An effective hybrid discrete differential evolution algorithm for the flow shop scheduling with intermediate buffers

In this paper, an effective hybrid discrete differential evolution (HDDE) algorithm is proposed to minimize the maximum completion time (makespan) for a flow shop scheduling problem with intermediate buffers located between two consecutive machines. Different from traditional differential evolution algorithms, the proposed HDDE algorithm adopted job permutation to represent individuals and applies job-permutation-based mutation and crossover operations to generate new candidate solutions. Moreover, a one-to-one selection scheme with probabilistic jumping is used to determine whether the candidates will become members of the target population in next generation. In addition, an efficient local search algorithm based on both insert and swap neighborhood structures is presented and embedded in the HDDE algorithm to enhance the algorithm’s local searching ability. Computational simulations and comparisons based on the well-known benchmark instances are provided. It shows that the proposed HDDE algorithm is not only capable to generate better results than the existing hybrid genetic algorithm and hybrid particle swarm optimization algorithm, but outperforms two recently proposed discrete differential evolution (DDE) algorithms as well. Especially, the HDDE algorithm is able to achieve excellent results for large-scale problems with up to 500 jobs and 20 machines.     

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.     

一种求解作业车间调度的混合粒子群算法*

针对车间作业调度问题,提出了一种混合了知识进化算法和粒子群优化的算法。算法主要是结合知识进化算法的进化选择机制和粒子群优化的局部快速收敛性特性,首先让粒子替代知识进化算法中的进化个体,在群体空间中按粒子群优化规则寻找局部最优,然后根据知识进化算法的全局选择机制寻找全局最优,最后,将车间作业调度问题的特点融入到所提出的混合算法中求解问题。采用基准数据进行测试的仿真实验,并比对标准遗传算法,结果表明所提算法的有效性。     

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.     

An effective hybrid DE-based algorithm for multi-objective flow shop scheduling with limited buffers

This paper proposes an effective hybrid algorithm based on differential evolution (DE), namely HDE, to solve multi-objective permutation flow shop scheduling problem (MPFSSP) with limited buffers between consecutive machines, which is a typical NP-hard combinatorial optimization problem with strong engineering background. Firstly, to make DE suitable for solving scheduling problems, a largest-order-value (LOV) rule is presented to convert the continuous values of individuals in DE to job permutations. Secondly, after the DE-based exploration, an efficient local search, which is designed based on the landscape of MPFSSP with limited buffers, is applied to emphasize exploitation. Thus, not only does the HDE apply the parallel evolution mechanism of DE to perform effective exploration (global search) in the whole solution space, but it also adopts problem-dependent local search to perform thorough exploitation (local search) in the promising sub-regions. In addition, the concept of Pareto dominance is used to handle the updating of solutions in sense of multi-objective optimization. Moreover, the convergence property of HDE is analyzed by using the theory of finite Markov chain. Finally, simulations and comparisons based on benchmarks demonstrate the effectiveness and efficiency of the proposed HDE.     

基于混合人工蜂群算法的多目标柔性作业车间调度问题研究

传统的优化算法在求解面对多目标柔性作业车间调度时,往往求解效率低且难以获得最优解。为了求解多目标柔性作业车间调度问题,设计了混合人工蜂群算法。种群的初始化采用了多种方法相结合的策略。在人工蜂群算法的不同阶段采用不同的搜索机制,在雇佣蜂阶段采用开发搜索,针对跟随蜂阶段蜜蜂跟随的对象的优秀解进行小幅度的更新,从而提高了搜索的表现。禁忌搜索与改进的人工蜂群算法相结合,有效的提升了获得最优解的概率。通过相关文献中的标准实例对设计的混合人工蜂群算法进行一系列求解测试,实验的结果有效的说明了算法在求解柔性作业车间调度问题时效果显著。通过求解结果对比表明人工蜂群算法的高效性和优越性。     

一种求解job shop问题的混合多目标遗传算法

提出一种基于操作编码、采用递进策略与非劣解局部搜索相结合的混合多目标遗传算法。通过将递进进化模式和非劣解局部搜索策略引入到算法结构,改善了算法对解空间的遍历性与算法的收敛性。采用改进算法对典型的jobshop算例进行三目标优化,所得结果验证了算法的有效性。     

Total flow time minimization in no-wait job shop using a hybrid discrete group search optimizer

The no-wait job shop scheduling problem is a well-known NP-hard problem and it is typically decomposed into timetabling subproblem and sequencing subproblem. By adopting favorable features of the group search technique, a hybrid discrete group search optimizer is proposed for finding high quality schedules in the no-wait job shops with the total flow time criterion. In order to find more promising sequences, the producer operator is designed as a destruction and construction (DC) procedure and an insertion-based local search, the scrounger operator is implemented by differential evolution scheme, and the ranger operator is designed by hybridizing best insert moves. An efficient initialization scheme based on Nawaz–Enscore–Ham (NEH) heuristic is designed to construct the initial population with both quality and diversity. A speed-up method is developed to accelerate the evaluation of the insertion neighborhood. Computational results based on well-known benchmark instances show that the proposed algorithm clearly outperforms a hybrid differential evolution algorithm and an iterated greedy algorithm. In addition, the proposed algorithm is comparable to a local search method based on optimal job insertion, especially for large-size instances.     

一种新的混合优化算法及其在车间调度中的应用

提出了一种解决车间调度问题的新方法, 该方法将序优化思想融入巢分区算法框架, 采用"序比较"的方法进行算法的局部寻优. "序"的指数收敛性加快了巢分区算法的局部收敛速度, 从而提高了算法整体的优化效率. 最优计算量分配技术则依据在线数据对计算量进行合理的分配, 进一步提高算法的收敛速度和结果的可靠性. 混合算法继承了巢分区算法的全局搜索特性以及序优化的快速收敛性. 用该算法解决标准 Jobshop 调度问题, 并与序优化方法和模拟退火算法进行比较, 发现本文算法在收敛速度与优化质量方面均优于这些算法.     

Multi-center variable-scale search algorithm for combinatorial optimization problems with the multimodal property

Combinatorial optimization problems (COPs) are discrete problems arising from aerospace, bioinformatics, manufacturing, and other fields. One of the classic COPs is the scheduling problem. Moreover, these problems are usually multimodal optimization problems with a quantity of global and local optima. As a result, many search algorithms can easily become trapped into local optima. In this article, we propose a multi-center variable-scale search algorithm for solving both single-objective and multi-objective COPs. The algorithm consists of two distinct points. First, the multi-center strategy chooses several individuals with better performance as the only parents of the next generation, which means that there are a number of separate searching areas around the searching center. Second, the next generation of the population is produced by a variable-scale strategy with an exponential equation based on the searching center. The equation is designed to control the neighborhood scale, and adaptively realize the large-scale and small-scale searches at different search stages to balance the maintenance of diversity and convergence speed. In addition, an approach of adjusting centers is proposed concerning the number and distribution of centers for solving multi-objective COPs. Finally, the proposed algorithm is applied to three COPs, including the well-known flexible job shop scheduling problem, the unrelated parallel machine scheduling problem, and the test task scheduling problem. Both the single-objective optimization algorithm and the multi-objective optimization algorithm demonstrate competitive performance compared with existing methods.     

求解流水线调度问题的万有引力搜索算法

研究了以最大完工时间为目标的流水线调度问题,使用万有引力算法求解调度问题,提出了一种最大排序规则,利用物体间各个位置分量值存在的大小次序关系,并结合随机键编码的方法产生,将物体的连续位置转变成了一个可行的调度方案;提出了一种边界变异的策略使得越界的物体不再聚集在边界上,而是分布在边界附近的可行空间内,从而增加种群的多样性;结合交换算子和插入算子提出了一种新的局部搜索算法,有效地避免了算法陷入局部最优值,进一步提高了解的质量.最后证明了算法的收敛性,并且计算了算法的时间复杂度和空间复杂度,仿真实验说明了所得算法的有效性.     

混合粒子群算法求解多目标柔性作业车间调度问题

柔性作业车间调度问题是生产管理领域和组合优化领域的重要分支.本文提出一种基于Pareto支配的混合粒子群优化算法求解多目标柔性作业车间调度问题.首先采用基于工序排序和机器分配的粒子表达方式,并直接在离散域进行位置更新.其次,提出基于BaldWinian学习策略和模拟退火技术相结合的多目标局部搜索策略,以平衡算法的全局探索能力和局部开发能力.然后引入Pareto支配的概念来比较粒子的优劣性,并采用外部档案保存进化过程中的非支配解.最后用于求解该类问题的经典算例,并与已有算法进行比较,所提算法在收敛性和分布均匀性方面均具有明显优势.     

A hybrid TP+PLS algorithm for bi-objective flow-shop scheduling problems

This paper presents a new, carefully designed algorithm for five bi-objective permutation flow shop scheduling problems that arise from the pairwise combinations of the objectives (i) makespan, (ii) the sum of the completion times of the jobs, and (iii) both, the weighted and non-weighted total tardiness of all jobs. The proposed algorithm combines two search methods, two-phase local search and Pareto local search, which are representative of two different, but complementary, paradigms for multi-objective optimization in terms of Pareto-optimality. The design of the hybrid algorithm is based on a careful experimental analysis of crucial algorithmic components of these two search methods. We compared our algorithm to the two best algorithms identified, among a set of 23 candidate algorithms, in a recent review of the bi-objective permutation flow-shop scheduling problem. We have reimplemented carefully these two algorithms in order to assess the quality of our algorithm. The experimental comparison in this paper shows that the proposed algorithm obtains results that often dominate the output of the two best algorithms from the literature. Therefore, our analysis shows without ambiguity that the proposed algorithm is a new state-of-the-art algorithm for the bi-objective permutation flow-shop problems studied in this paper.     

求解Job Shop调度问题的混合蚁群算法研究

为了解决单一算法求解Job Shop调度问题存在的不足，该文提出了一种混合算法，将蚁群算法用于全局搜索。针对蚁群算法易于陷入局部最优的情况，提出了一种基于关键工序的邻域搜索方法，将使用此邻域搜索方法的TS算法作为局部搜索策略。利用TS算法较强的局部搜索能力，提高了蚁群算法的优化能力，达到改善Job Shop调度问题解的质量。实验结果表明，混合算法在较短的时间内，找到了FT10、LA24、LA36等典型benchmarks问题的最优解，得到的makespan的平均值较并行遗传算法(PGA)和TSAB算法均有所提高。     

A bi-objective possibilistic programming model for open shop scheduling problems with sequence-dependent setup times, fuzzy processing times, and fuzzy due dates

We are concerned with an open shop scheduling problem having sequence-dependent setup times. A novel bi-objective possibilistic mixed-integer linear programming model is presented. Sequence-dependent setup times, fuzzy processing times and fuzzy due dates with triangular possibility distributions are the main constraints of this model. An open shop scheduling problem with these considerations is close to the real production scheduling conditions. The objective functions are to minimize total weighted tardiness and total weighted completion times. To solve small-sized instances for Pareto-optimal solutions, an interactive fuzzy multi-objective decision making (FMODM) approach, called TH method proposed by Torabi and Hassini, is applied. Using this method, an equivalent auxiliary single-objective crisp model is obtained and solved optimally by the Lingo software. For medium to large size examples, a multi-objective particle swarm optimization (MOPSO) algorithm is proposed. This algorithm consists of a decoding procedure using a permutation list to reduce the search area in the solution space. Also, a local search algorithm is applied to generate good initial particle positions. Finally, to evaluate the effectiveness of the MOPSO algorithm, the results are compared with the ones obtained by the well-known SPEA-II, using design of experiments (DOE) based on some performance metrics.     

A hybrid discrete artificial bee colony algorithm for permutation flowshop scheduling problem

To minimize the makespan in permutation flowshop scheduling problems, a hybrid discrete artificial bee colony (HDABC) algorithm is presented. In the HDABC, each solution to the problem is called a food source and represented by a discrete job permutation. First, the initial population with certain quality and diversity is generated from Greedy Randomized Adaptive Search Procedure (GRASP) based on Nawaz–Enscore–Ham (NEH) heuristics. Second, the discrete operators and algorithm, such as insert, swap, path relinking and GRASP are applied to generate new solution for the employed bees, onlookers and scouts. Moreover, local search is applied to the best one. The presented algorithm is tested on scheduling problem benchmarks. Experimental results show its efficiency.     

A machine-learning based memetic algorithm for the multi-objective permutation flowshop scheduling problem

In recent years, the historical data during the search process of evolutionary algorithms has received increasing attention from many researchers, and some hybrid evolutionary algorithms with machine-learning have been proposed. However, the majority of the literature is centered on continuous problems with a single optimization objective. There are still a lot of problems to be handled for multi-objective combinatorial optimization problems. Therefore, this paper proposes a machine-learning based multi-objective memetic algorithm (ML-MOMA) for the discrete permutation flowshop scheduling problem. There are two main features in the proposed ML-MOMA. First, each solution is assigned with an individual archive to store the non-dominated solutions found by it and based on these individual archives a new population update method is presented. Second, an adaptive multi-objective local search is developed, in which the analysis of historical data accumulated during the search process is used to adaptively determine which non-dominated solutions should be selected for local search and how the local search should be applied. Computational results based on benchmark problems show that the cooperation of the above two features can help to achieve a balance between evolutionary global search and local search. In addition, many of the best known Pareto fronts for these benchmark problems in the literature can be improved by the proposed ML-MOMA.     

An effective hybrid PSO-based algorithm for flow shop scheduling with limited buffers

In this paper, an effective hybrid algorithm based on particle swarm optimization (HPSO) is proposed for permutation flow shop scheduling problem (PFSSP) with the limited buffers between consecutive machines to minimize the maximum completion time (i.e., makespan). First, a novel encoding scheme based on random key representation is developed, which converts the continuous position values of particles in PSO to job permutations. Second, an efficient population initialization based on the famous Nawaz–Enscore–Ham (NEH) heuristic is proposed to generate an initial population with certain quality and diversity. Third, a local search strategy based on the generalization of the block elimination properties, named block-based local search, is probabilistically applied to some good particles. Moreover, simulated annealing (SA) with multi-neighborhood guided by an adaptive meta-Lamarckian learning strategy is designed to prevent the premature convergence and concentrate computing effort on promising solutions. Simulation results and comparisons demonstrate the effectiveness of the proposed HPSO. Furthermore, the effects of some parameters are discussed.     

改进的离散型萤火虫优化算法求解柔性作业车间调度问题

针对传统的群智能优化算法在求解柔性作业车间调度问题(FJSP)时,存在寻优能力不足且易陷入局部最优等缺点,本文以最小化最大完工时间为目标,将萤火虫算法(FA)用于求解柔性作业车间调度问题,提出一种改进的离散型萤火虫算法(DFA)。首先,通过两段式编码建立FA连续优化问题与FJSP离散优化问题之间的联系;其次,设计一种群初始化方法,以确保初始解的质量以及多样性;然后,提出改进离散型萤火虫优化算法并引入局部搜索算法,加强算法的全局搜索能力和局部搜索能力;最后,对标准算例进行仿真,验证DFA算法求解FJSP的有效性。通过与遗传算法和粒子群优化算法进行仿真对比,表明了DFA求解FJSP的优越性。     

Maintenance costs and makespan minimization for assembly permutation flow shop scheduling by considering preventive and corrective maintenance

The joint optimization of production scheduling and maintenance planning has a significant influence on production continuity and machine reliability. However, limited research considers preventive maintenance (PM) and corrective maintenance (CM) in assembly permutation flow shop scheduling. This paper addresses the bi-objective joint optimization of both PM and CM costs in assembly permutation flow shop scheduling. We also propose a new mixed integer linear programming model for the minimization of the makespan and maintenance costs. Two lemmas are inferred to relax the expected number of failures and CM cost to make the model linear. A restarted iterated Pareto greedy (RIPG) algorithm is applied to solve the problem by including a new evaluation of the solutions, based on a PM strategy. The RIPG algorithm makes use of novel bi-objective-oriented greedy and referenced local search phases to find non-dominated solutions. Three types of experiments are conducted to evaluate the proposed MILP model and the performance of the RIPG algorithm. In the first experiment, the MILP model is solved with an epsilon-constraint method, showing the effectiveness of the MILP model in small-scale instances. In the remaining two experiments, the RIPG algorithm shows its superiority for all the instances with respect to four well-known multi-objective metaheuristics.