Solving production scheduling with earliness/tardiness penalties by constraint programming

This paper deals with an application of constraint programming in production scheduling with earliness and tardiness penalties that reflects the scheduling part of the Just-In-Time inventory strategy. Two scheduling problems are studied, an industrial case study problem of lacquer production scheduling, and also the job-shop scheduling problem with earliness/tardiness costs. The paper presents two algorithms that help the constraint programming solver to find solutions of these complex problems. The first algorithm, called the cost directed initialization, performs a greedy initialization of the search tree. The second one, called the time reversing transformation and designed for lacquer production scheduling, reformulates the problem to be more easily searchable when the default search or the cost directed initialization is used. The conducted experiments, using case study instances and randomly generated problem instances, show that our algorithms outperform generic approaches, and on average give better results than other nontrivial algorithms.     

Inference of regular languages using state merging algorithms with search

State merging algorithms have emerged as the solution of choice for the problem of inferring regular grammars from labeled samples, a known NP-complete problem of great importance in the grammatical inference area. These methods derive a small deterministic finite automaton from a set of labeled strings (the training set), by merging parts of the acceptor that corresponds to this training set. Experimental and theoretical evidence have shown that the generalization ability exhibited by the resulting automata is highly correlated with the number of states in the final solution.As originally proposed, state merging algorithms do not perform search. This means that they are fast, but also means that they are limited by the quality of the heuristics they use to select the states to be merged. Sub-optimal choices lead to automata that have many more states than needed and exhibit poor generalization ability.In this work, we survey the existing approaches that generalize state merging algorithms by using search to explore the tree that represents the space of possible sequences of state mergings. By using heuristic guided search in this space, many possible state merging sequences can be considered, leading to smaller automata and improved generalization ability, at the expense of increased computation time.We present comparisons of existing algorithms that show that, in widely accepted benchmarks, the quality of the derived solutions is improved by applying this type of search. However, we also point out that existing algorithms are not powerful enough to solve the more complex instances of the problem, leaving open the possibility that better and more powerful approaches need to be designed.     

求解运输问题的GAPSO算法

运输问题是一个应用非常广泛的问题,传统方法对于大规模的运输问题求解比较复杂,而一些基于随机搜索算法的方法对于其约束条件的处理又比较困难.基于运输问题约束条件的特殊性,设计了一种产生可行解的方法,将对约束条件的处理转化到了算法设计之中.在此基础上,又设计了基于遗传算法和粒子群优化算法的求解运输问题的GAPSO算法,为避开对非可行解的处理,该算法对迭代过程也进行了特殊设计,从而简化了运用随机搜索算法解决运输问题的过程.最后给出了三个实例验证,通过对验证结果分析和比较,说明该算法在时间复杂度和收敛性方面都具有其优良性,是行之有效的.     

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.     

Exhaustive and heuristic search approaches for learning a software defect prediction model

In this paper, we propose a software defect prediction model learning problem (SDPMLP) where a classification model selects appropriate relevant inputs, from a set of all available inputs, and learns the classification function. We show that the SDPMLP is a combinatorial optimization problem with factorial complexity, and propose two hybrid exhaustive search and probabilistic neural network (PNN), and simulated annealing (SA) and PNN procedures to solve it. For small size SDPMLP, exhaustive search PNN works well and provides an (all) optimal solution(s). However, for large size SDPMLP, the use of exhaustive search PNN approach is not pragmatic and only the SA–PNN allows us to solve the SDPMLP in a practical time limit. We compare the performance of our hybrid approaches with traditional classification algorithms and find that our hybrid approaches perform better than traditional classification algorithms.     

A Neurogenetic approach for the resource-constrained project scheduling problem

A variety of metaheuristic approaches have emerged in recent years for solving the resource-constrained project scheduling problem (RCPSP), a well-known NP-hard problem in scheduling. In this paper, we propose a Neurogenetic approach which is a hybrid of genetic algorithms (GA) and neural-network (NN) approaches. In this hybrid approach the search process relies on GA iterations for global search and on NN iterations for local search. The GA and NN search iterations are interleaved in a manner that allows NN to pick the best solution thus far from the GA pool and perform an intensification search in the solution's local neighborhood. Similarly, good solutions obtained by NN search are included in the GA population for further search using the GA iterations. Although both GA and NN approaches, independently give good solutions, we found that the hybrid approach gives better solutions than either approach independently for the same number of shared iterations. We demonstrate the effectiveness of this approach empirically on the standard benchmark problems of size J30, J60, J90 and J120 from PSPLIB.     

A simulation-based decision support system for a multi-echelon inventory problem with service level constraints

In this paper, we present a simulation-based decision support system for solving the multi-echelon constrained inventory problem. The goal is to determine the optimal setting of stocking levels to minimize the total inventory investment costs while satisfying the expected response time targets for each field depot. We derive new decision support algorithms to be applied in different scenarios, including small-sample and large-sample cases. The first case requires that the set of alternative solutions is known at the beginning of the experiment, and the number of evaluated solutions may depend on the simulation budget (i.e., the time available to solve the problem). In the second case, the alternative solutions are generated sequentially during the searching process, and we may terminate the algorithm when the specified sampling budget is exhausted. Empirical studies are conducted to compare the performance of the proposed algorithms with other conventional optimization approaches.     

Visualization blackboard-visualizing optimization by multipleprocessors

Classification problems that involve finding a vector α whose direction is in some sense optimal are considered. To overcome the relative slowness of general-purpose approaches, multiple processors are used. To understand the rather complex behavior of the resulting algorithms, a visualization tool that shows (for the 3-D case) the function, the locations of its local and global minima, and the positions of the processors as they search through the space has been developed. The tool is applicable to any problem domain and any optimization algorithm. It is illustrated on an algorithm for a medical problem     

A hybrid evolutionary multiobjective optimization strategy for the dynamic power supply problem in magnesia grain manufacturing

The supply trajectory of electric power for submerged arc magnesia furnace determines the yields and grade of magnesia grain during the manufacture process. As the two production targets (i.e., the yields and the grade of magnesia grain) are conflicting and the process is subject to changing conditions, the supply of electric power needs to be dynamically optimized to track the moving Pareto optimal set with time. A hybrid evolutionary multiobjective optimization strategy is proposed to address the dynamic multiobjective optimization problem. The hybrid strategy is based on two techniques. The first one uses case-based reasoning to immediately generate good solutions to adjust the power supply once the environment changes, and then apply a multiobjective evolutionary algorithm to accurately solve the problem. The second one is to learn the case solutions to guide and promote the search of the evolutionary algorithm, and the best solutions found by the evolutionary algorithm can be used to update the case library to improve the accuracy of case-based reasoning in the following process. Due to the effectiveness of mutual promotion, the hybrid strategy can continuously adapt and search in dynamic environments. Two prominent multiobjective evolutionary algorithms are integrated into the hybrid strategy to solve the dynamic multiobjective power supply optimization problem. The results from a series of experiments show that the proposed hybrid algorithms perform better than their component multiobjective evolutionary algorithms for the tested problems.     

Efficient Algorithms for the Inference of Minimum Size DFAs

This work describes algorithms for the inference of minimum size deterministic automata consistent with a labeled training set. The algorithms presented represent the state of the art for this problem, known to be computationally very hard.In particular, we analyze the performance of algorithms that use implicit enumeration of solutions and algorithms that perform explicit search but incorporate a set of techniques known as dependency directed backtracking to prune the search tree effectively.We present empirical results that show the comparative efficiency of the methods studied and discuss alternative approaches to this problem, evaluating their advantages and drawbacks.     

Improvements of constraint programming and hybrid methods for scheduling of tests on vehicle prototypes

In the automotive industry, a manufacturer must perform several hundreds of tests on prototypes of a vehicle before starting its mass production. Tests must be allocated to suitable prototypes and ordered to satisfy temporal constraints and various kinds of test dependencies. The manufacturer aims to minimize the number of prototypes required. We present improvements of constraint programming (CP) and hybrid approaches to effectively solve random instances from an existing benchmark. CP mostly achieves better solutions than the previous heuristic technique and genetic algorithm. We also provide customized search schemes to enhance the performance of general search algorithms. The hybrid approach applies mixed integer linear programming (MILP) to solve the planning part and CP to find the complete schedule. We consider several logical principles such that the MILP model can accurately estimate the prototype demand, while its size particularly for large instances does not exceed memory capacity. Moreover, the robustness is alleviated when we allow CP to partially change the allocation obtained from the MILP model. The hybrid method can contribute to optimal solutions in some instances.     

基于遗传算法的数码问题求解

在人工智能研究中，数码问题常被用来作为一些搜索算法的测试实例。数码问题的搜索空间巨大，对于24数码问题，目前最好的启发式搜索算法找到最优解(最少移动步数)通常也至少需要2．25小时^[1]。遗传算法具有简单、通用、鲁棒性强的特点，适合于在复杂而庞大的搜索空间中寻找最优解。该文给出了求解该问题的遗传算法，并针对遗传算法容易过早收敛的问题，对传统遗传算法进行了改进。通过用多个随机生成的]5数码和24数码问题作为测试实例，本算法均在较短的时间内找到了问题的解，从而证明了算法的有效性。     

Sequence-dependent group scheduling problem on unrelated-parallel machines

In this research we address a sequence-dependent group scheduling problem on a set of unrelated-parallel machines where the run time of each job differs on different machines. To benefit both producer and customers we attempt to minimize a linear combination of total weighted completion time and total weighted tardiness. Since the problem is shown to be NP-hard, meta-heuristic algorithms based on tabu search are developed to find the optimal/near optimal solution. For some small size yet complex problems, the results from these algorithms are compared to the optimal solutions found by CPLEX. The result obtained in all of these problems is that the tabu search algorithms could find solutions at least as good as CPLEX but in drastically shorter computational time, thus signifying the high degree of efficiency and efficacy attained by the former.     

Probabilistic design of optimal sequential decision-making algorithms in learning and control

This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that combines a problem formulation and a set of resolution methods. The formulation consists of an infinite-dimensional optimization problem. The methods come from approaches to search optimal solutions in the space of probability functions. Through the lenses of this overarching framework we revisit popular learning and control algorithms, showing that these naturally arise from suitable variations on the formulation mixed with different resolution methods. A running example, for which we make the code available, complements the survey. Finally, a number of challenges arising from the survey are also outlined.     

A simultaneous transit network design and frequency setting: Computing with bees

The transit network design problem belongs to the class of hard combinatorial optimization problem, whose optimal solution is not easy to find out. We consider in this paper the transit network design problem in a way that we simultaneously determine the links to be included in the transit network, assemble chosen links into bus routes, and determine bus frequency on each of the designed routes. Our approach to the transit network design problem is based on the Bee Colony Optimization (BCO) metaheuristic. The BCO algorithm is a stochastic, random-search technique that belongs to the class of population-based algorithms. This technique uses a similarity among the way in which bees in nature look for food, and the way in which optimization algorithms search for an optimum of a combinatorial optimization problem. The numerical experiments are performed on known benchmark problems. We clearly show that our approach, based on the BCO algorithm is competitive with the other approaches in the literature and that can generate high-quality solutions.     

On multiprocessor task scheduling using efficient state space search approaches

Obtaining an optimal schedule for a set of precedence-constrained tasks is a well-known NP-complete problem in its general form. In view of the intractability of the problem, most of the previous work relies on heuristics that try to find reasonably high quality solutions in an acceptable amount of time. While optimal polynomial-time algorithms are known only for a few simple cases (and in other cases can only be obtained through an exhaustive search with prohibitively high time complexity), they may be critically important for applications in which performance is the prime objective. Optimal solutions can also serve as a reference to test the performance of various heuristics. Moreover, an optimal schedule for a program at hand needs to be determined only once (and off-line) but the program using that schedule is in general executed several times. In this paper, we propose optimal algorithms for static scheduling of task graphs with arbitrary parameters to multiple homogeneous processors. The first algorithm is based on the A^* search technique and uses a computationally efficient cost function for guiding the search with reduced complexity. Additionally, we propose a number of effective state-pruning techniques to reduce the search space. For further lowering the complexity, we propose an efficient parallelization of the search algorithm. We parallelize the algorithm with reduced interprocessor communication as well as with static and dynamic load-balancing schemes to evenly distribute the search states to the processors. We also propose an approximate algorithm that guarantees a bounded deviation from the optimal solution but executes in a considerably shorter time. Based on an extensive experimental evaluation of the algorithms, we conclude that the parallel algorithm with pruning techniques is an efficient scheme for generating optimal solutions of reasonably large problems while the approximate algorithm is effective if slightly degraded solutions are acceptable.     

Nonlinear continuous multi-response problems: a novel two-phase hybrid genetic based metaheuristic

Generally the most real world production systems are tackling several different responses and the problem is optimizing these responses concurrently. This study strives to present a new two-phase hybrid genetic based metaheuristic for optimizing nonlinear continuous multi-response problems. Premature convergence and getting stuck in local optima, which makes the algorithm time consuming, are common problems dealing with genetic algorithms (GAs). So we hybridize GA with a clustering approach and particle swarm optimization algorithm (PSO) to make a balanced relationship between time consuming and premature termination. The proposed algorithm also tries to find Ideal Points (IPs) for response functions. IPs are considered as improvement measures that determine when PSO should start. PSO based local search exploit Pareto archive solutions to enhance performance of the algorithm by expanding the search space. Since there is no standard benchmark in this field, we use two case studies from distinguished paper in multi-response optimization and compare the results with some of the mentioned algorithms in the literature. Results show the outperformance of the proposed algorithm than all of them.     

Learning Bayesian networks by hill climbing: efficient methods based on progressive restriction of the neighborhood

Learning Bayesian networks is known to be an NP-hard problem and that is the reason why the application of a heuristic search has proven advantageous in many domains. This learning approach is computationally efficient and, even though it does not guarantee an optimal result, many previous studies have shown that it obtains very good solutions. Hill climbing algorithms are particularly popular because of their good trade-off between computational demands and the quality of the models learned. In spite of this efficiency, when it comes to dealing with high-dimensional datasets, these algorithms can be improved upon, and this is the goal of this paper. Thus, we present an approach to improve hill climbing algorithms based on dynamically restricting the candidate solutions to be evaluated during the search process. This proposal, dynamic restriction, is new because other studies available in the literature about restricted search in the literature are based on two stages rather than only one as it is presented here. In addition to the aforementioned advantages of hill climbing algorithms, we show that under certain conditions the model they return is a minimal I-map of the joint probability distribution underlying the training data, which is a nice theoretical property with practical implications. In this paper we provided theoretical results that guarantee that, under these same conditions, the proposed algorithms also output a minimal I-map. Furthermore, we experimentally test the proposed algorithms over a set of different domains, some of them quite large (up to 800 variables), in order to study their behavior in practice.     

Earliness–tardiness minimization on a single machine to schedule preventive maintenance tasks: metaheuristic and exact methods

In this paper, we consider the problem of scheduling a set of M preventive maintenance tasks to be performed on M machines. The machines are assigned to execute production tasks. We aim to minimize the total preventive maintenance cost such that the maintenance tasks have to continuously be run during the schedule horizon. Such a constraint holds when the maintenance resources are not sufficient. We solve the problem by two exact methods and meta-heuristic algorithms. As exact procedures we used linear programming and branch and bound methods. As meta-heuristics, we propose a local search approach as well as a genetic algorithm. Computational experiments are performed on randomly generated instances to show that the proposed methods produce appropriate solutions for the problem. The computational results show that the deviation of the meta-heuristics solutions to the optimal one is very small, which confirms the effectiveness of meta-heuristics as new approaches for solving hard scheduling problems.     

预制构件并行生产线资源配置与生产调度集成优化

并行生产线和特定工序生产资源共享模式可以显著改善客户满意度并节约成本.针对预制构件并行生产线资源配置与生产调度集成优化问题,基于分解策略和交替迭代优化思想,提出一种交替式混合果蝇-禁忌搜索算法(AHFOA＿TS)以最小化拖期惩罚费用.首先,通过快速启发式方法产生一较好初始解;然后,固定资源配置方案,为提高算法局部搜索能力,通过集成多种局部搜索方式,设计一种离散果蝇优化算法优化订单指派及调度方案;最后,固定订单指派及调度方案,为减少无效搜索次数,设计一种基于双层变异算子和精英劣解交叉策略的混合禁忌搜索算法以优化资源配置方案,如此两个阶段交替运行直至满足终止条件.此外,设计4种基于交替搜索框架的智能优化算法用于比较.计算结果表明, AHFOA＿TS算法能够更有效求解预制构件生产线资源配置和生产调度集成优化问题.