Blocking Flow Shop Scheduling Research Articles

Accelerated evaluation of blocking flowshop scheduling with total flow time criteria using a generalized critical machine-based approach

Despite the considerable advances in the research of the blocking flowshop scheduling problem (BFSP), several unresolved challenges persist. Algorithmic complexity presents hurdles. Although the insertion-based method is considered to generate superior solutions, its high computational demand diminishes the efficiency of algorithms, especially within large-scale sequences. The existing accelerated evaluation methods cannot utilize the existing information to quickly calculate the total flow time or the total tardiness time of the changed sequence after the job insertion, but recalculates it from scratch. This does not significantly reduce computational effort and needs to be further improved.In this paper, we delve into the intrinsic features of these challenges, proposing a generalized accelerated critical machine-based evaluation tailored for the total flow time and tardiness criteria of the BFSP with and without sequence-dependent setup times. First, we propose three theorems, one corollary, and their proofs based on the critical machine. Second, we propose the accelerated evaluation procedure based on these theorems to calculate the objectives related to the total flow time. Third, we also extend the proposed accelerated evaluation method to the BFSP with sequence-dependent setup times, aiming to significantly reduce the time complexity. Finally, we conduct four experiments on five well-known benchmarks (a total of 3540 test instances). Through statistical analysis, it becomes evident that our computational efforts have significantly decreased in computing both the total flow time and the total tardiness time. This performance enhancement is superior to the effectiveness of existing acceleration techniques.

An adaptive large neighbourhood search algorithm for blocking flowshop scheduling problem with sequence-dependent setup times

An adaptive large neighbourhood search algorithm for blocking flowshop scheduling problem with sequence-dependent setup times

A multi-objective discrete differential evolution algorithm for energy-efficient distributed blocking flow shop scheduling problem

ABSTRACT The energy problem in green manufacturing has attracted enormous attention from researchers and practitioners in the manufacturing domain with the global energy crisis and the aggravation of environmental pollution. The distributed blocking flow shop scheduling problem (DBFSP) has considerable application scenarios in connection with its widespread application in the industry under the background of intelligent manufacturing. A multi-objective discrete differential evolution (MODE) algorithm is proposed to solve the energy-efficient distributed blocking flow shop scheduling problem (EEDBFSP) with the objectives of the makespan and total energy consumption (TEC) in this paper. The cooperative initialisation strategy is proposed to generate the initial population of the EEDBFSP. The mutation, crossover, and selection operators are redesigned to enable the MODE algorithm as applied to discrete space. A local search strategy based on the knowledge of five operators is introduced to enhance the exploitation capability of the MODE algorithm in the EEDBFSP. The non-critical path energy-efficient strategy is proposed to reduce energy consumption according to the specific constraints in the EEDBFSP. The effectiveness of each strategy in the MODE algorithm is verified and compared with the state-of-the-art algorithms. The numerical results demonstrate that the MODE algorithm is the efficient optimiser for solving the EEDBFSP.

A collaborative iterated greedy algorithm with reinforcement learning for energy-aware distributed blocking flow-shop scheduling

Energy-aware scheduling has attracted increasing attention mainly due to economic benefits as well as reducing the carbon footprint at companies. In this paper, an energy-aware scheduling problem in a distributed blocking flow-shop with sequence-dependent setup times is investigated to minimize both makespan and total energy consumption. A mixed-integer linear programming model is constructed and a cooperative iterated greedy algorithm based on Q-learning (CIG) is proposed. In the CIG, a top-level Q-learning is focused on enhancing the utilization ratio of machines to minimize makespan by finding a scheduling policy from four sequence-related operations. A bottom-level Q-learning is centered on improving energy efficiency to reduce total energy consumption by learning the optimal speed governing policy from four speed-related operations. According to the structure characteristics of solutions, several properties are explored to design an energy-saving strategy and acceleration strategy. The experimental results and statistical analysis prove that the CIG is superior to the state-of-the-art competitors with improvement percentages of 20.16 % over 2880 instances from the well-known benchmark set in the literature.

An effective discrete monarch butterfly optimization algorithm for distributed blocking flow shop scheduling with an assembly machine

An effective discrete monarch butterfly optimization algorithm for distributed blocking flow shop scheduling with an assembly machine

Integrated Optimization of Blocking Flowshop Scheduling and Preventive Maintenance Using a Q-Learning-Based Aquila Optimizer

In recent years, integration of production scheduling and machine maintenance has gained increasing attention in order to improve the stability and efficiency of flowshop manufacturing systems. This paper proposes a Q-learning-based aquila optimizer (QL-AO) for solving the integrated optimization problem of blocking flowshop scheduling and preventive maintenance since blocking in the jobs processing requires to be considered in the practice manufacturing environments. In the proposed algorithmic framework, a Q-learning algorithm is designed to adaptively adjust the selection probabilities of four key population update strategies in the classic aquila optimizer. In addition, five local search methods are employed to refine the quality of the individuals according to their fitness level. A series of numerical experiments are carried out according to two groups of flowshop scheduling benchmark. Experimental results show that QL-AO significantly outperforms six peer algorithms and two state-of-the-art hybrid algorithms based on Q-Learning on the investigated integrated scheduling problem. Additionally, the proposed Q-learning and local search strategies are effective in improving its performance.

A Pareto-Based Discrete Jaya Algorithm for Multiobjective Carbon-Efficient Distributed Blocking Flow Shop Scheduling Problem

Carbon peaking and carbon neutrality, which are significant strategies for national sustainable development, have attracted enormous attention from researchers in the manufacturing domain. A Pareto-based discrete Jaya algorithm (PDJaya) is proposed to solve the carbon-efficient distributed blocking flow shop scheduling problem (CEDBFSP) with the criteria of total tardiness and total carbon emission in this paper. The mixed-integer linear programming model is presented for the CEDBFSP. An effective constructive heuristic is produced to generate the initial population. The new individual is generated by the update mechanism of PDJaya. The self-adaptive operator local search strategy is designed to enhance the exploitation capability of PDJaya. A critical-path-based carbon saving strategy is introduced to further reduce carbon emissions. The effectiveness of each strategy in the PDJaya is verified and compared with the state-of-the-art algorithms in the benchmark suite. The numerical results demonstrate that the PDJaya is the efficient optimizer for solving the CEDBFSP.

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.

A Hyperheuristic With Q-Learning for the Multiobjective Energy-Efficient Distributed Blocking Flow Shop Scheduling Problem.

Carbon peaking and carbon neutrality, which are the significant national strategy for sustainable development, have attracted considerable attention from production enterprises. In this study, the energy consumption is considered in the distributed blocking flow shop scheduling problem (DBFSP). A hyperheuristic with Q -learning (HHQL) is presented to address the energy-efficient DBFSP (EEDBFSP). Q -learning is employed to select an appropriate low-level heuristic (LLH) from a predesigned LLH set according to historical information fed back by LLH. An initialization method, which considers both total tardiness (TTD) and total energy consumption (TEC), is proposed to construct the initial population. The ε -greedy strategy is introduced to utilize the learned knowledge while retaining a certain degree of exploration in the process of selecting LLH. The acceleration operation of the job on the critical path is designed to optimize TTD. The deceleration operation of the job on the noncritical path is designed to optimize TEC. The statistical and computational experimentation in an extensive benchmark testified that the HHQL outperforms the other comparison algorithm regarding efficiency and significance in solving EEDBFSP.

LS-HH: A Learning-Based Selection Hyper-Heuristic for Distributed Heterogeneous Hybrid Blocking Flow-Shop Scheduling

As the development of economic globalization, the distributed manufacturing has become common in modern industries. The scheduling of production resources in multiple production centers becomes an emerging topic. This paper is the first attempt to address a distributed heterogeneous hybrid blocking flow-shop scheduling problem (DHHFSP-B) with the minimization of makespan. Compared with the traditional single flow-shop scheduling, DHHFSP-B considers the collaborative production of multiple hybrid flow lines with heterogeneous layout and processing performance as well as no intermediate buffers. We firstly present a mixed-integer linear programming model to formulate DHHFSP-B and then propose a learning-based selection hyper-heuristic framework (LS-HH) for solving it. The LS-HH contains high-level strategy and low-level heuristics. In the high-level strategy, a learning probability model is built to provide the guidance to choose the suitable perturbation heuristic during the optimization process. A simulated annealing-like move acceptance is employed to determine the updating of incumbent domain solution and prevent the search from trapping into local optimum. In the low-level heuristics, a constructive heuristic is proposed based on a novel assignment rule to create the initial domain solution. Four problem-specific perturbation heuristics and a variable neighborhood search-based improvement operator are employed to search the solution space. A comprehensive computational experiment is conducted. The comparative results show that the LS-HH significantly outperforms the Gurobi solver and several closely relevant optimization methods in solving the DHHFSP-B.

Simultaneous minimisation of mean and variation of waiting times in a two-stage proportionate blocking flow shop

We consider the two-stage proportionate blocking flow shop scheduling problem with the objective of simultaneously minimising the mean and the variation of job waiting times. We show that the problem can be solved in time by evaluating at most two candidate optimal sequences. In some cases, the shortest processing time (SPT) sequence is optimal for any set of processing times. In all other cases, the optimal sequence is either the SPT sequence or a V-shaped sequence. We show that the optimal solution value for the corresponding no-wait flow shop scheduling problem is no worse than the optimal solution value for the blocking flow shop problem. We then analyse the blocking flow shop problem with the option of rejecting jobs from the sequence by paying their job-specific rejection penalties. We show that the problem with the job rejection option can be solved in time by dynamic programming (DP). Finally, we show that our results also apply to the corresponding flow shop scheduling problem with synchronous job transfers.

Island neighboring heuristics harmony search algorithm for flow shop scheduling with blocking

• Island Neighboring Heuristics Harmony Search (INHS) for Flow Shop Scheduling is proposed. • Island model concept utilized in INHS to enhance solutions diversity. • Three neighboring heuristics are utilized in INHS to improve the local exploitation. • Two selection memory consideration methods are utilized: roulette-wheel and global-best. • Constraints are maintained during the search through repair strategy. This paper proposes an island neighboring heuristics harmony search algorithm (INHS) to tackle the blocking flow-shop scheduling problem. The island model is used to diversify the population and thus enhance the algorithm performance. The proposed method distributes the individuals in the population into different islands or sub-population. Then the harmony search algorithm iterates to look for and to develop a new solution enhanced by using neighboring heuristics. A migration process is applied, after a predefined number of iterations, to perform an exchange between some individuals in islands. The proposed algorithm is evaluated using 12 real-world datasets, each with 10 instances. A sensitivity analysis of the island model parameters is conducted to choose values that minimize the total flow time. The evaluation is conducted using two criteria, the number of evolutions and the Central Processing Unit (CPU) time using six comparative methods and sixteen comparative methods, respectively. For the first criterion, the proposed algorithm excels other comparative algorithms when solving instances of four datasets. For the second criterion, the proposed algorithm outperforms other comparative methods in six out of the twelve datasets. In conclusion, The obtained results prove the efficiency and competitiveness of the proposed algorithm when tackling the blocking flow-shop scheduling problem.

Blocking flowshop scheduling problems with release dates

In a flowshop, the current stage has to remain work-in-process and cannot release any task to the downstream stage once the buffer is stuffed. This scheduling phenomenon is called blocking, and it usually occurs in an industrial setting because of the buffer capacity or the product volume. This study addresses several blocking flowshop scheduling problems to individually optimize the following criteria, i.e. makespan, maximum lateness, or maximum delivery-completion time, in which the tasks are available at different release dates. Given that these scheduling problems are strongly NP-complete, exact and metaheuristic algorithms are designed for different scale instances. An effective branch and bound method is proposed to search exact solutions for small-scale instances within a given period, where well-designed branching rules and lower bounds prune considerable invalid nodes. Further, to seek high-quality feasible schedules in a short time, a discrete artificial bee colony algorithm is provided for medium-scale instances, where a dispatching-rule-based initialization, a series of efficient non-delay variable neighborhood search mechanisms, and a well-designed disturbing scheme enhance the optimization capability. Comprehensive computational tests are conducted to evaluate the effectiveness of the proposed algorithms.

A heuristic and meta-heuristic based on problem-specific knowledge for distributed blocking flow-shop scheduling problem with sequence-dependent setup times

The distributed production scenario with the sequence-dependent setup times (SDST) widely exists in the modern manufacturing system. This paper investigates the distributed blocking flow-shop scheduling problem with sequence-dependent setup times (SDST/DBFSP). Considering the complexity of the distributed scenario and SDSTs, a discrete heuristic and meta-heuristic is proposed by exploring the problem-specific knowledge. First, a knowledge-incorporated construction heuristic is proposed to reduce the blocking times and idle times generated by SDSTs. In the first stage of the meta-heuristic, an insertion-based neighborhood operator of different factories is developed to explore promising regions in the decision space. In the second stage, a local search operator is embedded to enhance the exploitation ability. Additionally, a simulated annealing-like acceptance criterion of the iterated greedy algorithm is employed to keep the diversity of the population. Finally, an insertion operation for critical factories is introduced to further improve the accuracy of the solutions. Moreover, a speedup method for the insertion neighborhood is expanded to reduce the computational complexity of SDST/DBFSP. In the part of the experiment, a deconstruction process is designed to gain insight into the contribution of each component in the proposed meta-heuristic. The proposed meta-heuristic is assessed through comparing with five state-of-the-art algorithms to demonstrate its effectiveness. The experimental results testified that the proposed meta-heuristic outperforms other algorithms regarding the significance of the SDST/DBFSP.

A self-learning hyper-heuristic for the distributed assembly blocking flow shop scheduling problem with total flowtime criterion

The distributed assembly blocking flow shop scheduling problem, which is a significant scenario in modern supply chains and manufacturing systems, has attracted significant attention from researchers and practitioners. To formulate the problem, a mixed-integer linear programming model is introduced to optimize the total flowtime. A constructive heuristic (HHNRa) and a self-learning hyper-heuristic (SLHH) are proposed to address the scheduling problem. HHNRa is designed based on the problem-specific knowledge to obtain initial solutions with high quality. A self-learning high-level strategy based on the historical success rate of low-level heuristics is presented to manipulate the low-level heuristics to operate in the solution space. In addition, a restart scheme with three distinct constructive heuristics is utilized to maintain the diversity of the solution. Based on 900 small-scale benchmark instances and 810 large-scale benchmark instances, comprehensive numerical experiments are conducted to evaluate the performance of the proposed SLHH algorithm. The results of the statistical analysis indicate that the proposed self-learning hyper-heuristic is superior to the compared state-of-the-art algorithms for the problem under consideration. Consequently, the proposed constructive heuristic and the self-learning hyper-heuristic are effective methods for the distributed assembly blocking flow shop scheduling problem.

A deep reinforcement learning based approach for dynamic distributed blocking flowshop scheduling with job insertions

The distributed blocking flowshop scheduling problem (DBFSP) with new job insertions is studied. Rescheduling all remaining jobs after a dynamic event like a new job insertion is unreasonable to an actual distributed blocking flowshop production process. A deep reinforcement learning (DRL) algorithm is proposed to optimise the job selection model, and local modifications are made on the basis of the original scheduling plan when new jobs arrive. The objective is to minimise the total completion time deviation of all products so that all jobs can be finished on time to reduce the cost of storage. First, according to the definitions of the dynamic DBFSP problem, a DRL framework based on multi-agent deep deterministic policy gradient (MADDPG) is proposed. In this framework, a full schedule is generated by the variable neighbourhood descent algorithm before a dynamic event occurs. Meanwhile, all newly added jobs are reordered before the agents make decisions to select the one that needs to be scheduled most urgently. This study defines the observations, actions and reward calculation methods and applies centralised training and distributed execution in MADDPG. Finally, a comprehensive computational experiment is carried out to compare the proposed method with the closely related and well-performing methods. The results indicate that the proposed method can solve the dynamic DBFSP effectively and efficiently.

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.

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.

Rescheduling of Distributed Manufacturing System with Machine Breakdowns

This study attempts to explore the dynamic scheduling problem from the perspective of operational research optimization. The goal is to propose a rescheduling framework for solving distributed manufacturing systems that consider random machine breakdowns as the production disruption. We establish a mathematical model that can better describe the scheduling of the distributed blocking flowshop. To realize the dynamic scheduling, we adopt an “event-driven” policy and propose a two-stage “predictive-reactive” method consisting of two steps: initial solution pre-generation and rescheduling. In the first stage, a global initial schedule is generated and considers only the deterministic problem, i.e., optimizing the maximum completion time of static distributed blocking flowshop scheduling problems. In the second stage, that is, after the breakdown occurs, the rescheduling mechanism is triggered to seek a new schedule so that both maximum completion time and the stability measure of the system can be optimized. At the breakdown node, the operations of each job are classified and a hybrid rescheduling strategy consisting of “right-shift repair + local reorder” is performed. For local reorder, we designed a discrete memetic algorithm, which embeds the differential evolution concept in its search framework. To test the effectiveness of DMA, comparisons with mainstream algorithms are conducted on instances with different scales. The statistical results show that the ARPDs obtained from DMA are improved by 88%.

A hybrid two-stage algorithm for solving the blocking flow shop scheduling problem with the objective of minimise the makespan

A hybrid two-stage algorithm for solving the blocking flow shop scheduling problem with the objective of minimise the makespan