求解并行机拖期与能耗成本优化调度的混合教一学算法

针对加工时间可控的并行机调度,提出了一类考虑拖期与能耗成本优化的调度问题。首先对调度问题进行了问题描述,并建立了整数线性规划模型以便于CPLEX求解。为了快速获得问题的满意解,提出了一种混合教-学算法。结合问题的性质,设计了编码与解码方法以克服标准教-学算法无法直接适用于离散问题的缺点。同时,构建了基于变邻域搜索的局部搜索算子以强化混合算法的搜索性能。最后,对加工时间可控的并行机调度问题进行了仿真实验,测试结果验证了本文构建的整数线性规划模型和混合算法的可行性和有效性。     

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.     

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.     

A tabu search algorithm with a new neighborhood structure for the job shop scheduling problem

Tabu search (TS) algorithms are among the most effective approaches for solving the job shop scheduling problem (JSP) which is one of the most difficult NP-complete problems. However, neighborhood structures and move evaluation strategies play the central role in the effectiveness and efficiency of the tabu search for the JSP. In this paper, a new enhanced neighborhood structure is proposed and applied to solving the job shop scheduling problem by TS approach. Using this new neighborhood structure combined with the appropriate move evaluation strategy and parameters, we tested the TS approach on a set of standard benchmark instances and found a large number of better upper bounds among the unsolved instances. The computational results show that for the rectangular problem our approach dominates all others in terms of both solution quality and performance.     

Variable neighborhood search for multi-objective resource allocation problems

The Resource Allocation Problem (RAP) is a classical problem in the field of operations management that has been broadly applied to real problems such as product allocation, project budgeting, resource distribution, and weapon-target assignment. In addition to focusing on a single objective, the RAP may seek to simultaneously optimize several expected but conflicting goals under conditions of resources scarcity. Thus, the single-objective RAP can be intuitively extended to become a Multi-Objective Resource Allocation Problem (MORAP) that also falls in the category of NP-Hard. Due to the complexity of the problem, metaheuristics have been proposed as a practical alternative in the selection of techniques for finding a solution. This study uses Variable Neighborhood Search (VNS) algorithms, one of the extensively used metaheuristic approaches, to solve the MORAP with two important but conflicting objectives—minimization of cost and maximization of efficiency. VNS searches the solution space by systematically changing the neighborhoods. Therefore, proper design of neighborhood structures, base solution selection strategy, and perturbation operators are used to help build a well-balanced set of non-dominated solutions. Two test instances from the literature are used to compare the performance of the competing algorithms including a hybrid genetic algorithm and an ant colony optimization algorithm. Moreover, two large instances are generated to further verify the performance of the proposed VNS algorithms. The approximated Pareto front obtained from the competing algorithms is compared with a reference Pareto front by the exhaustive search method. Three measures are considered to evaluate algorithm performance: D1_R, the Accuracy Ratio, and the number of non-dominated solutions. The results demonstrate the practicability and promise of VNS for solving multi-objective resource allocation problems.     

Parallel-machine scheduling problems with sequence-dependent setup times using an ACO,SA and VNS hybrid algorithm

This paper proposes a hybrid metaheuristic for the minimization of makespan in scheduling problems with parallel machines and sequence-dependent setup times. The solution approach is robust, fast, and simply structured, and comprises three components: an initial population generation method based on an ant colony optimization (ACO), a simulated annealing (SA) for solution evolution, and a variable neighborhood search (VNS) which involves three local search procedures to improve the population. The hybridization of an ACO, SA with VNS, combining the advantages of these three individual components, is the key innovative aspect of the approach. Two algorithms of a hybrid VNS-based algorithm, SA/VNS and ACO/VNS, and the VNS algorithm presented previously are used to compare with the proposed hybrid algorithm to highlight its advantages in terms of generality and quality for large instances.     

An effective hybrid teaching–learning-based optimization algorithm for permutation flow shop scheduling problem

Permutation flow shop scheduling (PFSP) is among the most studied scheduling settings. In this paper, a hybrid Teaching–Learning-Based Optimization algorithm (HTLBO), which combines a novel teaching–learning-based optimization algorithm for solution evolution and a variable neighborhood search (VNS) for fast solution improvement, is proposed for PFSP to determine the job sequence with minimization of makespan criterion and minimization of maximum lateness criterion, respectively. To convert the individual to the job permutation, a largest order value (LOV) rule is utilized. Furthermore, a simulated annealing (SA) is adopted as the local search method of VNS after the shaking procedure. Experimental comparisons over public PFSP test instances with other competitive algorithms show the effectiveness of the proposed algorithm. For the DMU problems, 19 new upper bounds are obtained for the instances with makespan criterion and 88 new upper bounds are obtained for the instances with maximum lateness criterion.     

A heuristic-based hybrid genetic-variable neighborhood search algorithm for task scheduling in heterogeneous multiprocessor system

Effective task scheduling, which is essential for achieving high performance in a heterogeneous multiprocessor system, remains a challenging problem despite extensive studies. In this article, a heuristic-based hybrid genetic-variable neighborhood search algorithm is proposed for the minimization of makespan in the heterogeneous multiprocessor scheduling problem. The proposed algorithm distinguishes itself from many existing genetic algorithm (GA) approaches in three aspects. First, it incorporates GA with the variable neighborhood search (VNS) algorithm, a local search metaheuristic, to exploit the intrinsic structure of the solutions for guiding the exploration process of GA. Second, two novel neighborhood structures are proposed, in which problem-specific knowledge concerned with load balancing and communication reduction is utilized respectively, to improve both the search quality and efficiency of VNS. Third, the proposed algorithm restricts the use of GA to evolve the task-processor mapping solutions, while taking advantage of an upward-ranking heuristic mostly used by traditional list scheduling approaches to determine the task sequence assignment in each processor. Empirical results on benchmark task graphs of several well-known parallel applications, which have been validated by the use of non-parametric statistical tests, show that the proposed algorithm significantly outperforms several related algorithms in terms of the schedule quality. Further experiments are carried out to reveal that the proposed algorithm is able to maintain high performance within a wide range of parameter settings.     

An efficient memetic algorithm for solving the job shop scheduling problem

The job shop scheduling problem (JSP) is well known as one of the most complicated combinatorial optimization problems, and it is a NP-hard problem. Memetic algorithm (MA) which combines the global search and local search is a hybrid evolutionary algorithm. In this paper, an efficient MA with a novel local search is proposed to solve the JSP. Within the local search, a systematic change of the neighborhood is carried out to avoid trapping into local optimal. And two neighborhood structures are designed by exchanging and inserting based on the critical path. The objective of minimizing makespan is considered while satisfying a number of hard constraints. The computational results obtained in experiments demonstrate that the efficiency of the proposed MA is significantly superior to the other reported approaches in the literature.     

改进型蝙蝠算法在作业车间调度问题中的应用

针对一类以最小化最大完工时间为目标的作业车间调度问题（Job Shop scheduling Problem,JSP）,提出了一种改进型蝙蝠算法（Improved Bat Algorithm,IBA）。为了克服基本蝙蝠算法在求解该类离散组合优化问题存在的局限性,首先对编码方案进行了设计,实现了算法中离散问题的连续编码;然后采用基于G&T算法和随机生成的方法初始化种群,以提高初始解的质量。此外,还引入了变邻域搜索策略,以避免算法早熟收敛,提高IBA算法的性能。最后,基于JSP问题的基准算例进行了大量仿真对比实验,结果显示了IBA算法的可行性和有效性。     

Variable neighborhood search for the linear ordering problem

Given a matrix of weights, the linear ordering problem (LOP) consists of finding a permutation of the columns and rows in order to maximize the sum of the weights in the upper triangle. This NP-complete problem can also be formulated in terms of graphs, as finding an acyclic tournament with a maximal sum of arc weights in a complete weighted graph. In this paper, we first review the previous methods for the LOP and then propose a heuristic algorithm based on the variable neighborhood search (VNS) methodology. The method combines different neighborhoods for an efficient exploration of the search space. We explore different search strategies and propose a hybrid method in which the VNS is coupled with a short-term tabu search for improved outcomes. Our extensive experimentation with both real and random instances shows that the proposed procedure competes with the best-known algorithms in terms of solution quality, and has reasonable computing-time requirements.Variable neighborhood search (VNS) is a metaheuristic method that has recently been shown to yield promising outcomes for solving combinatorial optimization problems. Based on a systematic change of neighborhood in a local search procedure, VNS uses both deterministic and random strategies in search for the global optimum.In this paper, we present a VNS implementation designed to find high quality solutions for the NP-hard LOP, which has a significant number of applications in practice. The LOP, for example, is equivalent to the so-called triangulation problem for input–output tables in economics. Our implementation incorporates innovative mechanisms to include memory structures within the VNS methodology. Moreover we study the hybridization with other methodologies such as tabu search.     

变邻域搜索算法综述

变邻域搜索算法(Variable Neighborhood Search,VNS)作为一种新的元启发式算法,已初步成功地用于解决优化问题,尤其是对于大规模组合优化问题效果良好。对VNS的扩展研究层出不穷,并将其成功地应用到旅行商问题、车辆路径问题、调度、图着色等问题中。简述了经典的元启发式算法,并依次论述了优化问题,VNS算法起源,VNS算法原理,VNS算法分析,扩展的VNS分析,VNS在初始解构造、邻域结构构造、局部搜索和停止准则几个方面的改进方法,针对不同版本的VNS归纳了其在各种优化问题应用情况。基于对改进的VNS的分类,从算法自身研究角度和实际应用角度提出了未来研究方向。     

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.     

A variable neighborhood search for minimizing single machine weighted earliness and tardiness with common due date

Although the concept of just-in-time (JIT) production systems has been proposed for over two decades, it is still important in real-world production systems. In this paper, we consider minimizing the total weighted earliness and tardiness with a restrictive common due date in a single machine environment, which has been proved as an NP-hard problem. Due to the complexity of the problem, metaheuristics, including simulated annealing, genetic algorithm, tabu search, among others, have been proposed for searching good solutions in reasonable computation times. In this paper, we propose a hybrid metaheuristic that uses tabu search within variable neighborhood search (VNS/TS). There are several distinctive features in the VNS/TS algorithm, including different ratio of the two neighborhoods, generating five points simultaneously in a neighborhood, implementation of the B/F local search, and combination of TS with VNS. By examining the 280 benchmark problem instances, the algorithm shows an excellent performance in not only the solution quality but also the computation time. The results obtained are better than those reported previously in the literature.     

An efficient incremental evaluation function for optimizing truck scheduling in a resource-constrained crossdock using metaheuristics

This paper addresses truck scheduling optimization in a resource-constrained crossdock. The truck scheduling problem decides on the succession of incoming and outgoing trucks at the dock doors of a crossdocking terminal such that the total crossdocking operation time is minimized. The paper tackles the optimization from the computational perspective by developing an incremental evaluation of the objective function in the body of single-solution based metaheuristics. It consists in evaluating only the transformation applied to the current solution rather than the complete evaluation of the neighbor solution. The proposed incremental neighborhood evaluation is integrated into two metaheuristics including tabu search (TS) and variable neighborhood search (VNS). In terms of solution quality vs. runtime, experimental results show that the incremental mechanism helps the two algorithms with dedicating their runtime to solution optimization rather than spending it on fitness evaluation when compared with a deterministic local search (LS) algorithm that exploits a simple complete evaluation of the objective function. This is in particular evident for the TS algorithm which obtains comparable results to LS while achieving on average 67.6% reduction in runtime for huge instances of scheduling 2048 trucks in a 256-door crossdock. Our findings on the efficiency of the proposed incremental evaluation are reinforced when the two metaheuristics are re-assessed with a complete evaluation of the objective function.     

Bi-criteria flexible job-shop scheduling with sequence-dependent setup times—Variable neighborhood search approach

In scheduling problems, taking the sequence-dependent setup times into account is one of the important issues that have recently been considered by researchers in the production scheduling field. In this paper, we consider flexible job-shop scheduling problem (FJSP) with sequence-dependent setup times to minimize makespan and mean tardiness. The FJSP consists of two sub-problems from which the first one is to assign each operation to a machine out of a set of capable machines, and the second one deals with sequencing the assigned operations on all machines. To solve this problem, a variable neighborhood search (VNS) algorithm based on integrated approach is proposed. In the presented optimization method, the external loop controlled the stop condition of algorithm and the internal loop executed the search process. To search the solution space, the internal loop used two main search engines, i.e. shake and local search procedures. In addition, neighborhood structures related to the sequencing problem and the assignment problem were employed to generate neighboring solutions. To evaluate the performance of the proposed algorithm, 20 test problems in different sizes are randomly generated. Consequently, computational results and comparisons validate the quality of the proposed approach.     

混合哈里斯鹰算法求解作业车间调度问题

针对哈里斯鹰算法（HHO）求解作业车间调度问题（JSP）时存在寻优能力差、易陷入局部最优等缺点提出了混合哈里斯鹰算法（HHHO）。首先,在种群初始化阶段引入混沌理论增加种群多样性;其次,在HHO搜索前期采用能量非线性递减和量子计算增强算法全局探索能力,在搜索后期采用邻域搜索算法增强算法局部开发能力;最后,选取了FT和LA系列算例测试了算法的性能,并与其他先进元启发式算法对比,验证了HHHO在求解JSP时的有效性和优越性。     

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.     

一种多目标置换流水车间调度问题的优化算法

针对最大完工时间最小和总流经时间最小的多目标置换流水车间调度问题(permutation flow shopscheduling problem, PFSP), 提出一种粒子群优化算法与变邻域搜索算法结合的混合粒子群优化(hybrid particleswarm optimization algorithm, HPSO)算法, 并使算法在集中搜索和分散搜索之间达到合理的平衡. 在该混合算法中,采用NEH 启发式算法进行种群初始化, 以提高初始解质量;运用随机键表示法设计基于升序排列规则(ranked-order-value, ROV), 将连续PSO 算法应用于置换流水车间调度问题;引入外部档案集存贮Pareto 解, 并采用强支配关系和聚集距离相结合的混合策略保证解集的分布性;采用Sigma 法和基于聚集距离的轮盘赌法进行全局最优解的选择;提出变邻域搜索算法, 对外部集中的Pareto 解作进一步地局部搜索. 最后, 运用提出的混合算法求解Taillard 基准测试集, 并将测试结果与SPEA2 算法进行比较, 验证该调度算法的有效性.     

改进果蝇算法求解混合流水车间调度问题

针对混合流水车间调度问题(HFSP),本文提出了一种新的基于果蝇算法和变邻域搜索的混合优化方法.首先,将关键块内的工序与同阶段其他机器上的工序进行交换,提出了一种基于关键路径的HFSP新邻域结构.其次,针对HFSP的阶段式解码特性,提出了一种邻域解的快速评估方法,并验证了快速评估方法的高效性.然后,基于提出的新邻域结构,并将N7和K-insertion邻域结构引入HFSP,设计了基于上述3种邻域结构的变邻域搜索方法,以此为基础提出了一种针对HFSP的混合优化方法.最后,通过对Carlier和Liao等经典测试集进行测试,验证了所提新邻域结构的可行性和有效性,并将该方法与其他文献的方法进行了对比,验证了所提方法的优越性.