Blocking Flow Shop Scheduling Problem 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 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.

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.

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.

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.

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.

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

Flow shop scheduling is an important tool for a variety of industrial system and it has important applications in manufacturing and engineering. This paper considers the blocking flow shop scheduling problem involving processing times and provides a hybrid approach based on artificial neural network and genetic algorithm technique. The objective of this paper is to focus on to minimise the makespan. In this paper, a multi-layer neural network algorithm is developed to find the initial schedule of jobs and then a genetic algorithm is designed to improve the initial sequence of jobs to obtained the best job schedule that minimise the makespan. A numerical example is illustrated to explain the proposed approach and demonstrate its effectiveness. The performance of our suggested hybrid model is compared with the various existing method in the literature and the results indicate that the proposed model performs significantly better than the other methods in the literature. The computational results that are presented in this paper are very encouraging and have shown that the proposed algorithm is superior.

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

Migrating birds optimization with a diversified mechanism for blocking flow shops to minimize idle and blocking time

Blocking flow shop scheduling problem widely exists in industrial processes, and most attention has focused on minimization of economic indicators, such as makespan, total flow time, and due-date-based functions, rather than energy-efficient indicators. This paper considers idle and blocking time criterion, which is closely related to machine energy consumption in blocking flow shops, and proposes a migrating birds optimization with a diversified mechanism (dMBO) for the problem. On the basis of the profile fitting (PF) heuristic and the characteristics of the idle and blocking time, an improved heuristic, named PFI, is proposed by modifying the PF and performing an insert procedure. A best insert operator and an insert-based local search are hybridized in the proposed migrating birds optimization algorithm to enhance its exploitation capability. In order to maintain the diversity of the flock in the algorithm, a diversified mechanism containing three tabu lists and one candidate pool is designed. Extensive computational results validate the effectiveness of the proposed PFI heuristic, and a statistical analysis of the computational results confirms the superiority of the dMBO over several other high-performing metaheuristics.

A population-based iterated greedy algorithm to minimize total flowtime for the distributed blocking flowshop scheduling problem

We consider the distributed blocking flowshop scheduling problem (DBFSP) which is a meaningful generalization of the blocking flowshop scheduling problem in the distributed production environment. The objective of minimizing the total flowtime is relevant and important in the current dynamic manufacturing environment, but, as far as we know, it has not been investigated in the DBFSP previously. In this paper, a population-based iterated greedy (PBIG) algorithm is proposed to solve the DBFSP with the total flowtime criterion, which takes the advantage of both the population-based search approach and the iterated greedy algorithm. First, an effective constructive heuristic is proposed by integrating two existing constructive approaches to initialize the population with a high level of quality and diversity. Second, three different procedures to generate the offspring solutions are tested for the effective exploration capability, each of which rationally combines the destruction, reconstruction and selection operator. Third, the insertion neighborhood and swap neighborhood are investigated to enhance the local exploitation ability and a hybrid local search procedure that utilizes simultaneously both the two neighborhoods are proposed. The comprehensive experimental evaluation based on a total of 720 well-known instances shows that the proposed algorithms outperform the existing effective algorithms at a significant margin.

An iterated greedy algorithm for the parallel blocking flow shop scheduling problem and sequence-dependent setup times

This paper deals with the problem of scheduling jobs in a parallel flow shop configuration under the blocking constraint, in which the setup time of machines depends not only on the job to be processed but also on the previously processed one, i.e., there are sequence-dependent setup times. The performance analysis of several iterated greedy algorithms with different initial solution procedures and local searches lets us define an efficient algorithm to minimize the maximum job completion time. Moreover, the computational evaluation showed the efficiency of searching in different neighborhood structures and noted the significant influence of the initial solution. However, contrary to other scheduling problems, starting with a high quality solution does not guarantee better performance of the algorithm.

Production scheduling for blocking flowshop in distributed environment using effective heuristics and iterated greedy algorithm

• We study a distributed blocking flowshop scheduling problem. • We present six effective constructive heuristics and an iterated greedy algorithm . • Two different destructions focusing on the problem characteristic are designed. • Three local search procedures based on the various neighbourhood are presented. • The computational experiments prove the effectiveness of presented algorithms. Production scheduling plays an important role in the intelligent decision support system and intelligent optimization decision technology. In the context of the globalization trend, the current production and management may extend from a single factory to a distributed production network. In this paper, we study the distributed blocking flowshop scheduling problem (DBFSP) that is an important generalization of the traditional blocking flowshop scheduling problem in the distributed environment. Six constructive heuristics and an iterated greedy (IG) algorithm are proposed to minimize the makespan, which provides procedures for obtaining efficient and effective solutions to make decision-making sounder. The first five heuristics are developed based on the well-known NEH2 heuristic [B. Naderi, R. Ruiz, The distributed permutation flowshop scheduling problem, Computers & Operations Research, 37 (4) (2010) 754–768.] and the last heuristic is presented by extending the PW heuristic [Q.K. Pan, L. Wang, Effective heuristics for the blocking flowshop scheduling problem with makespan minimization, Omega, 40 (2) (2012) 218–229.] to DBFSP in an effective way. The composite heuristics that combining constructive heuristics and local searches are also studied. The proposed composite heuristics are chosen to generate an initial solution with a high level of quality. Keeping the simplicity of the IG algorithm, three local search procedures, two destruction procedures, an improved reconstruction procedure, and a simulated annealing-like acceptance criterion are well designed based on the problem-specific knowledge to enhance the IG algorithm. The computational experiments are carried out based on the 720 benchmark instances from the literature. The results show that the proposed heuristics are very effective for solving the problem under consideration and the presented IG algorithm performs significantly better than the other state-of-the-art metaheuristics from the literature.