A variable neighbourhood search algorithm for the flexible job-shop scheduling problem

The flexible job-shop scheduling problem (FJSP) is a generalisation of the classical job-shop scheduling problem which allows an operation of each job to be executed by any machine out of a set of available machines. FJSP consists of two sub-problems which are assigning each operation to a machine out of a set of capable machines (routing sub-problem) and sequencing the assigned operations on the machines (sequencing sub-problem). This paper proposes a variable neighbourhood search (VNS) algorithm that solves the FJSP to minimise makespan. In the process of the presented algorithm, various neighbourhood structures related to assignment and sequencing problems are used for generating neighbouring solutions. To compare our algorithm with previous ones, an extensive computational study on 181 benchmark problems has been conducted. The results obtained from the presented algorithm are quite comparable to those obtained by the best-known algorithms for FJSP.     

Flexible job-shop scheduling with flexible workdays,preemption, overlapping in operations and satisfaction criteria: an industrial application

This paper addresses a real scheduling problem, namely, a complex flexible job-shop scheduling problem (FJSP) with special characteristics (flexible workdays, preemption and overlapping in operations), where the objective is to maximise a satisfaction criterion defined through goal programming. To allow for flexible workdays, the solution representation of the classical FJSP is extended to consider overtime decisions and a sequence of time-cell states, which is used to model resource capability. A new temporal-constraint-handling method is proposed to solve the problem of overlapping in operations in a flexible-workday environment. Three solution methods are proposed to solve this scheduling problem: a heuristic method based on priority rules, a goal-guided tabu search (GGTS) and an extended genetic algorithm (EGA). In the GGTS, the neighbourhood functions are defined based on elimination approaches, and five possible neighbourhood functions (N0???N1???N2???N3???N4) are presented. The effectiveness and efficiency of the three solution methods are verified using dedicated benchmark instances. Computational simulations and comparisons indicate that the proposed N4-based GGTS demonstrates performance competitive with that of the EGA and the GGTSs based on the other neighbourhood functions (N0, N1, N2 and N3) for solving the scheduling problem.     

Learning dispatching rules using random forest in flexible job shop scheduling problems

In this paper, we address the flexible job-shop scheduling problem (FJSP) with release times for minimising the total weighted tardiness by learning dispatching rules from schedules. We propose a random-forest-based approach called Random Forest for Obtaining Rules for Scheduling (RANFORS) in order to extract dispatching rules from the best schedules. RANFORS consists of three phases: schedule generation, rule learning with data transformation, and rule improvement with discretisation. In the schedule generation phase, we present three solution approaches that are widely used to solve FJSPs. Based on the best schedules among them, the rule learning with data transformation phase converts them into training data with constructed attributes and generates a dispatching rule with inductive learning. Finally, the rule improvement with discretisation improves dispatching rules with a genetic algorithm by discretising continuous attributes and changing parameters for random forest with the aim of minimising the average total weighted tardiness. We conducted experiments to verify the performance of the proposed approach and the results showed that it outperforms the existing dispatching rules. Moreover, compared with the other decision-tree-based algorithms, the proposed algorithm is effective in terms of extracting scheduling insights from a set of rules.     

基于Lévy Flight的混合GA在柔性作业车间调度问题中的性能分析

近年来,柔性作业车间调度问题(FJSP)由于其NP难特性与在制造系统中的广泛应用被大量关注。为提高该类问题求解效率,本文在标准Lévy flight的基础上提出了一种新的离散Lévy flight搜索策略,并将该策略与遗传算法框架结合,形成一种离散Lévy flight策略的混合遗传算法。该混合算法通过使用离散Lévy flight搜索策略对每代精英种群进行变步长搜索,提高了算法的局部搜索能力,增强了种群多样性。本文通过将CS、GA和TLBO等经典算法作为对比算法,对不同规模的54个FJSP算例进行实验,证明了所提出的算法具备更好的收敛效果与稳定性,适合于求解大规模FJSP。     

A memetic algorithm for multi-objective flexible job-shop problem with worker flexibility

In existing scheduling models, the flexible job-shop scheduling problem mainly considers machine flexibility. However, human factor is also an important element existing in real production that is often neglected theoretically. In this paper, we originally probe into a multi-objective flexible job-shop scheduling problem with worker flexibility (MO-FJSPW). A non-linear integer programming model is presented for the problem. Correspondingly, a memetic algorithm (MA) is designed to solve the proposed MO-FJSPW whose objective is to minimise the maximum completion time, the maximum workload of machines and the total workload of all machines. A well-designed chromosome encoding/decoding method is proposed and the adaptive genetic operators are selected by experimental studies. An elimination process is executed to eliminate the repeated individuals in population. Moreover, a local search is incorporated into the non-dominated sorting genetic algorithm II. In experimental phase, the crossover operator and elimination operator in MA are examined firstly. Afterwards, some extensive comparisons are carried out between MA and some other multi-objective algorithms. The simulation results show that the MA performs better for the proposed MO-FJSPW than other algorithms.     

A hybrid algorithm for total tardiness minimisation in flexible job shop: genetic algorithm with parallel VNS execution

This paper addresses the flexible-job-shop scheduling problem (FJSP) with the objective of minimising total tardiness. FJSP is the generalisation of the classical job-shop scheduling problem. The difference is that in the FJSP problem, the operations associated with a job can be processed on any set of alternative machines. We developed a new algorithm by hybridising genetic algorithm and variable neighbourhood search (VNS). The genetic algorithm uses advanced crossover and mutation operators to adapt the chromosome structure and the characteristics of the problem. Parallel-executed VNS algorithm is used in the elitist selection phase of the GA. Local search in VNS uses assignment of operations to alternative machines and changing of the order of the selected operation on the assigned machine to increase the result quality while maintaining feasibility. The purpose of parallelisation in the VNS algorithm is to minimise execution time. The performance of the proposed method is validated by numerical experiments on several representative problems and compared with adapted constructive heuristic algorithms’ (earliest due date, critical ratio and slack time per remaining operation) results.     

An effective discrete harmony search algorithm for flexible job shop scheduling problem with fuzzy processing time

This study addresses flexible job shop scheduling problem (FJSP) with fuzzy processing time. The fuzzy or uncertainty of processing time is one of seven characteristics in remanufacturing. A discrete harmony search (DHS) algorithm is proposed for FJSP with fuzzy processing time. The objective is to minimise maximum fuzzy completion time. A simple and effective heuristic rule is proposed to initialise harmony population. Extensive computational experiments are carried out using five benchmark cases with eight instances from remanufacturing. The proposed heuristic rule is evaluated using five benchmark cases. The proposed DHS algorithm is compared to six metaheuristics. The results and comparisons show the effectiveness and efficiency of DHS for solving FJSP with fuzzy processing time.     

A shuffled frog-leaping algorithm for flexible job shop scheduling with the consideration of energy consumption

Flexible job shop scheduling problem (FJSP) has been extensively investigated and objectives are often related to time. Energy-related objective should be considered fully in FJSP with the advent of green manufacturing. In this study, FJSP with the minimisation of workload balance and total energy consumption is considered and the conflicting between two objectives is analysed. A shuffled frog-leaping algorithm (SFLA) is proposed based on a three-string coding approach. Population and a non-dominated set are used to construct memeplexes according to tournament selection and the search process of each memeplex is done on its non-dominated member. Extensive experiments are conducted to test the search performance of SFLA and computational results show the conflicting between two objectives of FJSP and the promising advantages of SFLA on the considered FJSP.     

A hybrid artificial bee colony algorithm for flexible job shop scheduling with worker flexibility

The traditional flexible job shop scheduling problem (FJSP) considers machine flexibility but not worker flexibility. Given the influence and potential of human factors in improving production efficiency and decreasing the cost in practical production systems, we propose a mathematical model of an extended FJSP with worker flexibility (FJSPW). A hybrid artificial bee colony algorithm (HABCA) is presented to solve the proposed FJSPW. For the HABCA, effective encoding, decoding, crossover and mutation operators are designed, and a new effective local search method is developed to improve the speed and exploitation ability of the algorithm. The Taguchi method of Design of Experiments is used to obtain the best combination of key parameters of the HABCA. Extensive computational experiments carried out to compare the HABCA with some well-performing algorithms from the literature confirm that the proposed HABCA is more effective than these algorithms, especially on large-scale FJSPW instances.     

A GRASP algorithm for flexible job-shop scheduling problem with limited resource constraints

A greedy randomised adaptive search procedure (GRASP) is an iterative multi-start metaheuristic for difficult combinatorial optimisation. The GRASP iteration consists of two phases: a construction phase, in which a feasible solution is found and a local search phase, in which a local optimum in the neighbourhood of the constructed solution is sought. In this paper, a GRASP algorithm is presented to solve the flexible job-shop scheduling problem (FJSSP) with limited resource constraints. The main constraint of this scheduling problem is that each operation of a job must follow an appointed process order and each operation must be processed on an appointed machine. These constraints are used to balance between the resource limitation and machine flexibility. The model objectives are the minimisation of makespan, maximum workload and total workload. Representative benchmark problems are solved in order to test the effectiveness and efficiency of the GRASP algorithm. The computational result shows that the proposed algorithm produced better results than other authors’ algorithms.     

遗传算法的双目标柔性作业车间调度研究

研究了FMS环境下先进制造车间路径柔性的优化调度问题.同时考虑现代生产准时制的要求,建立了柔性作业车间调度问题的双目标数学优化模型,并给出了求解模型的遗传算法的具体实现过程;针对模型的特殊性,提出了染色体两层编码结构,将AOV网络图应用到解码和适应度函数的计算中,通过一个调度实例进行验证,给出了相应的选择、交叉、变异操作设计方案.     

An effective estimation of distribution algorithm for the flexible job-shop scheduling problem with fuzzy processing time

Considering the fuzzy nature of the data in real-world scheduling, an effective estimation of distribution algorithm (EDA) is proposed to solve the flexible job-shop scheduling problem with fuzzy processing time. A probability model is presented to describe the probability distribution of the solution space. A mechanism is provided to update the probability model with the elite individuals. By sampling the probability model, new individuals can be generated among the search region with promising solutions. Moreover, a left-shift scheme is employed for improving schedule solution when idle time exists on the machine. In addition, some fuzzy number operations are used to calculate scheduling objective value. The influence of parameter setting is investigated based on the Taguchi method of design of experiment, and a suitable parameter setting is suggested. Numerical testing results and comparisons with some existing algorithms are provided, which demonstrate the effectiveness of the proposed EDA.     

Bad-scenario-set robust scheduling for a job shop to hedge against processing time uncertainty

This paper proposed two robust scheduling formulations in real manufacturing systems based on the concept of bad scenario set to hedge against processing time uncertainty, which is described by discrete scenarios. Two proposed robust scheduling formulations are applied to an uncertain job-shop scheduling problem with the makespan as the performance criterion. The united-scenario neighbourhood (UN) structure is constructed based on bad scenario set for the scenario job-shop scheduling problem. A tabu search (TS) algorithm with the UN structure is developed to solve the proposed robust scheduling problem. An extensive experiment was conducted. The computational results show that the first robust scheduling formulation could be preferred to the second one for the discussed problem. It is also verified that the obtained robust solutions could hedge against the processing time uncertainty through decreasing the number of bad scenarios and the degree of performance degradation on bad scenarios. Moreover, the computational results demonstrate that the developed TS algorithm is competitive for the proposed robust scheduling formulations.     

Flexible job-shop scheduling problems with ‘AND’/‘OR’ precedence constraints

The purpose of this research is to solve flexible job-shop scheduling problems with ‘AND’/‘OR’ precedence constraints in the operations. We first formulate the problem as a Mixed-Integer Linear Program (MILP). The MILP can be used to compute optimal solutions for small-sized problems. We also developed a heuristic algorithm that can obtain a good solution for the problem regardless of its size. Moreover, we have developed a representation and schedule builder that always produces a legal and feasible solution for the problem, and developed genetic and tabu search algorithms based on the proposed schedule builder. The results of the computational experiments show that the developed meta-heuristics are very effective.     

A knowledge-guided fruit fly optimization algorithm for dual resource constrained flexible job-shop scheduling problem

Different from the classical job shop scheduling, the dual-resource constrained flexible job-shop scheduling problem (DRCFJSP) should deal with job sequence, machine assignment and worker assignment all together. In this paper, a knowledge-guided fruit fly optimisation algorithm (KGFOA) with a new encoding scheme is proposed to solve the DRCFJSP with makespan minimisation criterion. In the KGFOA, two types of permutation-based search operators are used to perform the smell-based search for job sequence and resource (machine and worker) assignment, respectively. To enhance the search capability, a knowledge-guided search stage is incorporated into the KGFOA with two new search operators particularly designed for adjusting the operation sequence and the resource assignment, respectively. Due to the combination of the knowledge-guided search and the smell-based search, global exploration and local exploitation can be balanced. Besides, the effect of parameter setting of the KGFOA is investigated and numerical tests are carried out using two sets of instances. The comparative results show that the KGFOA is more effective than the existing algorithms in solving the DRCFJSP.     

Variable neighbourhood search for dual-resource constrained flexible job shop scheduling

Dual-resource constrained flexible job shop scheduling problem (FJSP) is considered and an effective variable neighbourhood search (VNS) is presented, in which the solution to the problem is indicated as a quadruple string of the ordered operations and their resources. Two neighbourhood search procedures are sequentially executed to produce new solutions for two sub-problems of the problem, respectively. The search of VNS is restarted from a slightly perturbed version of the current solution of VNS when the determined number of iterations is reached. VNS is tested on some instances and compared with methods from literature. Computational results show the significant advantage of VNS on the problem.     

A GRASP algorithm for flexible job-shop scheduling with maintenance constraints

In most realistic situations, machines may be unavailable due to maintenance, pre-schedules and so on. The availability constraints are non-fixed in that the completion time of the maintenance task is not fixed and has to be determined during the scheduling procedure. In this paper a greedy randomised adaptive search procedure (GRASP) algorithm is presented to solve the flexible job-shop scheduling problem with non-fixed availability constraints (FJSSP-nfa). The GRASP algorithm is a metaheuristic algorithm which is characterised by multiple initialisations. Basically, it operates in the following manner: first a feasible solution is obtained, which is then further improved by a local search technique. The main objective is to repeat these two phases in an iterative manner and to preserve the best found solution. Representative FJSSP-nfa benchmark problems are solved in order to test the effectiveness and efficiency of the proposed algorithm.     

Mixed Self-adapting GA Optimal Scheduling Algorithm for a Multiple Resource Job-shop

With an aim at the job-shop scheduling problem of multiple resource constraints, this paper presents mixed self-adapting Genetic Algorithm （ GA ） , and establishes a job-shop optimal scheduling model of multiple resource constraints based on the effect of priority scheduling rules in the heuristic algorithm upon the scheduling target. New coding regulations or rules are designed. The sinusoidal function is adopted as the self-adapting factor, thus making cross probability and variable probability automatically change with group adaptability in such a way as to overcome the shortcoming in the heuristic algorithm and common GA, so that the operation efficiency is improved. The results from real example simulation and comparison with other algorithms indicate that the mixed self-adapting GA algorithm can well solve the job-shop optimal scheduling problem under the constraints of various kinds of production resources such as machine-tools and cutting tools.     

混合花朵授粉算法在作业车间调度中的应用

对最大完工时间最短的作业车间调度问题进行了研究,总结了当前求解作业车间调度问题的研究现状,提出一种花朵授粉算法与遗传算法的混合算法。混合算法以花朵授粉算法为基础,重新定义其全局搜索和局部搜索迭代公式,在同化操作过程中融入遗传算法的选择、优先交叉和变异操作,进一步增强算法的勘探能力。通过26个经典的基准算例仿真实验,并与近5年的其他算法比较,结果表明所提算法在求解作业车间调度问题具有一定优势。     

A hybrid artificial bee colony algorithm for a flexible job shop scheduling problem with overlapping in operations

Overlapping in operations is an effective technology for productivity improvement in modern manufacturing systems. Thus far, however, there are still rare works on flexible job shop scheduling problems (FJSPs) concerning this strategy. In this paper, we present a hybrid artificial bee colony (hyABC) algorithm to minimise the total flowtime for a FJSP with overlapping in operations. In the proposed hyABC, a dynamic scheme is introduced to fine-tune the search scope adaptively. In view of poor exploitation ability of artificial bee colony algorithm, a modified migrating birds optimisation algorithm (MMBO) is developed and integrated into the search process for better balancing global exploration and local exploitation. In MMBO, a forward share strategy with one-job based crossover is designed to make good use of valuable information from behind solutions. Besides, an improved downward share scheme is adopted to increase diversification of the population, and thus alleviate the premature convergence. Extensive experiments based on benchmark instances with different scales are carried out and comparisons with other recent algorithms identify the effectiveness of the proposed hyABC.