A hybrid harmony search algorithm for the flexible job shop scheduling problem

In this paper, a novel hybrid harmony search (HHS) algorithm based on the integrated approach, is proposed for solving the flexible job shop scheduling problem (FJSP) with the criterion to minimize makespan. First of all, to make the harmony search (HS) algorithm adaptive to the FJSP, the converting techniques are developed to convert the continuous harmony vector to a kind of discrete two-vector code for the FJSP. Secondly, the harmony vector is mapped into a feasible active schedule through effectively decoding the transformed two-vector code, which could largely reduce the search space. Thirdly, a resultful initialization scheme combining heuristic and random strategies is introduced to make the initial harmony memory (HM) occur with certain quality and diversity. Furthermore, a local search procedure is embedded in the HS algorithm to enhance the local exploitation ability, whereas HS is employed to perform exploration by evolving harmony vectors in the HM. To speed up the local search process, the improved neighborhood structure based on common critical operations is presented in detail. Empirical results on various benchmark instances validate the effectiveness and efficiency of our proposed algorithm. Our work also indicates that a well designed HS-based method is a competitive alternative for addressing the FJSP.     

Discrete harmony search algorithm for flexible job shop scheduling problem with multiple objectives

Flexible job-shop scheduling problem (FJSP) is a practically useful extension of the classical job shop scheduling problem. This paper proposes an effective discrete harmony search (DHS) algorithm to solve FJSP. The objectives are the weighted combination of two minimization criteria namely, the maximum of the completion time (Makespan) and the mean of earliness and tardiness. Firstly, we develop a new method for the initial machine assignment task. Some existing heuristics are also employed for initializing the harmony memory with discrete machine permutation for machine assignment and job permutation for operation sequencing. Secondly, we develop a new rule for the improvisation to produce a new harmony for FJSP incorporating machine assignment and operation sequencing. Thirdly, several local search methods are embedded to enhance the algorithm’s local exploitation ability. Finally, extensive computational experiments are carried out using well-known benchmark instances. Computational results and comparisons show the efficiency and effectiveness of the proposed DHS algorithm for solving the FJSP with weighted combination of two objectives.     

Discrepancy search for the flexible job shop scheduling problem

The flexible job shop scheduling problem (FJSP) is a generalization of the classical job shop problem in which each operation must be processed on a given machine chosen among a finite subset of candidate machines. The aim is to find an allocation for each operation and to define the sequence of operations on each machine, so that the resulting schedule has a minimal completion time. We propose a variant of the climbing discrepancy search approach for solving this problem. We also present various neighborhood structures related to assignment and sequencing problems. We report the results of extensive computational experiments carried out on well-known benchmarks for flexible job shop scheduling. The results demonstrate that the proposed approach outperforms the best-known algorithms for the FJSP on some types of benchmarks and remains comparable with them on other ones.     

多目标柔性作业调度的优化研究

针对以生产周期、生产成本、设备利用率为目标的柔性作业调度问题,基于混合遗传算法提出了一种新的优化求解方法。首先建立了该类问题的调度模型,基于工序编码的染色体决定了工序调度的优先级;利用无量纲的标准化处理方法统一目标量纲;然后,利用层次分析法将多目标问题转化为单目标问题,同时为了保证算法的收敛性,在基本遗传算法框架的基础上集成了禁忌搜索算法,从而延缓或避免了早熟收敛的发生。最后通过实验仿真,证明提出的方法可以有效解决该类多目标柔性作业调度问题。     

Path-relinking Tabu search for the multi-objective flexible job shop scheduling problem

The multi-objective flexible job shop scheduling problem is solved using a novel path-relinking algorithm based on the state-of-the-art Tabu search algorithm with back-jump tracking. A routing solution is identified by problem-specific neighborhood search, and is then further refined by the Tabu search algorithm with back-jump tracking for a sequencing decision. The resultant solution is used to maintain the medium-term memory where the best solutions are stored. A path-relinking heuristics is designed to generate diverse solutions in the most promising areas. An improved version of the algorithm is then developed by incorporating an effective dimension-oriented intensification search to find solutions that are located near extreme solutions. The proposed algorithms are tested on benchmark instances and its experimental performance is compared with that of algorithms in the literature. Comparison results show that the proposed algorithms are competitive in terms of its computation performance and solution quality.     

A hybrid discrete differential evolution algorithm for the no-idle permutation flow shop scheduling problem with makespan criterion

This paper presents a hybrid discrete differential evolution (HDDE) algorithm for the no-idle permutation flow shop scheduling problem with makespan criterion, which is not so well studied. The no-idle condition requires that each machine must process jobs without any interruption from the start of processing the first job to the completion of processing the last job. A novel speed-up method based on network representation is proposed to evaluate the whole insert neighborhood of a job permutation and employed in HDDE, and moreover, an insert neighborhood local search is modified effectively in HDDE to balance global exploration and local exploitation. Experimental results and a thorough statistical analysis show that HDDE is superior to the existing state-of-the-art algorithms by a significant margin.     

An integrated search heuristic for large-scale flexible job shop scheduling problems

The flexible job shop scheduling problem (FJSP) is a generalization of the classical job shop scheduling problem (JSP), where each operation is allowed to be processed by any machine from a given set, rather than one specified machine. In this paper, two algorithm modules, namely hybrid harmony search (HHS) and large neighborhood search (LNS), are developed for the FJSP with makespan criterion. The HHS is an evolutionary-based algorithm with the memetic paradigm, while the LNS is typical of constraint-based approaches. To form a stronger search mechanism, an integrated search heuristic, denoted as HHS/LNS, is proposed for the FJSP based on the two algorithms, which starts with the HHS, and then the solution is further improved by the LNS. Computational simulations and comparisons demonstrate that the proposed HHS/LNS shows competitive performance with state-of-the-art algorithms on large-scale FJSP problems, and some new upper bounds among the unsolved benchmark instances have even been found.     

An efficient search method for multi-objective flexible job shop scheduling problems

Flexible job shop scheduling is very important in both fields of production management and combinatorial optimization. Owing to the high computational complexity, it is quite difficult to achieve an optimal solution to this problem with traditional optimization approaches. Motivated by some empirical knowledge, we propose an efficient search method for the multi-objective flexible job shop scheduling problems in this paper. Through the work presented in this work, we hope to move a step closer to the ultimate vision of an automated system for generating optimal or near-optimal production schedules. The final experimental results have shown that the proposed algorithm is a feasible and effective approach for the multi-objective flexible job shop scheduling problems.     

相关工件车间调度问题的拓扑算法

针对加工装配型离散制造企业实际生产的特点,提出了一类用于表示工序之间偏序关系的相关工件车间调度问题。为了利用已有的求解表示工序之间的线序关系的传统车间调度算法求解相关工件车间调度问题,设计了一种拓扑算法,该算法能够将工序之间的偏序关系转化为线序关系,将相关工件车间调度问题转化为传统的车间调度问题,通过实证研究,结果表明了拓扑算法是可行和高效的。     

A GEP-based reactive scheduling policies constructing approach for dynamic flexible job shop scheduling problem with job release dates

Flexible job shop scheduling problem (FJSSP) is generalization of job shop scheduling problem (JSSP), in which an operation may be processed on more than one machine each of which has the same function. Most previous researches on FJSSP assumed that all jobs to be processed are available at the beginning of scheduling horizon. The assumption, however, is always violated in practical industries because jobs usually arrive over time and can not be predicted before their arrivals. In the paper, dynamic flexible job shop scheduling problem (DFJSSP) with job release dates is studied. A heuristic is proposed to implement reactive scheduling for the dynamic scheduling problem. An approach based on gene expression programming (GEP) is also proposed which automatically constructs reactive scheduling policies for the dynamic scheduling. In order to evaluate the performance of the reactive scheduling policies constructed by the proposed GEP-based approach under a variety of processing conditions three factors, such as the shop utilization, due date tightness, problem flexibility, are considered in the simulation experiments. The scheduling performance measure considered in the simulation is the minimization of makespan, mean flowtime and mean tardiness, respectively. The results show that GEP-based approach can construct more efficient reactive scheduling policies for DFJSSP with job release dates under a big range of processing conditions and performance measures in the comparison with previous approaches.     

A hybrid variable neighborhood search algorithm for solving the limited-buffer permutation flow shop scheduling problem with the makespan criterion

This paper investigates the limited-buffer permutation flow shop scheduling problem (LBPFSP) with the makespan criterion. A hybrid variable neighborhood search (HVNS) algorithm hybridized with the simulated annealing algorithm is used to solve the problem. A method is also developed to decrease the computational effort needed to implement different types of local search approaches used in the HVNS algorithm. Computational results show the higher efficiency of the HVNS algorithm as compared with the state-of-the-art algorithms. In addition, the HVNS algorithm is competitive with the algorithms proposed in the literature for solving the blocking flow shop scheduling problem (i.e., LBPFSP with zero-capacity buffers), and finds 54 new upper bounds for the Taillard's benchmark instances.     

An effective asexual genetic algorithm for solving the job shop scheduling problem

By using the notion of elite pool, this paper presents an effective asexual genetic algorithm for solving the job shop scheduling problem. Based on mutation operations, the algorithm selectively picks the solution with the highest quality from the pool and after its modification, it can replace the solution with the lowest quality with such a modified solution. The elite pool is initially filled with a number of non-delay schedules, and then, in each iteration, the best solution of the elite pool is removed and mutated in a biased fashion through running a limited tabu search procedure. A decision strategy which balances exploitation versus exploration determines (i) whether any intermediate solution along the run of tabu search should join the elite pool, and (ii) whether upon joining a new solution to the pool, the worst solution should leave the pool. The genetic algorithm procedure is repeated until either a time limit is reached or the elite pool becomes empty. The results of extensive computational experiments on the benchmark instances indicate that the success of the procedure significantly depends on the employed mechanism of updating the elite pool. In these experiments, the optimal value of the well-known 10 × 10 instance, ft10, is obtained in 0.06 s. Moreover, for larger problems, solutions with the precision of less than one percent from the best known solutions are achieved within several seconds.     

New local diversification techniques for flexible job shop scheduling problem with a multi-agent approach

The Flexible Job Shop problem is among the hardest scheduling problems. It is a generalization of the classical Job Shop problem in that each operation can be processed by a set of resources and has a processing time depending on the resource used. The objective is to assign and to sequence the operations on the resources so that they are processed in the smallest time. In our previous work, we have proposed two Multi-Agent approaches based on the Tabu Search (TS) meta-heuristic. Depending on the location of the optimisation core in the system, we have distinguished between the global optimisation approach where the TS has a global view on the system and the local optimisation approach (FJS MATSLO) where the optimisation is distributed among a collection of agents, each of them has its own local view. In this paper, firstly, we propose new diversification techniques for the second approach in order to get better results and secondly, we propose a new promising approach combining the two latter ones. Experimental results are also presented in this paper in order to evaluate these new techniques.     

基于改进离散和声算法的批量流水线调度研究

针对批量流水线调度问题,提出了以总流经时间为目标的改进离散和声算法。与基本的和声算法相比,该算法首先采用了基于工件序列的编码方式,使其直接应用于调度问题,同时运用NEH和SWAP方法产生初始和声库,保证了初始种群具有较高的质量和多样性。使用自适应和声微调概率参数和INSERT方法产生新解,提高了算法的优化性能。为了提高算法的局部搜索能力,结合交换扰动策略和插入邻域搜索算法给出了两种混合求解策略。仿真实验表明所提算法的有效性。     

Genetic tabu search for the fuzzy flexible job shop problem

This paper tackles the flexible job-shop scheduling problem with uncertain processing times. The uncertainty in processing times is represented by means of fuzzy numbers, hence the name fuzzy flexible job-shop scheduling. We propose an effective genetic algorithm hybridised with tabu search and heuristic seeding to minimise the total time needed to complete all jobs, known as makespan. To build a high-quality and diverse set of initial solutions we introduce a heuristic method which benefits from the flexible nature of the problem. This initial population will be the starting point for the genetic algorithm, which then applies tabu search to every generated chromosome. The tabu search algorithm relies on a neighbourhood structure that is proposed and analysed in this paper; in particular, some interesting properties are proved, such as feasibility and connectivity. Additionally, we incorporate a filtering mechanism to reduce the neighbourhood size and a method that allows to speed-up the evaluation of new chromosomes. To assess the performance of the resulting method and compare it with the state-of-the-art, we present an extensive computational study on a benchmark with 205 instances, considering both deterministic and fuzzy instances to enhance the significance of the study. The results of these experiments clearly show that not only does the hybrid algorithm benefit from the synergy among its components but it is also quite competitive with the state-of-the-art when solving both crisp and fuzzy instances, providing new best-known solutions for a number of these test instances.     

A parallel membrane inspired harmony search for optimization problems: A case study based on a flexible job shop scheduling problem

Harmony search is an emerging meta-heuristic optimization algorithm that is inspired by musical improvisation processes, and it can solve various optimization problems. Membrane computing is a distributed and parallel model for solving hard optimization problems. First, we employed some previously proposed approaches to improve standard harmony search by allowing its parameters to be adaptive during the processing steps. Information from the best solutions was used to improve the speed of convergence while preventing premature convergence to a local minimum. Second, we introduced a parallel framework based on membrane computing to improve the harmony search. Our approach utilized the parallel membrane computing model to execute parallelized harmony search efficiently on different cores, where the membrane computing communication characteristics were used to exchange information between the solutions on different cores, thereby increasing the diversity of harmony search and improving the performance of harmony search. Our simulation results showed that the application of the proposed approach to different variants of harmony search yielded better performance than previous approaches. Furthermore, we applied the parallel membrane inspired harmony search to the flexible job shop scheduling problem. Experiments using well-known benchmark instances showed the effectiveness of the algorithm.     

猫群优化算法求解柔性作业车间调度问题

根据柔性作业车间的生产特点,对基本猫群优化算法进行设计和改进,提出了一种改进型猫群优化算法（Improved Cat Swarm Optimization,ICSO）,用于优化车间内工件的最大完工时间。算法给出了两段式个体位置编码方式和基于启发式算法的种群初始化策略;采用自适应行为模式选择方法,使其能够有效协调算法全局和局部搜索;提出了基于多样化搜寻算子的搜寻模式,增强算法的全局搜索能力;提出了基于莱维飞行的跟踪模式,增强算法的局部搜索能力。此外,算法中还引入了跳跃机制,使算法性能能够得到进一步的改善。实验数据表明ICSO算法在求解FJSP问题方面具有一定的有效性。     

多阶段人机协同求解动态柔性作业车间调度问题

针对柔性作业车间生产环境中机器故障的动态调度问题, 以最小最大完工时间和最小偏差为目标, 结合车间调度人员的经验建立多阶段人机协同动态调度策略. 在不同阶段该策略的调度人员可参与优化过程, 提高方案的可行性和稳定性. 设计外部精英库中最优解的更新方法, 依据海明距离保留具有相同目标值的多种调度方案. 最后通过实例仿真验证了该模型和算法的有效性、可行性和稳定性, 更便于有效地指导生产实践.

     

Effective ensembles of heuristics for scheduling flexible job shop problem with new job insertion

This study investigates the flexible job shop scheduling problem (FJSP) with new job insertion. FJSP with new job insertion includes two phases: initializing schedules and rescheduling after each new job insertion. Initializing schedules is the standard FJSP problem while rescheduling is an FJSP with different job start time and different machine start time. The time to do rescheduling is the same as the time of new job insertion. Four ensembles of heuristics are proposed for scheduling FJSP with new job insertion. The objectives are to minimize maximum completion time (makespan), to minimize the average of earliness and tardiness (E/T), to minimize maximum machine workload (Mworkload) and total machine workload (Tworkload). Extensive computational experiments are carried out on eight real instances from remanufacturing enterprise. The results and comparisons show the effectiveness of the proposed heuristics for solving FJSP with new job insertion.     

离散和声求解带启动时间批量流水线调度问题

分别在有等待和无等待的情况下,深入分析了带有启动时间的批量调度问题,以最小化最大完成时间为目标,提出了两种离散和声搜索算法。针对算法本质连续而问题离散的矛盾,对和声搜索算法进行改进。首先提出了基于工序的编码方式,采用inver-over和重组两种离散算子产生候选解的进化机制;并利用改进的NEH(Nawaz-Enscore-Ham)方法进行初始化,产生的高质量和多样化的初始种群有效地指导了算法的进化方向,提高收敛速度;最后将一种简单而有效的局部邻域搜索方法嵌入到和声搜索算法中以增强其局部搜索能力。仿真实验和比较结果表明了所提算法的有效性。