柔性Job shop集成化计划调度模型及其求解算法

考虑不同加工工艺路径的成本因素，从集成化的角度研究了柔性Job shop计划和调度问题，针对问题的结构特点，建立了两层混合整数规划模型，提出门槛接受，遗传算法与启发式规则相结合的混合求解算法，综合考虑各层次决策问题进行求解，实例计算表明，该算法可迅速求得问题的近优解，表现出良好的求解性能。     

柔性作业车间调度问题的一种启发式算法

为了研究多目标柔性作业车间调度问题,基于甘特图和搭积木经验进行了分析,提出了一种组合优先规则和基于此优先规则的启发式算法.组合优先规则面向完工时间、关键机床负荷和总负荷三个指标,改变规则中各数据项的比例可调整三个指标所占的比例;算法采用随机方式调整三个指标的比例,并微调最优解对应的比例.能随机产生多个高质量调度解.算法...     

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.     

A fast estimation of distribution algorithm for dynamic fuzzy flexible job-shop scheduling problem

Due to the complicated circumstances in workshop, most of the conventional scheduling algorithms fail to meet the requirements of instantaneity, complexity, and dynamicity in job-shop scheduling problems. Compared with the static algorithms, dynamic scheduling algorithms can better fulfill the requirements in real situations. Considering that both flexibility and fuzzy processing time are common in reality, this paper focuses on the dynamic flexible job-shop scheduling problem with fuzzy processing time (DfFJSP). By adopting a series of transforming procedures, the original DfFJSP is simplified as a traditional static fuzzy flexible job-shop problem, which is more suitable to take advantage of the existing algorithms. In this paper, estimation of distribution algorithm (EDA) is brought into address the post-transforming problem. An improved EDA is developed through making use of several elements omitted in original EDA, including the historical-optimal solution and the standardized solution vectors. The improved algorithm is named as fast estimation of distribution algorithm (fEDA) since it performs better in convergence speed and computation precision, compared with the original EDA. To sum up, the ingenious transformation and the effective fEDA algorithm provide an efficient and practical way to tackle the dynamic flexible fuzzy job-shop scheduling problem.     

Genetic algorithms-based fuzzy regression analysis

 This paper describes the concept of fuzzy regression analysis based on genetic algorithms. It is shown that the performance of fuzzy regression models may be improved and fuzzy modeling technique can be simplified by incorporating genetic algorithms into regression analysis procedure. The effectiveness of the proposed approach is illustrated through simulation of fuzzy linear regression model obtained by other authors and comparison of the results. The paper further demonstrates the applications of the approach to the manufacturing and business problems.     

柔性Flow-Shop调度的遗传算法优化

柔性Flow-shop调度问题（Flexible Flow-shop Scheduling Problem,FFSP）是一般Flow-shop调度问题的推广,由于在某些工序上存在并行机器,所以比一般的Flow-shop调度问题更复杂。为了有效地解决柔性Flow-shop调度问题,用遗传算法求解,给出了一种改进的编码方法,能够保证个体的合法性;并根据编码方法提出了矩阵解码方法。最后以某汽车发动机厂金加工车间的生产调度实例进行仿真,通过比较表明了算法的有效性。     

基于改进蝙蝠算法的柔性流水车间排产优化问题研究

为解决柔性流水车间调度问题( flexible flow shop scheduling problem,FFSP),提出了一种基于精英个体集的自适应蝙蝠算法(self-adaptive elite bat algorithm,SEBA)。针对蝙蝠算法存在求解离散问题具有局限性、易陷入局部极值、优化结果精度低等问题,该算法采用ROV(ranked order value)编码方式,使算法适用于求解离散型的FFSP问题;提出基于汉明距离的精英个体集,由多个适应度高但相似度低的精英个体轮流引导种群进化,增强种群进化活力,避免寻优过程陷入局部极值;提出自适应位置更新机制,提高算法优化精度。最后采用不同规模的标准实例对改进算法进行测试,与已有算法进行对比,实验结果验证了改进蝙蝠算法求解FFSP问题的有效性。     

Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm

The traditional production scheduling problem considers performance indicators such as processing time, cost, and quality as optimization objectives in manufacturing systems; however, it does not take energy consumption or environmental impacts completely into account. Therefore, this paper proposes an energy-efficient model for flexible flow shop scheduling (FFS). First, a mathematical model for a FFS problem, which is based on an energy-efficient mechanism, is described to solve multi-objective optimization. Since FFS is well known as a NP-hard problem, an improved, genetic-simulated annealing algorithm is adopted to make a significant trade-off between the makespan and the total energy consumption to implement a feasible scheduling. Finally, a case study of a production scheduling problem for a metalworking workshop in a plant is simulated. The experimental results show that the relationship between the makespan and the energy consumption may be apparently conflicting. In addition, an energy-saving decision is performed in a feasible scheduling. Using the decision method, there could be significant potential for minimizing energy consumption.     

新型离散蝙蝠算法求解柔性流水车间调度问题

针对以最小化完工时间为目标的柔性流水车间调度问题,提出了一种新型离散蝙蝠算法。介绍了蝙蝠算法的基本思想,重新定义速度与位置的加法操作来实现粒子的位移,给出了算法的具体实现方案。通过实例仿真和算法比较验证了算法的优化性能,实验结果表明该算法可以有效地求解柔性流水车间调度问题。     

A novel hybrid meta-heuristic algorithm for solving multi objective flexible job shop scheduling

Finding feasible scheduling that optimize all objective functions for flexible job shop scheduling problem (FJSP) is considered by many researchers. In this paper, the novel hybrid genetic algorithm and simulated annealing (NHGASA) is introduced to solve FJSP. The NHGASA is a combination of genetic algorithm and simulated annealing to propose the algorithm that is more efficient than others. The three objective functions in this paper are: minimize the maximum completion time of all the operations (makespan), minimize the workload of the most loaded machine and minimize the total workload of all machines. Pareto optimal solution approach is used in NHGASA for solving FJSP. Contrary to the other methods that assign weights to all objective functions to reduce them to one objective function, in the NHGASA and during all steps, problems are solved by three objectives. Experimental results prove that the NHGASA that uses Pareto optimal solutions for solving multi-objective FJSP overcome previous methods for solving the same benchmarks in the shorter computational time and higher quality.     

超启发式遗传算法求解模糊柔性作业车间调度

本文提出一种混合超启发式遗传算法(HHGA),用于求解一类采用三角模糊数表示工件加工时间的模糊柔性作业车间调度问题(FFJSP),优化目标为最小化最大模糊完工时间(即makespan).首先,详细分析现有三角模糊数排序准则性质,并充分考虑取大操作的近似误差和模糊度,设计一种更为准确的三角模糊数排序准则,可合理计算FFJSP和其他各类调度问题解的目标函数值.其次,为实现对FFJSP解空间不同区域的有效搜索, HHGA将求解过程分为两层,高层利用带自适应变异算子的遗传算法对6种特定操作(即6种有效邻域操作)的排列进行优化;低层将高层所得的每种排列作为一种启发式算法,用于对低层相应个体进行操作来执行紧凑的变邻域局部搜索并生成新个体,同时加入模拟退火机制来避免搜索陷入局部极小.最后,仿真实验和算法比较验证了所提排序准则和HHGA的有效性.     

How to make constrained fuzzy arithmetic efficient

 In the standard fuzzy arithmetic, the vagueness of fuzzy quantities always increases. G. J. Klir [2, 3] suggests an alternative – the constrained fuzzy arithmetic – which reduces this effect. On the other hand, it significantly increases the complexity of computations in comparison to the classical calculus of fuzzy quantities. So far, little attention was paid to the problems of implementation of the constrained fuzzy arithmetic, especially to its computational efficiency. We point out the related problems and outline the ways of their solution. We suggest to decompose the whole expression, classify all its subexpressions with respect to their individual computational complexity and precompute the corresponding subresults according to this classification.     

Constructions of fuzzy functions based on fuzzy equalities

 The strong (perfect) fuzzy function have been applied to approximate reasoning and vague algebra in the literature of fuzzy sets. The construction of strong (perfect) fuzzy functions possesses an important role for their applications. In the presented paper, some of the results on the construction of strong (perfect) fuzzy functions are improved, and several new and desirable results in this direction are obtained. Furthermore, it is also shown that how these results can be used to point out the connections between fuzzy functions in the classical sense and the strong (perfect) fuzzy functions.     

Mathematical modeling and heuristic approaches to 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 in medium and actual size problem with traditional optimization approaches owing to the high computational complexity. For solving the realistic case with more than two jobs, two types of approaches have been used: hierarchical approaches and integrated approaches. In hierarchical approaches assignment of operations to machines and the sequencing of operations on the resources or machines are treated separately, i.e., assignment and sequencing are considered independently, where in integrated approaches, assignment and sequencing are not differentiated. In this paper, a mathematical model and heuristic approaches for flexible job shop scheduling problems (FJSP) are considered. Mathematical model is used to achieve optimal solution for small size problems. Since FJSP is NP-hard problem, two heuristics approaches involve of integrated and hierarchical approaches are developed to solve the real size problems. Six different hybrid searching structures depending on used searching approach and heuristics are presented in this paper. Numerical experiments are used to evaluate the performance of the developed algorithms. It is concluded that, the hierarchical algorithms have better performance than integrated algorithms and the algorithm which use tabu search and simulated annealing heuristics for assignment and sequencing problems consecutively is more suitable than the other algorithms. Also the numerical experiments validate the quality of the proposed algorithms.     

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.     

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.     

改进人工蜂群算法求解模糊柔性作业车间调度问题

模糊柔性作业车间调度问题(FFJSP)是柔性作业车间调度问题(FJSP)的拓展,具有很强的现实意义.针对FFJSP,本文提出了一种基于领域搜索的改进人工蜂群算法.该算法以最小化最大模糊完工时间为目标.首先,为了提高初始种群的多样性,引入混沌理论来初始化种群.其次,为了提高算法的局部搜索能力,采用4种邻域结构对蜜源进行邻域搜索.为了进一步优化蜜源和加快种群的收敛速度,采用了一种新颖的交叉操作.并且在解码的过程中采用左移策略,从而很好地利用机器的空闲时间.最后,选取了3组通用数据集来测试算法的性能,并与代表性算法进行比较.结果表明,对于大部分实例,本文所提出的的算法的结果要优于与之对比的算法.     

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.     

A unified framework of opening and closure operators with respect to arbitrary fuzzy relations

 This paper is devoted to a general concept of openness and closedness with respect to arbitrary fuzzy relations – along with appropriate opening and closure operators. It is shown that the proposed framework unifies existing concepts, in particular, the one for fuzzy preorderings as well as the triangular norm-based approach to fuzzy mathematical morphology. The author acknowledges support of the K _plus Competence Center Program which is funded by the Austrian Government, the Province of Upper Austria, and the Chamber of Commerce of Upper Austria.     

A GA/TS algorithm for the stage shop scheduling problem

This paper presents a special case of the general shop called stage shop problem. The stage shop is a more realistic generalization of the mixed shop problem. In the stage shop problem, each job has several stages of operations. In order to solve the stage shop problem with makespan objective function, an existing neighborhood of job shop is used. In this neighborhood, few enhanced conditions are proposed to prevent cycle generation. In addition, a new neighborhood for operations that belong to the same job is presented. These neighborhoods are applied to the stage shop problem in a tabu search framework. A genetic algorithm is used to obtain good initial solutions. An existing lower bound of the job shop is adapted to our problem and the computational results have been compared to it. Our algorithm has reached the optimal solutions for more than half of the problem instances.