Depth-limited search for real-time problem solving

We propose depth-limited heuristic search as a general paradigm for real-time problem solving in a dynamic environment. When combined with iterative-deepening, it provides the ability to commit to an action almost instantaneously, but allows the quality of that decision to improve as long as time is available. Once a deadline is reached, the best decision arrived at is executed. We illustrate the paradigm in three different settings, corresponding to single-agent search, two-player games, and multi-agent problem solving. First we review two-player minimax search with alpha-beta pruning. Minimax can be extended to themaxn algorithm for more than two players, which admits a much weaker form of alpha-beta pruning. Finally, we explore real-time search algorithms for single-agent problems. Minimax is specialized tominimin, which allows a very powerfulalpha pruning algorithm. In addition,real-time-A ^* allows backtracking while still guaranteeing a solution and making locally optimal decisions.This research was supported by an NSF Presidential Young Investigator Award, NSF Grant IRI-8801939, and and equipment grant from Hewlett-Packard. Thanks to Valerie Aylett for drawing the figures.     

A genetic algorithm with tabu search procedure for flexible job shop scheduling with transportation constraints and bounded processing times

In this paper, we propose a model for Flexible Job Shop Scheduling Problem (FJSSP) with transportation constraints and bounded processing times. This is a NP hard problem. Objectives are to minimize the makespan and the storage of solutions. A genetic algorithm with tabu search procedure is proposed to solve both assignment of resources and sequencing problems on each resource. In order to evaluate the proposed algorithm's efficiency, five types of instances are tested. Three of them consider sequencing problems with or without assignment of processing or/and transport resources. The fourth and fifth ones introduce bounded processing times which mainly characterize Surface Treatment Facilities (STFs). Computational results show that our model and method are efficient for solving both assignment and scheduling problems in various kinds of systems.     

用蚁群算法求解Job-Shop问题的机器分解方法

针对生产调度中Job-Shop问题,蚁群算法在求解Job-Shop问题时有计算量大的缺点,为了提高求解效率,将机器分解方法引入蚁群算法.机器分解方法在每次迭代中蚂蚁仅在子图中构造部分解,并与上次迭代中其他机器上的顺序共同构成本次解,提高了蚁群算法求解Job-Shop问题的效率.并且在算法中提出了一种新的状态转移规则和设计了蚂蚁起点位置的方法.通过在Benchmark算例上的仿真,与原有的一类集中式求解的蚁群算法作了比较,结果显示改进后的算法取得了较好的结果,大大缩短了计算时间,说明机器分解方法的有效性.     

基于粒子群优化和禁忌搜索的混合调度算法

提出了用于解决作业车间调度问题的离散版粒子群优化算法。该算法采用基于先后表编码方案和新的位移更新模型,使具有连续本质的粒子群优化算法直接适用于车间调度问题。同时,利用粒子群优化算法的全局搜索能力和禁忌搜索算法的自适应优点,将粒子群优化算法和禁忌搜索结合起来,设计了广义粒子群优化算法和粒子群—禁忌搜索交替算法两种混合调度算法。实验结果表明,两种混合调度算法能够有效地、高质量地解决作业车间调度问题。     

A hybrid genetic tabu search algorithm for solving job shop scheduling problems: a case study

In recent decades many attempts have been made at the solution of Job Shop Scheduling Problem using a varied range of tools and techniques such as Branch and Bound at one end of the spectrum and Heuristics at the other end. However, the literature reviews suggest that none of these techniques are sufficient on their own to solve this stubborn NP-hard problem. Hence, it is postulated that a suitable solution method will have to exploit the key features of several strategies. We present here one such solution method incorporating Genetic Algorithm and Tabu Search. The rationale behind using such a hybrid method as in the case of other systems which use GA and TS is to combine the diversified global search and intensified local search capabilities of GA and TS respectively. The hybrid model proposed here surpasses most similar systems in solving many more traditional benchmark problems and real-life problems. This, the system achieves by the combined impact of several small but important features such as powerful chromosome representation, effective genetic operators, restricted neighbourhood strategies and efficient search strategies along with innovative initial solutions. These features combined with the hybrid strategy employed enabled the system to solve several benchmark problems optimally, which has been discussed elsewhere in Meeran and Morshed (8th Asia Pacific industrial engineering and management science conference, Kaohsiung, Taiwan, 2007). In this paper we bring out the system’s practical usage aspect and demonstrate that the system is equally capable of solving real life Job Shop problems.     

An effective operations permutation-based discrete harmony search approach for the flexible job shop scheduling problem with makespan criterion

The Flexible Job Shop Scheduling Problem (FJSSP) represents a challenging applicative problem for metaheuristic algorithms because it imposes the development of innovative domain-dependent search operators that have to deal both with its combined discrete and permutation nature. Emerging as an effective approach for the resolution of a broad spectrum of hard optimization problems, some few discrete declinations of the Harmony Search (HS) algorithm have been recently proposed for tackling the FJSSP. Recent advances include an investigation of an innovative and promising permutation-based proposal. Accordingly, this paper proposes an Effective Operations Permutation-based Discrete Harmony Search (EOP-DHS) approach for FJSSP with Makespan criterion. The approach adopts an integrated two-part “affectation-sequencing” representation of the solution harmony and a dedicated improvisation operator particularly adapted to the integer-valued and operations permutation-based used coding scheme. Besides, a Modified Intelligent Mutation (MIM) operator is integrated to the adopted framework in order to enhance its overall search ability. Mainly, by balancing maximum machine workload during the overall search process, MIM operator allows essentially maintaining and enhancing the reciprocal equilibrium of diversification and intensification abilities of the proposed EOP-DHS algorithm. Conducted numerical experimentations on 188 benchmarking instances validate the proposal comparatively to a representative set of previously deployed metaheuristic approaches to FJSSP with Makespan criterion. Furthermore, main contribution of the paper is extended with an experimental procedure proving the effectiveness of the adopted permutation-based HS scheme for the resolution of combinatorial optimization problems. Hard benchmarking instances of the classical Job Shop Scheduling Problem (JSSP) are thus considered for exemplification.     

Scheduling task graphs optimally with A*

Scheduling tasks onto the processors of a parallel system is a crucial part of program parallelisation. Due to the NP-hard nature of the task scheduling problem, scheduling algorithms are based on heuristics that try to produce good rather than optimal schedules. Nevertheless, in certain situations it is desirable to have optimal schedules, for example for time-critical systems or to evaluate scheduling heuristics. This paper investigates the task scheduling problem using the A* search algorithm which is a best-first state space search. The adaptation of the A* search algorithm for the task scheduling problem is referred to as the A* scheduling algorithm. The A* scheduling algorithm can produce optimal schedules in reasonable time for small to medium sized task graphs with several tens of nodes. In comparison to a previous approach, the here presented A* scheduling algorithm has a significantly reduced search space due to a much improved consistent and admissible cost function f(s) and additional pruning techniques. Experimental results show that the cost function and the various pruning techniques are very effective for the workload. Last but not least, the results show that the proposed A* scheduling algorithm significantly outperforms the previous approach.     

An optimal method for the preemptive job shop scheduling problem

In this study, a powerful solution methodology is developed for minimizing makespan in the preemptive Job Shop Scheduling Problem (pJSSP). Some new properties of the problem are stated and proved via theorems on the basis of which a new dominant set is introduced for the problem. These properties give rise to a dramatic decrease in the search space and provide the potential for exact methods to be successfully used in the solution of this notoriously NP-hard problem. The exact method presented here is a branch and bound algorithm developed on the basis of a new disjunctive graph. Its efficiency is enhanced by the effective use of such techniques as dominance rules or lower bounds. The capability of the approach is investigated by using it to solve the well-known benchmark problems and comparing the results obtained with those from the best methods in common use. The results indicate that the proposed method is capable of optimally solving 24 open benchmark problems including the famous 10×10 problems. Additionally, it is the first optimal method ever developed to find optimal solutions to some large-scale problems of the size 30×10 and 50×10.     

遗传算法在Job-Shop问题上的应用

在车间作业调度数学表达模型的基础上,应用遗传算法对车间作业调度问题进行研究,为了满足遗传算法对解的多样性的要求,提出了一个调度问题的编码方法,并定义了解锁规则且给出了解码过程,最后给出实例说明设计的有效性。     

Exact methods for the resource levelling problem

We present a project scheduling problem subject to general temporal constraints where the utilization of a set of renewable resources has to be smoothed over time. For solving the NP-hard optimization problem, we point out some important structural properties and introduce a new enumeration scheme. Combining this enumeration scheme with some branch-and-bound techniques, we propose an appropriate solution procedure for the project scheduling problem at hand. To outline the practical importance of resource levelling, we sketch exemplary the optimization of mid-term planning schedules with regard to the resource requirements of IT projects. Finally, we present results from a comprehensive computational study on problem instances of the well-known rlp_j10 and rlp_j20 test sets devised by Kolisch et al. (Benchmark Instances for Project Scheduling Problems, Kluwer, Boston, 1999).     

Production Control of a Flexible Manufacturing System in a Job Shop Environment

This paper provides an application oriented analysis of local search procedures for Operation Scheduling and Shop Floor Management of a major German manufacturer of cigarette machines. The heuristics applied are the Threshold- and Simulated Annealing-Algorithm considering Job Shop as well as embedded FMS production features. In this context a new neighbourhood search technique is developed, which is based on a small set of local neighbourhoods and is flexible with respect to the performance measurements of production control. By this approach the scheduling, loading and workload allocation problems of a production facility consisting of an embedded FMS and a conventional Job Shop can be solved simultaneously.     

Parallel Logic Programming for Problem Solving

We present a new model for parallel evaluation of logic programs. This model can exploit the main sources of parallelism that the language of logic expresses: Independent AND parallelism and OR parallelism, together with a secondary source emerging as a consequence of the Independent AND Parallelism: the producer/consumer parallelism. The efficiency is derived from the use of ordered structures for managing the information generated throughout the search process. The model is suitable for evaluating programs with a high degree of non-determinism because it never generates two processes for solving the same subgoal and hence it can exploit the same real parallelism generating a lower number of processes than other models. As an application example, we consider the Job Shop Scheduling problem. We report experimental results showing that logic programs can be designed that exhibit parallelism, and that the use of heuristic information translates into speedup in obtaining answers.     

Time-constrained project scheduling

We propose a new approach for scheduling with strict deadlines and apply this approach to the Time-Constrained Project Scheduling Problem (TCPSP). To be able to meet these deadlines, it is possible to work in overtime or hire additional capacity in regular time or overtime. For this problem, we develop a two stage heuristic. The key of the approach lies in the first stage in which we construct partial schedules. In these partial schedules, jobs may be scheduled for a shorter duration than required. The second stage uses an ILP formulation of the problem to turn a partial schedule into a feasible schedule, and to perform a neighborhood search. The developed heuristic is quite flexible and, therefore, suitable for practice. We present experimental results on modified RCPSP benchmark instances. The two stage heuristic solves many instances to optimality, and if we substantially decrease the deadline, the rise in cost is only small.     

A restart local search algorithm for solving maximum set k-covering problem

The maximum set k-covering problem (MKCP) is a famous combinatorial optimization problem with widely many practical applications. In our work, we design a restart local search algorithm for solving MKCP, which is called RNKC. This algorithm effectively makes use of several advanced ideas deriving from the random restart mechanism and the neighborhood search method. RNKC designs a new random restart method to deal with the serious cycling problem of local search algorithms. Thanks to the novel neighborhood search method that allows a neighborhood exploration of as many feasible search areas as possible, the RNKC can obtain some greatly solution qualities. Comprehensive results on the classical instances show that the RNKC algorithm competes very favorably with a famous commercial solver CPLEX. In particular, it discovers some improved and great results and matches the same solution quality for some instances.

     

一种求解Job Shop 调度问题的改进遗传算法

传统遗传算法在求解Job Shop调度问题时存在收敛速度慢,易于早熟的缺点。在病毒遗传算法(VEGA)和灾变遗传算法的基础上提出了一种带有灾变因子的病毒遗传算法(IVEGA-C)。该算法在传统遗传算法的基本结构上加入了病毒感染操作和灾变操作,病毒感染操作实现了同代个体之间横向传递进化信息,灾变操作采用灭绝操作。正是这种改进加快了遗传算法的收敛速度,避免了早熟现象和陷入局部最优解。通过仿真实验验证了IVEGA-C算法在解决Job Shop调度问题中的性能优于传统GA算法和VEGA算法。最后给出了应用该算法的一个实例。     

A resource-constrained assembly job shop scheduling problem with Lot Streaming technique

To ensure effective shop floor production, it is vital to consider the capital investment. Among most of the operational costs, resource must be one of the critical cost components. Since each operation consumes resources, the determination of resource level is surely a strategic decision. For the first time, the application of Lot Streaming (LS) technique is extended to a Resource-Constrained Assembly Job Shop Scheduling Problem (RC_AJSSP). In general, AJSSP first starts with Job Shop Scheduling Problem (JSSP) and then appends an assembly stage for final product assembly. The primary objective of the model is the minimization of total lateness cost of all final products. To enhance the model usefulness, two more experimental factors are introduced as common part ratio and workload index. Hence, an innovative approach with Genetic Algorithm (GA) is proposed. To examine its goodness, Particle Swarm Optimization (PSO) is the benchmarked method. Computational results suggest that GA can outperform PSO in terms of optimization power and computational effort for all test problems.     

基于蚁群算法的车间作业调度问题研究

对基于蚁群算法的车间作业调度问题求解进行了研究,在分析了传统蚁群算法求解车间作业调度问题容易出现早熟、收敛于局部最优解以及搜索速度慢的缺陷,提出了一种改进的混合蚁群算法。该方法在信息素更新规则上利用信息素局部更新策略和全局更新策略来进行信息素的更新,并将领域搜索与蚁群算法相结合,从而求得问题的可行解。最后,基于benchmarks问题进行了实验仿真,实验结果证明该改进混合算法的有效性及可行性。     

Graphics processing unit‐accelerated bounding for branch‐and‐bound applied to a permutation problem using data access optimization

Branch‐and‐bound (B&B) algorithms are attractive methods for solving to optimality combinatorial optimization problems using an implicit enumeration of a dynamically built tree‐based search space. Nevertheless, they are time‐consuming when dealing with large problem instances. Therefore, pruning tree nodes (subproblems) is traditionally used as a powerful mechanism to reduce the size of the explored search space. Pruning requires to perform the bounding operation, which consists of applying a lower bound function to the subproblems generated during the exploration process. Preliminary experiments performed on the Flow‐Shop scheduling problem (FSP) have shown that the bounding operation consumes over 98% of the execution time of the B&B algorithm. In this paper, we investigate the use of graphics processing unit (GPU) computing as a major complementary way to speed up the search. We revisit the design and implementation of the parallel bounding model on GPU accelerators. The proposed approach enables data access optimization. Extensive experiments have been carried out on well‐known FSP benchmarks using an Nvidia Tesla C2050 GPU card. Compared to a CPU‐based single core execution using an Intel Core i7‐970 processor without GPU, speedups higher than 100 times faster are achieved for large problem instances. At an equivalent peak performance, GPU‐accelerated B&B is twice faster than its multi‐core counterpart. Copyright © 2013 John Wiley & Sons, Ltd.     

Windows环境下的禁忌搜索法解Job—shop问题

本文应用禁忌搜索算法来解决复杂的车间调度问题,介绍了禁忌搜索算法的基本概念和各项参数,讨论了基于禁忌搜索的调度方案,并给出了调度方案的编程实现。     

约束满足自适应神经网络求解车间调度问题

提出一种基于约求满足的自适应神经网络方法求解车间作业调度问题。在该算法中,神经网络在运行过程中能够根据问题的约束类型、约束满足情况、启发式规则的选择来自适应调节神经元之间的连接权值,从而求得问题的可行解。仿真实验证明了算法的有效性。