Q-Learning-Assisted Meta-Heuristics for Scheduling Distributed Hybrid Flow Shop Problems

The flow shop scheduling problem is important for the manufacturing industry.Effective flow shop scheduling can bring great benefits to the industry.However,there are few types of research on Distributed Hybrid Flow Shop Problems(DHFSP)by learning assisted meta-heuristics.This work addresses a DHFSP with minimizing the maximum completion time(Makespan).First,a mathematical model is developed for the concerned DHFSP.Second,four Q-learning-assisted meta-heuristics,e.g.,genetic algorithm(GA),artificial bee colony algorithm(ABC),particle swarm optimization(PSO),and differential evolution(DE),are proposed.According to the nature of DHFSP,six local search operations are designed for finding high-quality solutions in local space.Instead of randomselection,Q-learning assists meta-heuristics in choosing the appropriate local search operations during iterations.Finally,based on 60 cases,comprehensive numerical experiments are conducted to assess the effectiveness of the proposed algorithms.The experimental results and discussions prove that using Q-learning to select appropriate local search operations is more effective than the random strategy.To verify the competitiveness of the Q-learning assistedmeta-heuristics,they are compared with the improved iterated greedy algorithm(IIG),which is also for solving DHFSP.The Friedman test is executed on the results by five algorithms.It is concluded that the performance of four Q-learning-assisted meta-heuristics are better than IIG,and the Q-learning-assisted PSO shows the best competitiveness.

An Elite-Class Teaching-Learning-Based Optimization for Reentrant Hybrid Flow Shop Scheduling with Bottleneck Stage

Bottleneck stage and reentrance often exist in real-life manufacturing processes;however,the previous research rarely addresses these two processing conditions in a scheduling problem.In this study,a reentrant hybrid flow shop scheduling problem(RHFSP)with a bottleneck stage is considered,and an elite-class teaching-learning-based optimization(ETLBO)algorithm is proposed to minimize maximum completion time.To produce high-quality solutions,teachers are divided into formal ones and substitute ones,and multiple classes are formed.The teacher phase is composed of teacher competition and teacher teaching.The learner phase is replaced with a reinforcement search of the elite class.Adaptive adjustment on teachers and classes is established based on class quality,which is determined by the number of elite solutions in class.Numerous experimental results demonstrate the effectiveness of new strategies,and ETLBO has a significant advantage in solving the considered RHFSP.

Competitive and Cooperative-Based Strength Pareto Evolutionary Algorithm for Green Distributed Heterogeneous Flow Shop Scheduling

This work aims to resolve the distributed heterogeneous permutation flow shop scheduling problem(DHPFSP)with minimizing makespan and total energy consumption(TEC).To solve this NP-hard problem,this work proposed a competitive and cooperative-based strength Pareto evolutionary algorithm(CCSPEA)which contains the following features:1)An initialization based on three heuristic rules is developed to generate a population with great diversity and convergence.2)A comprehensive metric combining convergence and diversity metrics is used to better represent the heuristic information of a solution.3)A competitive selection is designed which divides the population into a winner and a loser swarms based on the comprehensive metric.4)A cooperative evolutionary schema is proposed for winner and loser swarms to accelerate the convergence of global search.5)Five local search strategies based on problem knowledge are designed to improve convergence.6)Aproblem-based energy-saving strategy is presented to reduce TEC.Finally,to evaluate the performance of CCSPEA,it is compared to four state-of-art and run on 22 instances based on the Taillard benchmark.The numerical experiment results demonstrate that 1)the proposed comprehensive metric can efficiently represent the heuristic information of each solution to help the later step divide the population.2)The global search based on the competitive and cooperative schema can accelerate loser solutions convergence and further improve the winner’s exploration.3)The problembased initialization,local search,and energy-saving strategies can efficiently reduce the makespan and TEC.4)The proposed CCSPEA is superior to the state-of-art for solving DHPFSP.

A Discrete Artificial Bee Colony Algorithm for Minimizing the Total Flow Time in the Blocking Flow Shop Scheduling

A discrete artificial bee colony algorithm is proposed for solving the blocking flow shop scheduling problem with total flow time criterion. Firstly, the solution in the algorithm is represented as job permutation. Secondly, an initialization scheme based on a variant of the NEH (Nawaz-Enscore-Ham) heuristic and a local search is designed to construct the initial population with both quality and diversity. Thirdly, based on the idea of iterated greedy algorithm, some newly designed schemes for employed bee, onlooker bee and scout bee are presented. The performance of the proposed algorithm is tested on the well-known Taillard benchmark set, and the computational results demonstrate the effectiveness of the discrete artificial bee colony algorithm. In addition, the best known solutions of the benchmark set are provided for the blocking flow shop scheduling problem with total flow time criterion.

A Decomposition and Coordination Scheduling Method for Flow-shop Problem Based on TOC

There are many flow shop problems of throughput (denoted by FSPT) with constraints of due date in real production planning and scheduling. In this paper, a decomposition and coordination algorithm is proposed based on the analysis of FSPT and under the support of TOC (theory of constraint). A flow shop is at first decomposed into two subsystems named PULL and PUSH by means of bottleneck. Then the subsystem is decomposed into single machine scheduling problems,so the original NP-HARD problem can be transferred into a serial of single machine optimization problems finally. This method reduces the computational complexity, and has been used in a real project successfully.

Anomalies in Special Permutation Flow Shop Scheduling Problems

Recent researches show that there are some anomalies,which are not satisfied with common sense,appearing in some special permutation flow shop scheduling problems(PFSPs).These anomalies can be divided into three different types,such as changing the processing time of some operations,changing the number of total jobs and changing the number of total machines.This paper summarizes these three types of anomalies showing in the special PFSPs and gives some examples to make them better understood.The extended critical path is proposed and the reason why these anomalies happen in special PFSPs is given:anomalies will occur in these special PFSPs when the time of the operations on the reverse critical path changes.After that,the further reason for these anomalies is presented that when any one of these three types of anomalies happens,the original constraint in the special PFSPs is destroyed,which makes the anomalies appear.Finally,the application of these anomalies in production practice is given through examples and also with the possible research directions.The main contribution of this research is analyzing the intial reason why the anomalies appear in special PFSPs and pointing out the application and the possible research directions of all these three types of anomalies.

Flow shop rescheduling problem under rush orders

In the environment of customization, disturbances such as rush orders and material shortages often occur in the manufacturing system, so rescheduling is necessary for the manufacturing system. The rescheduling methodology should be able to dispose of the disturbance efficiently so as to keep production going smoothly. This aims researching flow shop rescheduling problem (FSRP) necessitated by rush orders. Disjunctive graph is employed to demonstrate the FSRP. For a flow shop processing n jobs, after the original schedule has been made, and z out of n jobs have been processed in the flow shop, x rush orders come, so the original n jobs together with x rush orders should be rescheduled immediately so that the rush orders would be processed in the shortest time and the original jobs could be processed subject to some optimized criteria. The weighted mean flow time of both original jobs and rush orders is used as objective function. The weight for rush orders is much bigger than that of the original jobs, so the rush orders should be processed early in the new schedule. The ant colony optimization (ACO) algorithm used to solve the rescheduling problem has a weakness in that the search may fall into a local optimum. Mutation operation is employed to enhance the ACO performance. Numerical experiments demonstrated that the proposed algorithm has high computation repeatability and efficiency.

An effective discrete artificial bee colony algorithm for flow shop scheduling problem with intermediate buffers

An effective discrete artificial bee colony(DABC) algorithm is proposed for the flow shop scheduling problem with intermediate buffers(IBFSP) in order to minimize the maximum completion time(i.e makespan). The effective combination of the insertion and swap operator is applied to producing neighborhood individual at the employed bee phase. The tournament selection is adopted to avoid falling into local optima, while, the optimized insert operator embeds in onlooker bee phase for further searching the neighborhood solution to enhance the local search ability of algorithm. The tournament selection with size 2 is again applied and a better selected solution will be performed destruction and construction of iterated greedy(IG) algorithm, and then the result replaces the worse one. Simulation results show that our algorithm has a better performance compared with the HDDE and CHS which were proposed recently. It provides the better known solutions for the makespan criterion to flow shop scheduling problem with limited buffers for the Car benchmark by Carlier and Rec benchmark by Reeves. The convergence curves show that the algorithm not only has faster convergence speed but also has better convergence value.

Differential evolution algorithm for hybrid flow-shop scheduling problems

Aiming at the hybrid flow-shop （HFS） scheduling that is a complex NP-hard combinatorial problem with wide engineering background, an effective algorithm based on differential evolution （DE） is proposed. By using a special encoding scheme and combining DE based evolutionary search and local search, the exploration and exploitation abilities are enhanced and well balanced for solving the HFS problems. Simulation results based on some typical problems and comparisons with some existing genetic algorithms demonstrate the proposed algorithm is effective, efficient and robust for solving the HFS problems.

A novel hybrid estimation of distribution algorithm for solving hybrid flowshop scheduling problem with unrelated parallel machine

The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this work, a novel mathematic model for the hybrid flow shop scheduling problem with unrelated parallel machine(HFSPUPM) was proposed. Additionally, an effective hybrid estimation of distribution algorithm was proposed to solve the HFSPUPM, taking advantage of the features in the mathematic model. In the optimization algorithm, a new individual representation method was adopted. The(EDA) structure was used for global search while the teaching learning based optimization(TLBO) strategy was used for local search. Based on the structure of the HFSPUPM, this work presents a series of discrete operations. Simulation results show the effectiveness of the proposed hybrid algorithm compared with other algorithms.

Integrated Production and Transportation Scheduling Method in Hybrid Flow Shop

The connection between production scheduling and transportation scheduling is getting closer in smart manufacturing system, and both of those problems are summarized as NP-hard problems. However, only a few studies have considered them simultaneously. This paper solves the integrated production and transportation scheduling problem(IPTSP) in hybrid flow shops, which is an extension of the hybrid flow shop scheduling problem(HFSP). In addition to the production scheduling on machines, the transportation scheduling process on automated guided vehicles(AGVs)is considered as another optimization process. In this problem, the transfer tasks of jobs are performed by a certain number of AGVs. To solve it, we make some preparation(including the establishment of task pool, the new solution representation and the new solution evaluation), which can ensure that satisfactory solutions can be found efficiently while appropriately reducing the scale of search space. Then, an effective genetic tabu search algorithm is used to minimize the makespan. Finally, two groups of instances are designed and three types of experiments are conducted to evaluate the performance of the proposed method. The results show that the proposed method is effective to solve the integrated production and transportation scheduling problem.

A Novel Particle Swarm Optimization for Flow Shop Scheduling with Fuzzy Processing Time

Since in most practical cases the processing time of scheduling is not deterministic, flow shop scheduling model with fuzzy processing time is established. It is assumed that the processing times of jobs on the machines are described by triangular fuzzy sets. In order to find a sequence that minimizes the mean makespan and the spread of the makespan, Lee and Li fuzzy ranking method is adopted and modified to solve the problem. Particle swarm optimization (PSO) is a population-based stochastic approximation algorithm that has been applied to a wide range of problems, but there is little reported in respect of application to scheduling problems because of its unsuitability for them. In the paper, PSO is redefined and modified by introducing genetic operations such as crossover and mutation to update the particles, which is called GPSO and successfully employed to solve the formulated problem. A series of benchmarks with fuzzy processing time are used to verify GPSO. Extensive experiments show the feasibility and effectiveness of the proposed method.

MODIFIED BOTTLENECK-BASED PROCEDURE FOR LARGE-SCALE FLOW-SHOP SCHEDULING PROBLEMS WITH BOTTLENECK

A new bottleneck-based heuristic for large-scale flow-shop scheduling problems with a bottleneck is proposed, which is simpler but more tailored than the shifting bottleneck （SB） procedure. In this algorithm, a schedule for the bottleneck machine is first constructed optimally and then the non-bottleneck machines are scheduled around the bottleneck schedule by some effective dispatching rules. Computational results show that the modified bottleneck-based procedure can achieve a tradeoff between solution quality and computational time comparing with SB procedure for medium-size problems. Furthermore it can obtain a good solution in quite short time for large-scale scheduling problems.

Scheduling on 2-Machine Flow Shops Considering Disturbance on Job Processing Times

In this paper the scheduling problem to minimize the expected makespan is discussed on two-machine flow shops with random disturbance on job processing times. The problem is represented by a stochastic programming model. We approximate the stochastic problem by a deterministic problem which can be solved by Johnson's rule. The estimation of approximation error is also discussed by analyzing the stochastic model and its approximate LP model.

MULTI-SHOP SCHEDULING PROBLEM

A new concept of multi-shop （M ） is put forward which contains all basic shops including open shop （O）, job shop （J ）, flow shop （F ） and hybrid flow shop （H ） so that these basic shop can be scheduled together. Several algorithms including ant colony optimization （ACO）, most work remaining （MWR）, least work remaining （LWR）, longest processing time （LPT） and shortest processing time （SPT） are used for scheduling the M. Numerical experiments of the M adopting data of some car and reC series benchmark instances are tested. The results show that the ACO algorithm has better performance for scheduling the M than the other algorithms, if minimizing the makespan （ Cmax^＊） is taken as the objective function. As a comparison, the separate shops contained in the M are also scheduled by the ACO algorithm for the same objective function, when the completing time of the jobs in the previous shop is taken as the ready time of these jobs in the following shop. The results show that the M has the advantage of shortening the makespan upon separate shops.

A Penalty Groups-Assisted Iterated Greedy Integrating Idle Time Insertion:Solving the Hybrid Flow Shop Group Scheduling with Delivery Time Windows

The hybrid flow shop group scheduling problem(HFGSP)with the delivery time windows has been widely studied owing to its better flexibility and suitability for the current just-in-time production mode.However,there are several unresolved challenges in problem modeling and algorithmic design tailored for HFGSP.In our study,we place emphasis on the constraint of timeliness.Therefore,this paper first constructs a mixed integer linear programming model of HFGSP with sequence-dependent setup time and delivery time windows to minimize the total weighted earliness and tardiness(TWET).Then a penalty groups-assisted iterated greedy integrating idle time insertion(PG IG ITI)is proposed to solve the above problem.In the PG IG ITI,a double decoding strategy is proposed based on the earliest available machine rule and the idle time insertion rule to calculate the TWET value.Subsequently,to reduce the amount of computation,a skip-based destruction and reconstruction strategy is designed,and a penalty groups-assisted local search is proposed to further improve the quality of the solution by disturbing the penalized groups,i.e.,early and tardy groups.Finally,through comprehensive statistical experiments on 270 test instances,the results prove that the proposed algorithm is effective compared to four state-of-the-art algorithms.

基于遗传算法的混合Flow-shop调度方法

混合Flow-shop调度问题 (Hybrid flow-shop scheduling problem, HFSP),是一般Flow-shop调度问题的推广,由于在某些工序上存在并行机器,所以比一般的Flow-shop调度问题更复杂。本文提出了遗传算法求解混合Flow-shop调度问题的方法,给出了一种新的编码方法,设计了相应的交叉和变异操作算子,能够保证个体的合法性,同时又具有遗传算法本身所要求的随机性。最后给出了某汽车发动机厂金加工车间的生产调度实例,表明了此算法的有效性。

两机flow-shop类型模具热处理车间批调度算法

总结模具热处理车间生产调度的特点,在工件动态到达的情况下,研究了两阶段均为批处理机、各批次加工时间为定值的流水车间批调度问题。以最小化最大完成时间为目标建立混合整数规划数学模型,证明问题是NP难并给出最优目标函数值的下界,构建并证明一种求解大规模问题最优解的算法。算法首先求解分批数量上下界,然后构造数学模型并求解在给定分批数量下对应的最优解,最后通过对比各给定分批数量下得到的解并得到全局最优解。对于小规模问题,通过与传统分枝定界法得到的最优解相比较,说明所提算法能得到问题的最优解且计算时间更短;对于大规模问题,在不同生产状况下随机产生多组数据、对所提算法进行验证,结果显示该算法是有效的。

基于混合差分进化的混排Flow-shop分批优化调度

考虑到实际环境中的订单批量性,研究Flow-shop制造过程分批优化调度。针对制造过程中不同产品所含批量之间允许交叉生产的情况,考虑传输批量大小约束,建立了问题模型。基于分批生产策略设计了一种混合差分进化算法来优化确定批量划分和排序优化。该算法采用两级染色体编码,对划分染色体和排序染色体分别采用前面所设计的进化过程。为了进一步缩短完工时间,在算法解码过程中基于分批传输策略进行二次划分,得到小传输子批。通过实验仿真对所提方法进行比较分析,验证了所设计划分方法的有效性以及算法的优化性能。

柔性Flow-Shop调度的遗传算法优化

柔性Flow-shop调度问题(Flexible Flow-shop Scheduling Problem,FFSP)是一般Flow-shop调度问题的推广,由于在某些工序上存在并行机器,所以比一般的Flow-shop调度问题更复杂。为了有效地解决柔性Flow-shop调度问题,用遗传算法求解,给出了一种改进的编码方法,能够保证个体的合法性;并根据编码方法提出了矩阵解码方法。最后以某汽车发动机厂金加工车间的生产调度实例进行仿真,通过比较表明了算法的有效性。