200 problems, respectively. Computational experiments were carried out to evaluate the performance of IG_NM in comparison with MILP and the most recent methods of literature of distributed flow shop scheduling problems. Statistical results show that in the trade-off between effectiveness and efficiency the proposed IG_NM outperformed other metaheuristics of the literature.

Multi-local search-based general variable neighborhood search for distributed flow shop scheduling in heterogeneous multi-factories

Heterogeneous multi-factories in different regions bring a challenge to managers in distributed production scheduling. This paper studies a distributed flow shop scheduling problem in heterogeneous multi-factories (DHFSP) with different processing capabilities of machines and electricity prices in multi-factories. The mixed-integer linear programming model (MILP) of the DHFSP is established, where different time-of-use electricity prices and states of machines (running and idle) are integrated. The proposed MILP model is based on position and time-indexed variables where the position of a job in the sequence is modeled and the time horizon is discretized into time slots. Every job on a machine corresponds to a series of position and time-indexed decision variables A multi-local search-based general variable neighborhood search (MGVNS) is presented to address the DHFSP. The earliest due date rule and a distributed version of NEH (Nawaz–Enscore–Ham) are combined to generate a promising initial solution. Four efficient greedy local search methods that move jobs between heterogeneous multi-factories and within the critical factory are presented. The properties of DHFSP are used to reduce the computing time of objectives. A right-shifting procedure is presented to save the electricity cost by considering the total electricity cost consumed by the processing of the jobs and the idle state of the machine between two adjacent jobs. The experiments and investigation are provided on large-sized instances to demonstrate the effectiveness and efficiency of MGVNS. The effectiveness of initialization, accelerated methods, right-shifting procedure, and local search methods are also significant. From the managerial insights, the proposed model can be extended to many real scenarios, such as semiconductor or automobile production, by integrating specific production constraints. The proposed model and scheduling methods provide an economical way to generate efficient schedules to balance the production efficiency and cost.

A knowledge-driven constructive heuristic algorithm for the distributed assembly blocking flow shop scheduling problem

The distributed flow shop scheduling problem (DFSP) has become widespread due to the increasing advantages of multi-factories manufacturing in recent years. The distributed assembly blocking flow shop scheduling problem (DABFSP), which aims at minimizing the maximum assembly completion time, is considered in this paper. A knowledge-driven constructive heuristic (KDH) algorithm is proposed to address the above problem. Three different kinds of neighborhood knowledge are refined by analyzing the characteristic of the problem and quantified to design the KDH algorithm. The jobs belonging to the same production are assigned to the different factories to advance the starting time of assembly, which is quantified as knowledge 1. The assembly sequence of the product is determined according to the processing sequence of the job in the processing factory, which is defined as knowledge 2. The jobs belonging to the same product are distributed together in each processing factory, which is quantified as knowledge 3. The performance of the KDH algorithm is verified on the benchmark instance, which comprises 900 small-scale instances and 810 large-scale instances. The experimental results demonstrate that the KDH algorithm is superior to state-of-the-art algorithms in the aspect of addressing DABFSP.

A collaborative iterative greedy algorithm for the scheduling of distributed heterogeneous hybrid flow shop with blocking constraints

The hybrid flow shop and distributed flow shop problems have been extensively studied due to their wide industrial applications. However, the distributed heterogeneous hybrid flow shop problems (DHHFSP) with blocking constraints have not yet been well studied up to date. This paper considers how to arrange a variety of jobs to different heterogeneous factories, and each factory has a minimal makespan. The innovations of this paper lie in presenting a mathematical model of the DHHFSP with blocking constraints and designing a collaborative iterative greedy (CIG) algorithm. The CIG contains the problem-specific initialization strategy, the neighborhood search strategy, the destruction-reconstruction strategy, and the local intensification strategy. The cross-factory and inner-factory neighborhood search strategies based on two swap operators are adopted to reduce the blocking time. The local intensification strategy is developed to optimize the scheduling sequence of each factory. The proposed algorithm is empirically compared with five state-of-the-art algorithms on 60 different instance sets. The experimental results show that the proposed algorithm significantly outperforms the compared ones in terms of objective values and relative percentage deviation values.