基于混合微粒群优化的多目标柔性Job-shop调度

应用传统方法求解多目标柔性Job-shop调度问题是十分困难的,微粒群优化采用基于种群的搜索方式,融合了局部搜索和全局搜索,具有很高的搜索效率.模拟退火算法使用概率来避免陷入局部最优,整个搜索过程可由冷却表来控制.通过对这两种算法的合理组合,建立了一种快速且易于实现的新的混合优化算法.实例计算以及与其他算法的比较说明,该算法是求解多目标柔性Job-shop调度问题的可行且高效的方法.     

An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems

Scheduling for the flexible job-shop is very important in both fields of production management and combinatorial optimization. However, it is quite difficult to achieve an optimal solution to this problem with traditional optimization approaches owing to the high computational complexity. The combining of several optimization criteria induces additional complexity and new problems. Particle swarm optimization is an evolutionary computation technique mimicking the behavior of flying birds and their means of information exchange. It combines local search (by self experience) and global search (by neighboring experience), possessing high search efficiency. Simulated annealing (SA) as a local search algorithm employs certain probability to avoid becoming trapped in a local optimum and has been proved to be effective for a variety of situations, including scheduling and sequencing. By reasonably hybridizing these two methodologies, we develop an easily implemented hybrid approach for the multi-objective flexible job-shop scheduling problem (FJSP). The results obtained from the computational study have shown that the proposed algorithm is a viable and effective approach for the multi-objective FJSP, especially for problems on a large scale.     

多目标粒子群优化算法在柔性车间调度中的应用

将粒子群优化(Particle Swarm Optimization,PSO)算法和混沌搜索方法结合在一起,提出一种求解多目标柔性作业车间调度问题(Flexible job shop scheduling problem,FJSP)的新算法,利用混沌对PSO的参数进行自适应优化来有效平衡算法的全局搜索和局部开挖能力,并采用混沌局部优化策略来改善算法的搜索性能.此外,为了搜索到问题的所有非劣解,采用基于模糊逻辑的适应度函数来评价粒子.对于四个典型FJSP实例的实验验证了算法的可行性和有效性.     

An effective and distributed particle swarm optimization algorithm for flexible job-shop scheduling problem

Flexible job-shop scheduling problem (FJSP) is very important in many research fields such as production management and combinatorial optimization. The FJSP problems cover two difficulties namely machine assignment problem and operation sequencing problem. In this paper, we apply particle swarm optimization (PSO) algorithm to solve this FJSP problem aiming to minimize the maximum completion time criterion. Various benchmark data taken from literature, varying from Partial FJSP and Total FJSP, are tested. Experimental results proved that the developed PSO is enough effective and efficient to solve the FJSP. Our other objective in this paper, is to study the distribution of the PSO-solving method for future implementation on embedded systems that can make decisions in real time according to the state of resources and any unplanned or unforeseen events. For this aim, two multi-agent based approaches are proposed and compared using different benchmark instances.     

变邻域杂草算法在多目标柔性作业车间调度中的应用*

针对最小化最大完工时间、总机床负荷最小及最大负载最小的多目标柔性作业车间调度问题,提出了变邻域杂草算法。首先,基于随机键编码方式,构造单链杂草,实现了杂草空间到调度空间的映射。其次,迭代后期执行变邻域搜索,对精英杂草局部深入挖掘,并通过反解码过程将调度空间的优良解反馈回杂草空间。对比实验表明,变邻域杂草算法在求解多目标基准问题时,非劣解集中解的数量和质量有一定优势。变邻域杂草算法是求解多目标柔性作业车间调度问题的有效方法。     

解决作业车间调度的微粒群退火算法*

针对微粒群优化算法在求解作业车间调度问题时存在的易早熟、搜索准确度差等缺点,在微粒群优化算法的基础上引入了模拟退火算法,从而使得算法同时具有全局搜索和跳出局部最优的能力,并且增加了对不可行解的优化,从而提高了算法的搜索效率;同时,在模拟退火算法中引入自适应温度衰变系数,使得SA算法能根据当前环境自动调整搜索条件,从而避免了微粒群优化算法易早熟的缺点。对经典JSP问题的仿真实验表明,与其他算法相比,该算法是一种切实可行、有效的方法。     

Flexible job-shop scheduling with parallel variable neighborhood search algorithm

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. FJSP is NP-hard and mainly presents two difficulties. 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 the machines. This paper proposes a parallel variable neighborhood search (PVNS) algorithm that solves the FJSP to minimize makespan time. Parallelization in this algorithm is based on the application of multiple independent searches increasing the exploration in the search space. The proposed PVNS uses various neighborhood structures which carry the responsibility of making changes in assignment and sequencing of operations for generating neighboring solutions. The results obtained from the computational study have shown that the proposed algorithm is a viable and effective approach for the FJSP.     

An object-oriented approach for multi-objective flexible job-shop scheduling problem

Flexible manufacturing systems are very complex to control and it is difficult to generate controlling systems for this problem domain. Flexible job-shop scheduling problem (FJSP) is one of the instances in this domain. It is a problem which inherits the job-shop scheduling problem (JSP) characteristics. FJSP has additional routing sub-problem in addition to JSP. In routing sub-problem each operation is assigned to a machine out of a set of capable machines. In scheduling sub-problem the sequence of assigned operations is obtained while optimizing the objective function(s). In this paper an object-oriented (OO) approach is presented for multi-objective FJSP along with simulated annealing optimization algorithm. Solution approaches in the literature generally use two-string encoding scheme to represent this problem. However, OO analysis, design and programming methodology help to present this problem on a single encoding scheme effectively which result in a practical integration of the problem solution to manufacturing control systems where OO paradigm is frequently used. OO design of FJSP is achieved by using UML class diagram and this design reduces the problem encoding to a single data structure where operation object of FJSP could hold its data about alternative machines in its own data structure hierarchically. Many-to-many associations between operations and machines are transformed into two one-to-many associations by inserting a new class between them. Minimization of the following three objective functions are considered in this paper: maximum completion time, workload of the most loaded machine and total workload of all machines. Some benchmark sets are run in order to show the effectiveness of the proposed approach. It is proved that using OO approach for multi-objective FJSP contributes to not only building effective manufacturing control systems but also achieving effective solutions.     

基于模糊物元模型的高维多目标FJSP研究*

为解决高维多目标柔性作业车间调度问题,提出了一种基于模糊物元模型与粒子群算法的模糊粒子群算法（Fuzzy Particle Swarm Optimization,FPSO）。该算法以模糊物元分析理论为依据,采用复合模糊物元与基准模糊物元之间的欧式贴近度作为适应度值引导粒子群算法的进化,并引入具有容量限制的外部存储器保留较优的Pareto非支配解以供决策者选择。此外,构建了优化目标为最大完工时间、设备总负荷、加工成本、最大设备负荷与加工质量的高维多目标优化模型,并以Kacem基准问题与实际生产数据为例进行仿真模拟与对比分析。结果表明,该算法具有良好的收敛性且搜索到的非支配解分布性较好,能够有效地应用于求解高维多目标柔性作业车间调度问题。     

Optimisation of distributed manufacturing flexible job shop scheduling by using hybrid genetic algorithms

In contrast to traditional job-shop scheduling problems, various complex constraints must be considered in distributed manufacturing environments; therefore, developing a novel scheduling solution is necessary. This paper proposes a hybrid genetic algorithm (HGA) for solving the distributed and flexible job-shop scheduling problem (DFJSP). Compared with previous studies on HGAs, the HGA approach proposed in this study uses the Taguchi method to optimize the parameters of a genetic algorithm (GA). Furthermore, a novel encoding mechanism is proposed to solve invalid job assignments, where a GA is employed to solve complex flexible job-shop scheduling problems (FJSPs). In addition, various crossover and mutation operators are adopted for increasing the probability of finding the optimal solution and diversity of chromosomes and for refining a makespan solution. To evaluate the performance of the proposed approach, three classic DFJSP benchmarks and three virtual DFJSPs were adapted from classical FJSP benchmarks. The experimental results indicate that the proposed approach is considerably robust, outperforming previous algorithms after 50 runs.     

一种动态双种群果蝇优化算法求解FJSP

为了有效解决柔性作业车间调度问题(FJSP),提出了一种具有较强进化机制的动态双种群果蝇优化算法(DDFOA),该算法采用自适应移动步长,并动态地将种群划分为先进子种群和后进子种群,其中先进子种群侧重局部搜索,后进子种群负责全局搜索。同时针对柔性作业车间调度问题,设计了合适的编码转化方案。最后,对算法的收敛性进行了证明,并选用经典算例对其进行仿真实验,仿真结果验证了DDFOA求解FJSP的有效性。     

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.     

A hybrid meta-heuristic algorithm for optimization of crew scheduling

Crew scheduling problem is the problem of assigning crew members to the flights so that total cost is minimized while regulatory and legal restrictions are satisfied. The crew scheduling is an NP-hard constrained combinatorial optimization problem and hence, it cannot be exactly solved in a reasonable computational time. This paper presents a particle swarm optimization (PSO) algorithm synchronized with a local search heuristic for solving the crew scheduling problem. Recent studies use genetic algorithm (GA) or ant colony optimization (ACO) to solve large scale crew scheduling problems. Furthermore, two other hybrid algorithms based on GA and ACO algorithms have been developed to solve the problem. Computational results show the effectiveness and superiority of the proposed hybrid PSO algorithm over other algorithms.     

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.     

An effective ant colony optimization algorithm for multi-objective job-shop scheduling with equal-size lot-splitting

This paper proposes several novel hybrid ant colony optimization (ACO)-based algorithms to resolve multi-objective job-shop scheduling problem with equal-size lot splitting. The main issue discussed in this paper is lot-splitting of jobs and tradeoff between lot-splitting costs and makespan. One of the disadvantages of ACO is its uncertainty on time of convergence. In order to enrich search patterns of ACO and improve its performance, five enhancements are made in the proposed algorithms including: A new type of pheromone and greedy heuristic function; Three new functions of state transition rules; A nimble local search algorithm for the improvements of solution quality; Mutation mechanism for divisive searching; A particle swarm optimization (PSO)-based algorithm for adaptive tuning of parameters. The objectives that are used to measure the quality of the generated schedules are weighted-sum of makespan, tardiness of jobs and lot-splitting cost. The developed algorithms are analyzed extensively on real-world data obtained from a printing company and simulated data. A mathematical programming model is developed and paired-samples t-tests are performed between obtained solutions of mathematical programming model and proposed algorithms in order to verify effectiveness of proposed algorithms.     

A hybrid Jaya algorithm for solving flexible job shop scheduling problem considering multiple critical paths

As an extension of the classical job shop scheduling problem, flexible job shop scheduling problem (FJSP) is considered as a challenge in manufacturing systems for its complexity and flexibility. Meta-heuristic algorithms are shown effective in solving FJSP. However, the multiple critical paths issue, which has not been formally discussed in the existing literature, is discovered to be a primary obstacle for further optimization by meta-heuristics. In this paper, a hybrid Jaya algorithm integrated with Tabu search is proposed to solve FJSP for makespan minimization. Two Jaya operators are designed to improve solutions under a two-vector encoding scheme. During the local search phase, three approaches are proposed to deal with multiple critical paths and have been evaluated by experimental study and qualitative analyses. An incremental parameter setting strategy and a makespan estimation method are employed to speed up the searching process. The proposed algorithm is compared with several state-of-the-art algorithms on three well-known FJSP benchmark sets. Extensive experimental results suggest its superiority in both optimality and stability. Additionally, a real world scheduling problem, including six instances with different scales, is applied to further prove its ability in handling large-scale scheduling problems.     

Mathematical modeling and a hybridized bacterial foraging optimization algorithm for the flexible job-shop scheduling problem with sequencing flexibility

The flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem (JSP) in which operations can be performed by a set of candidate capable machines. An extended version of the FJSP, entitled sequencing flexibility, is studied in this work, which considers precedence between the operations in the form of a directed acyclic graph instead of a sequential order. In this work, a mixed integer linear programming (MILP) formulation is presented to minimize weighted tardiness for the FJSP with sequencing flexibility. Due to the NP-hardness of the problem, a novel biomimicry hybrid bacterial foraging optimization algorithm (HBFOA) is developed, which is inspired by the behavior of E. coli bacteria in its search for food. The developed HBFOA search method is hybridized with simulated annealing (SA). Additionally, the algorithm has been enhanced by a local search method based on the manipulation of critical operations. Classical dispatching rules have been employed to create the initial swarm of HBFOA, and a new dispatching rule named minimum number of operations has been devised. The developed approach has been packaged in the form of a decision support system (DSS) developed on top of Microsoft Excel—a tool most small and mid-range enterprises (SME) use heavily for planning. A case study with local industry is presented to validate the proposed HBFOA and MILP. Additional numerical experiments using literature benchmarks are further used for validation. The results demonstrate that the HBFOA outperformed the classical dispatching rules and the best integer solution of MILP when minimizing the weighted tardiness and offered comparable results for the makespan instances.     

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.     

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.     

变邻域遗传算法在车间物流调度中的应用

针对含有自动引导小车(Automated Guided Vehicle,AGV)的离散化车间物流调度问题,以最小化物流任务时间惩罚成本和最小化运载小车的总行驶距离为优化目标,构建离散化车间多目标物流调度优化模型,设计一种基于Pareto寻优的多目标混合变邻域搜索遗传算法(VNSGA-II).以遗传算法为基础,通过使用NSGA-II的Pareto分层和拥挤度计算方法评估种群优劣实现多目标优化,为了提高算法的寻优能力,避免算法陷入局部最优,通过添加保优记忆库对精英个体进行保护,并利用变邻域搜索算法在搜索过程中的局部寻优能力,针对本文模型特点,设计6个随机邻域结构,来达到算法求解最优值的目标.并提出了基于关键AGV小车的插入邻域和基于关键物流任务的交换邻域调整策略以进一步降低成本.最后,以某离散车间物流调度为实例,分别使用VNSGA-II、带精英策略的快速非支配排序遗传算法Ⅱ(Nondominated Sorting Genetic AlgorithmⅡ,NSGA-II)和强Pareto进化算法(Strong Pareto Evolutionary Algorithm 2,SPEA2)对问题进行求解,计算结果表明,VNSGA-II能得到更好的Pareto解集,验证了算法的有效性和可行性.