A hybrid variable neighborhood search for solving the hybrid flow shop scheduling problem

This paper proposes a hybrid variable neighborhood search (HVNS) algorithm that combines the chemical-reaction optimization (CRO) and the estimation of distribution (EDA), for solving the hybrid flow shop (HFS) scheduling problems. The objective is to minimize the maximum completion time. In the proposed algorithm, a well-designed decoding mechanism is presented to schedule jobs with more flexibility. Meanwhile, considering the problem structure, eight neighborhood structures are developed. A kinetic energy sensitive neighborhood change approach is proposed to extract global information and avoid being stuck at the local optima. In addition, contrary to the fixed neighborhood set in traditional VNS, a dynamic neighborhood set update mechanism is utilized to exploit the potential search space. Finally, for the population of local optima solutions, an effective EDA-based global search approach is investigated to direct the search process to promising regions. The proposed algorithm is tested on sets of well-known benchmark instances. Through the analysis of experimental results, the high performance of the proposed HVNS algorithm is shown in comparison with four efficient algorithms from the literature.     

应用强化学习算法求解置换流水车间调度问题

面对日益增长的大规模调度问题,新型算法的开发越显重要.针对置换流水车间调度问题,提出了一种基于强化学习Q-Learning调度算法.通过引入状态变量和行为变量,将组合优化的排序问题转换成序贯决策问题,来解决置换流水车间调度问题.采用所提算法对OR-Library提供Flow-shop国际标准算例进行测试,并与已有的一些算法对比,结果表明算法的有效性.     

求解批量流水线调度问题的和声算法

针对以最大完工时间和总流经时间为目标的批量流水线调度问题,提出了改进的和声调度算法。该算法采用基于最大位置值(LPV)规则的编码方式,使具有连续性质的和声算法应用于求解调度问题;提出新的初始化方法,应用了多种群进化的思想更新和声库,并结合和声算法和模拟退火算法各自的特点,给出了两种混合调度算法。仿真实验表明所提算法的可行性和有效性。     

Evolutionary algorithms for scheduling m-machine flow shop with lot streaming

This paper addresses the problem of making sequencing and scheduling decisions for n jobs–m-machines flow shops under lot sizing environment. Lot streaming (Lot sizing) is the process of creating sub lots to move the completed portion of a production sub lots to down stream machines. There is a scope for efficient algorithms for scheduling problems in m-machine flow shop with lot streaming. In recent years, much attention is given to heuristics and search techniques. Evolutionary algorithms that belong to search heuristics find more applications in recent research. Genetic algorithm (GA) and hybrid genetic algorithm (HEA) also known as hybrid evolutionary algorithm fall under evolutionary heuristics. On this concern this paper proposes two evolutionary algorithms namely, GA and HEA to evolve best sequence for makespan/total flow time criterion for m-machine flow shop involved with lot streaming and set-up time. The following two algorithms are used to evaluate the performance of the proposed GA and HEA: (i) Baker's algorithm (BA), an optimal solution procedure for two-machine flow shop problem with lot streaming and makespan objective criterion and (ii) simulated annealing algorithm (SA) for m-machine flow shop problem with lot streaming and makespan and total flow time criteria.     

An improved particle swarm optimization algorithm for flowshop scheduling problem

The flowshop scheduling problem has been widely studied and many techniques have been applied to it, but few algorithms based on particle swarm optimization (PSO) have been proposed to solve it. In this paper, an improved PSO algorithm (IPSO) based on the “alldifferent” constraint is proposed to solve the flow shop scheduling problem with the objective of minimizing makespan. It combines the particle swarm optimization algorithm with genetic operators together effectively. When a particle is going to stagnate, the mutation operator is used to search its neighborhood. The proposed algorithm is tested on different scale benchmarks and compared with the recently proposed efficient algorithms. The results show that the proposed IPSO algorithm is more effective and better than the other compared algorithms. It can be used to solve large scale flow shop scheduling problem effectively.     

The economic lot scheduling problem in limited-buffer flexible flow shops: Mathematical models and a discrete fruit fly algorithm

This paper considers the lot scheduling problem in the flexible flow shop with limited intermediate buffers to minimize total cost which includes the inventory holding and setup costs. The single available mathematical model by Akrami et al. (2006) for this problem suffers from not only being non-linear but also high size-complexity. In this paper, two new mixed integer linear programming models are developed for the problem. Moreover, a fruit fly optimization algorithm is developed to effectively solve the large problems. For model’s evaluation, this paper experimentally compares the proposed models with the available model. Moreover, the proposed algorithm is also evaluated by comparing with two well-known algorithms (tabu search and genetic algorithm) in the literature and adaption of three recent algorithms for the flexible flow shop problem. All the results and analyses show the high performance of the proposed mathematical models as well as fruit fly optimization algorithm.     

面向多目标流水车间调度的多种群多目标遗传算法

针对制造型企业普遍存在的流水车间调度问题,建立了以最小化最迟完成时间和总延迟时间为目标的多目标调度模型,并提出一种基于分解方法的多种群多目标遗传算法进行求解.该算法将多目标流水车间调度问题分解为多个单目标子问题,并分阶段地将这些子问题引入到算法迭代过程进行求解.算法在每次迭代时,依据种群的分布情况选择各子问题的最好解及与其相似的个体分别为当前求解的子问题构造子种群,通过多种群的进化完成对多个子问题最优解的并行搜索.通过对标准测试算例进行仿真实验,结果表明所提出的算法在求解该问题上能够获得较好的非支配解集.     

求解车间调度问题的自适应混合粒子群算法

针对最小完工时间的流水车间作业调度问题,提出了一种自适应混合粒子群进化算法--AHPSO,将遗传操作有效地结合到粒子群算法中.定义了粒子相似度及粒子能量,粒子相似度阈值随迭代次数动态自适应变化,而粒子能量阈值与群体进化程度及其自身进化速度相关.此外,针对算法运行后期进化速度慢的缺点,提出了一种基于邻域的随机贪心策略进一步提高算法的性能.最后将此算法在不同规模的实例上进行了测试,并与其他几种具有代表性的算法进行了比较,实验结果表明,无论是在求解质量还是稳定性方面都优于其他几种算法,并且能够有效求解大规模车间作业问题.     

批量无等待调度问题的微粒群蛙跳混合优化算法*

将离散微粒群与蛙跳算法相结合解决以最大完工时间为指标的批量无等待流水线调度问题.结合微粒群算法较强的全局收敛能力和蛙跳算法较强的深度搜索能力,设计了三种混合算法,平衡了算法的全局开发能力和局部探索能力.对随机生成不同规模的实例进行了广泛的实验,仿真实验结果的比较表明了所得混合算法的有效性和高效性.     

Two-machine flow shop scheduling problem with blocking,multi-task flexibility of the first machine,and preemption

Blocking flow shop scheduling problem has been extensively studied in recent years; however, some applications mentioned for this problem have some additional characteristics that have not been well considered. Multi-task flexibility of machines and preemption are two of such characteristics. Multi-task flexible machines are capable of processing the operations of at least one other machine in the system. In addition, if preemption is allowed, the solution space grows, and solutions that are more efficient may be obtained. In this study, the two-machine flow shop scheduling problem with blocking, multi-task flexibility of the first machine, and preemption is investigated by considering the minimization of makespan as criterion. It is proved that the complexity of the problem is strongly NP-hard. Because of preemption and multi-task flexibility, there are infinite schedules for each sequence; however, it is shown that a dominant schedule can be defined for each sequence. Two mathematical models are proposed for optimally solving the small-sized instances. Furthermore, a variable neighborhood search algorithm (VNS) and a new variant of it, namely, dynamic VNS (DVNS), are presented to find high quality solutions for large-sized instances. Unlike the VNS algorithm, the DVNS algorithm does not need tuning for the shaking phase. Nevertheless, computational results show that DVNS has even a slightly better performance. The VNS and DVNS algorithms are also compared with some of the best-performing metaheuristics already developed for the flow shop scheduling problem with blocking and minimization of makespan as criterion. Computational results reveal that both algorithms are superior to the others for large-sized instances.     

An immunoglobulin-based artificial immune system for solving the hybrid flow shop problem

We consider the n-job, k-stage problem in a hybrid flow shop (HFS) with the objective of minimizing the maximum completion time, or makespan, which is an NP-hard problem. An immunoglobulin-based artificial immune system algorithm, called IAIS algorithm, is developed to search for the best sequence. IAIS, which is better fit the natural immune system, improves the existing AIS by the process before/after encounter with antigens. Before encounter with antigens, a new method of somatic recombination is presented; after encounter with antigens, an isotype switching is proposed. The isotype switching is a new approach in artificial immune system, and its purpose is to produce antibodies with the same protection but different function to defense the antigen. To verify IAIS, comparisons with the existing immune-based algorithms and other non-immune-based algorithms are made. Computational results show that IAIS is very competitive for the hybrid flow shop scheduling problem.     

SOLVING THE OPEN SHOP SCHEDULING PROBLEM VIA A HYBRID GENETIC-VARIABLE NEIGHBORHOOD SEARCH ALGORITHM

In this article, a hybrid metaheuristic method for solving the open shop scheduling problem (OSSP) is proposed. The optimization criterion is the minimization of makespan and the solution method consists of four components: a randomized initial population generation, a heuristic solution included in the initial population acquired by a Nawaz-Enscore-Ham (NEH)-based heuristic for the flow shop scheduling problem, and two interconnected metaheuristic algorithms: a variable neighborhood search and a genetic algorithm. To our knowledge, this is the first hybrid application of genetic algorithm (GA) and variable neighborhood search (VNS) for the open shop scheduling problem. Computational experiments on benchmark data sets demonstrate that the proposed hybrid metaheuristic reaches a high quality solution in short computational times. Moreover, 12 new hard, large-scale open shop benchmark instances are proposed that simulate realistic industrial cases.     

求解多目标流水车间调度Pareto最优解的遗传强化算法

针对多目标流水车间调度Pareto最优问题, 本文建立了以最大完工时间和最大拖延时间为优化目标的多目标流水车间调度问题模型, 并设计了一种基于Q-learning的遗传强化学习算法求解该问题的Pareto最优解. 该算法引入状态变量和动作变量, 通过Q-learning算法获得初始种群, 以提高初始解质量. 在算法进化过程中, 利用Q表指导变异操作, 扩大局部搜索范围. 采用Pareto快速非支配排序以及拥挤度计算提高解的质量以及多样性, 逐步获得Pareto最优解. 通过与遗传算法、NSGA-II算法和Q-learning算法进行对比实验, 验证了改进后的遗传强化算法在求解多目标流水车间调度问题Pareto最优解的有效性.     

Hybrid monkey search algorithm for flow shop scheduling problem under makespan and total flow time

This paper addresses a sub-population based hybrid monkey search algorithm to solve the flow shop scheduling problem which has been proved to be non-deterministic polynomial time hard (NP-hard) type combinatorial optimization problems. Minimization of makespan and total flow time are the objective functions considered. In the proposed algorithm, two different sub-populations for the two objectives are generated and different dispatching rules are used to improve the solution quality. To the best of our knowledge, this is the first application of monkey search algorithm to solve the flow shop scheduling problems. The performance of the proposed algorithm has been tested with the benchmark problems addressed in the literature. Computational results reveal that the proposed algorithm outperforms many other heuristics and meta-heuristics addressed in the literature.     

A new ant colony algorithm for makespan minimization in permutation flow shops

The problem of scheduling in permutation flow shop with the objective of minimizing the maximum completion time, or makespan, is considered. A new ant colony optimization algorithm is developed for solving the problem. A novel mechanism is employed in initializing the pheromone trails based on an initial sequence. Moreover, the pheromone trail intensities are limited between lower and upper bounds which change dynamically. When a complete sequence of jobs is constructed by an artificial ant, a local search is performed to improve the performance quality of the solution. The proposed ant colony algorithm is applied to Taillard’s benchmark problems. Computational experiments suggest that the algorithm yields better results than well-known ant colony optimization algorithms available in the literature.     

Solving a bi-criteria permutation flow-shop problem using shuffled frog-leaping algorithm

Flow shop problems as a typical manufacturing challenge have gained wide attention in academic fields. In this paper, we consider a bi-criteria permutation flow shop scheduling problem, where the weighted mean completion time and the weighted mean tardiness are to be minimized simultaneously. Due to the complexity of the problem, it is very difficult to obtain optimum solution for this kind of problems by means of traditional approaches. Therefore, a new multi-objective shuffled frog-leaping algorithm (MOSFLA) is introduced for the first time to search locally Pareto-optimal frontier for the given problem. To prove the efficiency of the proposed algorithm, various test problems are solved and the reliability of the proposed algorithm, based on some comparison metrics, is compared with three distinguished multi-objective genetic algorithms, i.e. PS-NC GA, NSGA-II, and SPEA-II. The computational results show that the proposed MOSFLA performs better than the above genetic algorithms, especially for the large-sized problems.     

Variable neighborhood search for two-agent flow shop scheduling problem

Multi-agent scheduling in flow shop environment is seldom considered. In this paper flow shop scheduling problem with two agents is studied and its feasibility model is considered, in which the goal is to minimize the makespan of the first agent and the total tardiness of the second agent simultaneously under the given upper bounds. A simple variable neighborhood search (VNS) algorithm is proposed, in which a learning neighborhood structure is constructed to produce new solutions and a new principle is applied to decide if the current solution can be replaced with the new one. VNS is tested on a number of instances and the computational results show the promising advantage of VNS when compared to other algorithms of the problem.     

Two-stage hybrid flow shop scheduling on parallel batching machines considering a job-dependent deteriorating effect and non-identical job sizes

In this paper, we investigate a specialized two-stage hybrid flow shop scheduling problem with parallel batching machines considering a job-dependent deteriorating effect and non-identical job sizes simultaneously. A novel concept of three-dimensional wasted volume based on the job normal processing time, job size, and job deteriorating rate is first proposed. Some structural properties, as well as a heuristic algorithm, are developed to solve the single parallel batching machine scheduling problem. Since the two-stage hybrid flow shop scheduling problem is NP-hard, a hybrid EDA-DE algorithm combining estimation of distribution algorithm (EDA) and differential evolution (DE) algorithm is proposed to tackle the studied problem. In addition, the Taguchi method of design of experiments (DOE) is implemented to tune the parameters of the EDA-DE. Finally, a series of computational experiments are carried out to compare the performance of the proposed hybrid EDA-DE algorithm and some recent existing algorithms from the literature, and the comparative results validate the effectiveness and efficiency of the proposed algorithm.     

自适应混合粒子群算法求解置换流水车间调度问题

为更有效地解决以最大完工时间最小化为目标的置换流水车间调度问题,提出了一种自适应混合粒子群算法（SHPSO）。该算法结合Q学习设计了参数自适应更新策略,以平衡算法的探索和开发;同时引入粒子停滞判断方法,使用平局决胜机制和Taillard加速算法改进基于迭代贪婪的局部搜索策略,对全局极值进行局部搜索,帮助粒子跳出局部最优。实验结果表明,SHPSO算法取得的平均相对百分偏差（RPDavg）对比其他四种改进PSO算法至少下降了83.2%,在求解质量上具有明显优势。     

多机Flow shop加权完成时间调度问题的启发式算法分析

因实际生产中调度问题的规模很大，分析其近似算法的绝对性能比很难，有时甚至不可行，所以研究近似算法的渐近性能比就很有必要，本文针对多机Flowshop加权完成时间调度问题，使用单机松弛和概率分析方法，证明了基于加权最短处理时间需求的启发式算法是渐近最优的．