A Parallel Multilevel Metaheuristic for Graph Partitioning

One significant problem of optimisation which occurs in many scientific areas is that of graph partitioning. Several heuristics, which pertain to high quality partitions, have been put forward. Multilevel schemes can in fact improve the quality of the solutions. However, the size of the graphs is very large in many applications, making it impossible to effectively explore the search space. In these cases, parallel processing becomes a very useful tool overcoming this problem. In this paper, we propose a new parallel algorithm which uses a hybrid heuristic within a multilevel scheme. It is able to obtain very high quality partitions and improvement on those obtained by other algorithms previously put forward.     

The nozzle guide vane problem: Partitioning a heterogeneous inventory

In this paper we describe a problem which is encountered in the maintenance of gas turbine engines used in commercial and military aircraft. In particular, we address the problem of selecting a set of nozzle guide vanes, from a heterogeneous inventory of vanes, for the nozzle assembly of an engine. We formulate this problem as a partitioning problem for a heterogeneous population. Given the combinatorial complexity of the problem we develop a heuristic algorithm which is shown to be very effective in obtaining the maximum number of partitions.     

An approach for solving competitive location problems with variable demand using multicore systems

A planar competitive location and design problem with variable demand is considered. The assumption that the demand may vary depending on the conditions of the market makes the problem more realistic, but it also increases its complexity, and therefore, the computational effort needed to solve it. In this paper, a modification of a heuristic recently proposed to cope with the problem is presented, which allows, on the one hand, to obtain the same solutions as the original heuristic more quickly and, on the other hand, to handle larger size problems. Furthermore, a parallel version of the algorithm, suitable for being run in most of today’s personal computers, has also been proposed. The parallel algorithm has been implemented using the OpenMP library and the results show an ideal efficiency up to at least eight processors (the largest number of available processing elements). The effectiveness of the parallel algorithm has also been measured. From the computational results, it can be inferred that the proposed parallelization is robust.     

Single machine scheduling to minimize total weighted earliness subject to minimal number of tardy jobs

Motivated by just-in-time manufacturing, we consider a single machine scheduling problem with dual criteria, i.e., the minimization of the total weighted earliness subject to minimum number of tardy jobs. We discuss several dominance properties of optimal solutions. We then develop a heuristic algorithm with time complexity O(n³) and a branch and bound algorithm to solve the problem. The computational experiments show that the heuristic algorithm is effective in terms of solution quality in many instances while the branch and bound algorithm is efficient for medium-size problems.     

Adaptive sample size and importance sampling in estimation-based local search for the probabilistic traveling salesman problem

The probabilistic traveling salesman problem is a paradigmatic example of a stochastic combinatorial optimization problem. For this problem, recently an estimation-based local search algorithm using delta evaluation has been proposed. In this paper, we adopt two well-known variance reduction procedures in the estimation-based local search algorithm: the first is an adaptive sampling procedure that selects the appropriate size of the sample to be used in Monte Carlo evaluation; the second is a procedure that adopts importance sampling to reduce the variance involved in the cost estimation. We investigate several possible strategies for applying these procedures to the given problem and we identify the most effective one. Experimental results show that a particular heuristic customization of the two procedures increases significantly the effectiveness of the estimation-based local search.     

Lock-Gain Based Graph Partitioning

We propose a new heuristic for the graph partitioning problem. Based on the traditional iterative improvement framework, the heuristic uses a new type of gain in selecting vertices to move between partitions. The new type of gain provides a good explanation for the performance difference of tie-breaking strategies in KL-based iterative improvement graph partitioning algorithms. The new heuristic performed excellently. Theoretical arguments supporting its efficacy are also provided. As the proposed heuristic is considered a good candidate for local optimization engines in metaheuristics, we combined it with a genetic algorithm as a sample case and obtained a surprising result that even the average results over 1,000 runs equalled the best known for most graphs.     

Tree search for the stacking problem

The stacking problem is a hard combinatorial optimization problem with high practical interest in, for example, steel storage or container port operations. In this problem, a set of items is stored in a warehouse for a period of time, and a crane is used to place them in a limited number of stacks. Since the entrance and exit of items occurs in an arbitrary order, items may have to be relocated in order to reach and deliver other items below them. The objective of the problem is to find a feasible sequence of movements that delivers all items, while minimizing the total number of movements. We study the scalability of an exact approach to this problem, and propose two heuristic methods to solve it approximately. The two heuristic approaches are a multiple simulation algorithm using semi-greedy construction heuristics, and a stochastic best-first tree search algorithm. The two methods are compared in a set of challenging instances, revealing a superior performance of the tree search approach in most cases.     

汽车滚装码头泊位调度优化模型与算法研究

本文研究滚装码头混合泊位分配和劳动力分配的联合调度优化问题。首先,考虑潮汐时间窗约束、装卸劳动力约束、泊位缆桩分布约束以及泊位不规则布局因素,建立以最小化船舶总服务时间为目标的混合整数规划模型。其次,采用内外嵌套算法设计策略,提出求解该类问题的组合算法。其中,外层是多种群并行进化的遗传算法,生成多种船舶计划顺序,内层为基于规则的启发式算法,用于计算给定计划顺序的目标函数值。然后,基于实际运营数据,生成多组不同规模的算例进行全面数值实验,结果表明所提出的算法可在10分钟内求解包含50艘船、100个泊段的算例。最后,开展基于真实滚装码头运营实例的案例分析,对所提模型和算法在实际码头调度问题中的适用性与高效性进行验证。     

Consensus of partitions : a constructive approach

Given a profile (family) ?? of partitions of a set of objects or items X, we try to establish a consensus partition containing a maximum number of joined or separated pairs in X that are also joined or separated in the profile. To do so, we define a score function, S _?? associated to any partition on X. Consensus partitions for ?? are those maximizing this function. Therefore, these consensus partitions have the median property for the profile and the symmetric difference distance. This optimization problem can be solved, in certain cases, by integer linear programming. We define a polynomial heuristic which can be applied to partitions on a large set of items. In cases where an optimal solution can be computed, we show that the partitions built by this algorithm are very close to the optimum which is reached in practically all the cases, except for some sets of bipartitions.     

An Application of a Multi-Objective Tabu Search Algorithm to a Bicriteria Flowshop Problem

This paper proposes a new tabu search algorithm for multi-objective combinatorial problems with the goal of obtaining a good approximation of the Pareto-optimal or efficient solutions. The algorithm works with several paths of solutions in parallel, each with its own tabu list, and the Pareto dominance concept is used to select solutions from the neighborhoods. In this way we obtain at each step a set of local nondominated points. The dispersion of points is achieved by a clustering procedure that groups together close points of this set and then selects the centroids of the clusters as search directions. A nice feature of this multi-objective algorithm is that it introduces only one additional parameter, namely, the number of paths. The algorithm is applied to the permutation flowshop scheduling problem in order to minimize the criteria of makespan and maximum tardiness. For instances involving two machines, the performance of the algorithm is tested against a Branch-and-Bound algorithm proposed in the literature, and for more than two machines it is compared with that of a tabu search algorithm and a genetic local search algorithm, both from the literature. Computational results show that the heuristic yields a better approximation than these algorithms.     

A column generation approach for an emission-oriented vehicle routing problem on a multigraph

In this work, an emission-minimizing vehicle routing problem with heterogeneous vehicles and a heterogeneous road and traffic network is considered as it is typical in urban areas. Depending on the load of the vehicle, there exist multiple emission-minimal arcs for traveling between two locations. To solve the vehicle routing problem efficiently, a column generation approach is presented. At the core of the procedure an emission-oriented elementary shortest path problem on a multigraph is solved by a backward labeling algorithm. It is shown that the labeling algorithm can be sped up by adjusting the dual master program and by restricting the number of labels propagated in the sub-problem. The column generation technique is used to setup a fast heuristic as well as a branch-and-price algorithm. Both procedures are evaluated based on test instances with up to 100 customers. It turns out that the heuristic approach is very effective and generates near-optimal solutions with gaps below 0.1% on average while only requiring a fraction of the runtime of the exact approach.     

Coordinated condition-based repair strategies for components of a multi-component maintenance system with discounts

This paper presents a heuristic algorithm for computing upper and lower control limit values for the repair of components (which need not be identical) in a multi-component system. The cost structure is composed of repair, operating and failure costs. An essential feature of the model is that reduction in repair costs can be achieved by coordinating the repair of several components and thus paying set-up costs only once. The algorithm searches for a simple rule per component in order to minimise long-run average cost per unit of time for the system as a whole. This opportunistic rule per component has a simple structure: it consists of an upper limit inducing mandatory repair and of several lower limits. Each lower limit corresponds to the potential for saving an amount of repair costs when an opportunity for a specific coordination presents itself. The heuristic procedure is based on decomposition producing single-component problems. Each single-component problem is solved as a Markov decision problem, allowing the model to cope with a large number of components.     

A penalty-shift-insertion-based algorithm to minimize total flow time in no-wait flow shops

This paper proposes a penalty-shift-insertion (PSI)-based algorithm for the no-wait flow shop scheduling problem to minimize total flow time. In the first phase, a penalty-based heuristic, derived from Vogel’s approximation method used for the classic transportation problem is used to generate an initial schedule. In the second phase, a known solution is improved using a forward shift heuristic. Then the third phase improves this solution using a job-pair and a single-job insertion heuristic. Results of the computational experiments with a large number of randomly generated problem instances show that the proposed PSI algorithm is relatively more effective and efficient in minimizing total flow time in a no-wait flow shop than the state-of-the-art procedures. Statistical significance of better results obtained by the proposed algorithm is also reported.     

Routing and wavelength assignment in optical networks using bin packing based algorithms

This paper addresses the problem of routing and wavelength assignment (RWA) of static lightpath requests in wavelength routed optical networks. The objective is to minimize the number of wavelengths used. This problem has been shown to be NP-complete and several heuristic algorithms have been developed to solve it. We suggest very efficient, yet simple, heuristic algorithms for the RWA problem developed by applying classical bin packing algorithms. The heuristics were tested on a series of large random networks and compared with an efficient existing algorithm for the same problem. Results indicate that the proposed algorithms yield solutions significantly superior in quality, not only with respect to the number of wavelength used, but also with respect to the physical length of the established lightpaths. Comparison with lower bounds shows that the proposed heuristics obtain optimal or near optimal solutions in many cases.     

一种双目标带约束工件成类的平行机器调度启发式规则

提出了一种快速而有效的启发式规则(fam ily slack,简称FSLACK),来求解极小化总延误时间和极小化最大完工时间两个目标,工件按产品类型成组,带模具数量约束的平行机器生产调度问题.本文提出的FSLACK与EDD、LPT及SLACK进行了比较.随机订单的测试结果表明,本文提出的启发式规则在求解双目标带约束工件成类的平行机器调度问题上是有效的.这表明该算法可以应用在成型加工业的现场作业调度.     

具有机器适用限制的分布式置换流水车间问题的模型与算法

考虑具有机器适用限制的多个不同置换流水车间的调度问题. 机器适用限制指的是每个工件只能分配到其可加工工厂集合. 所有置换流水车间拥有的机器数相同但是具有不同的加工能力. 首先, 针对该问题建立了基于位置的混合整数线性规划模型; 进而, 对一般情况和三种特殊情况给出了具有较小近似比的多项式时间算法. 其次, 基于NEH方法提出了启发式算法NEHg, 并给出了以NEHg为上界的分支定界算法. 最后, 通过例子说明了NEHg启发式算法和分支定界算法的计算过程, 并进行大量的实验将NEHg与NEH算法结果进行比较, 从而验证了NEHg算法的有效性.     

A multi-heuristic approach for solving the pre-marshalling problem

Minimizing the number of reshuffling operations at maritime container terminals incorporates the pre-marshalling problem (PMP) as an important problem. Based on an analysis of existing solution approaches we develop new heuristics utilizing specific properties of problem instances of the PMP. We show that the heuristic performance is highly dependent on these properties. We introduce a new method that exploits a greedy heuristic of four stages, where for each of these stages several different heuristics may be applied. Instead of using randomization to improve the performance of the heuristic, we repetitively generate a number of solutions by using a combination of different heuristics for each stage. In doing so, only a small number of solutions is generated for which we intend that they do not have undesirable properties, contrary to the case when simple randomization is used. Our experiments show that such a deterministic algorithm significantly outperforms the original nondeterministic method. The improvement is twofold, both in the quality of found solutions, and in the computational effort.     

Effective Heuristic Procedures for a Field Technician Scheduling Problem

This paper addresses a field technician scheduling problem faced by many service providers in telecommunication industry. The problem is to assign a set of jobs, at different locations with time windows, to a group of field technicians with different job skills. Such a problem can be viewed as a generalization of the well-known vehicle routing problem with time windows since technician skills need to be matched with job types. We designed and tested several heuristic procedures for solving the problem, namely a greedy heuristic, a local search algorithm, and a greedy randomized adaptive search procedure (GRASP). Our computational results indicate that GRASP is the most effective among them but requires more CPU time. However, the unique structure of GRASP allows us to exploit parallelism to achieve linear speed-up with respect to the number of machines used.     

Convergence Criteria for Hierarchical Overlapping Coordination of Linearly Constrained Convex Design Problems

Decomposition of multidisciplinary engineering system design problems into smaller subproblems is desirable because it enhances robustness and understanding of the numerical results. Moreover, subproblems can be solved in parallel using the optimization technique most suitable for the underlying mathematical form of the subproblem. Hierarchical overlapping coordination (HOC) is an interesting strategy for solving decomposed problems. It simultaneously uses two or more design problem decompositions, each of them associated with different partitions of the design variables and constraints. Coordination is achieved by the exchange of information between decompositions. This article presents the HOC algorithm and several new sufficient conditions for convergence of the algorithm to the optimum in the case of convex problems with linear constraints. One of these equivalent conditions involves the rank of the constraint matrix that is computationally efficient to verify. Computational results obtained by applying the HOC algorithm to quadratic programming problems of various sizes are included for illustration.     

A fast heuristic algorithm for the maximum concurrent <Emphasis Type="Italic">k</Emphasis>-splittable flow problem

In this paper, we propose a fast heuristic algorithm for the maximum concurrent k-splittable flow problem. In such an optimization problem, one is concerned with maximizing the routable demand fraction across a capacitated network, given a set of commodities and a constant k expressing the number of paths that can be used at most to route flows for each commodity. Starting from known results on the k-splittable flow problem, we design an algorithm based on a multistart randomized scheme which exploits an adapted extension of the augmenting path algorithm to produce starting solutions for our problem, which are then enhanced by means of an iterative improvement routine. The proposed algorithm has been tested on several sets of instances, and the results of an extensive experimental analysis are provided in association with a comparison to the results obtained by a different heuristic approach and an exact algorithm based on branch and bound rules.