An Application of Tabu Search Heuristic for the Maximum Edge-Weighted Subgraph Problem

The purpose of this article is to describe an efficient search heuristic for the Maximum Edge-weighted Subgraph (MEwS) problem. This problem requires to find a subgraph such that the sum of the weights associated with the edges of the subgraph is maximized subject to a cardinality constraint. In this study a tabu search heuristic for the MEwS problem is proposed. Different algorithms to obtain an initial solution are presented. One neighborhood search strategy is also proposed. Preliminary computational results are reported for randomly generated test problems of MEwS problem with different densities and sizes. For most of test problems, the tabu search heuristic found good solutions. In addition, for large size test problems, the tabu search outperformed the local search heuristic appearing in the literature.     

Approximative solution methods for multiobjective combinatorial optimization

In this paper we present a review of approximative solution methods, that is, heuristics and metaheuristics designed for the solution of multiobjective combinatorial optimization problems (MOCO). First, we discuss questions related to approximation in this context, such as performance ratios, bounds, and quality measures. We give some examples of heuristics proposed for the solution of MOCO problems. The main part of the paper covers metaheuristics and more precisely non-evolutionary methods. The pioneering methods and their derivatives are described in a unified way. We provide an algorithmic presentation of each of the methods together with examples of applications, extensions, and a bibliographic note. Finally, we outline trends in this area. The research of M. Ehrgott has been partially supported by University of Auckland grant 3602178/9275 and grant Ka 477/27-1 of the Deutsche Forschungsgemeinschaft (DFG).     

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.     

An Adaptive Algorithm for Vector Partitioning

The vector partition problem concerns the partitioning of a set A of n vectors in d-space into p parts so as to maximize an objective function c which is convex on the sum of vectors in each part. Here all parameters d, p, n are considered variables. In this paper, we study the adjacency of vertices in the associated partition polytopes. Using our adjacency characterization for these polytopes, we are able to develop an adaptive algorithm for the vector partition problem that runs in time O(q(L)v) and in space O(L), where q is a polynomial function, L is the input size and v is the number of vertices of the associated partition polytope. It is based on an output-sensitive algorithm for enumerating all vertices of the partition polytope. Our adjacency characterization also implies a polynomial upper bound on the combinatorial diameter of partition polytopes. We also establish a partition polytope analogue of the lower bound theorem, indicating that the output-sensitive enumeration algorithm can be far superior to previously known algorithms that run in time polynomial in the size of the worst-case output.     

Adaptive Reservoir Evolutionary Algorithm: An Evolutionary On-Line Adaptation Scheme for Global Function Optimization

This paper introduces a novel global optimization heuristic algorithm based on the basic paradigms of Evolutionary Algorithms (EA). The algorithm greatly extends a previous strategy proposed by the authors in Munteanu and Lazarescu (1998). In the newly designed algorithm the exploration/exploitation of the search space is adapted on-line based on the current features of the landscape that is being searched. The on-line adaptation mechanism involves a decision process as to whether more exploitation or exploration is needed depending on the current progress of the algorithm and on the current estimated potential of discovering better solutions. The convergence with probability 1 in finite time and discrete space is analyzed, as well as an extensive comparison with other evolutionary optimization heuristics is performed on a set of test functions.     

Metaheuristics in Combinatorial Optimization

The emergence of metaheuristics for solving difficult combinatorial optimization problems is one of the most notable achievements of the last two decades in operations research. This paper provides an account of the most recent developments in the field and identifies some common issues and trends. Examples of applications are also reported for vehicle routing and scheduling problems.     

A Taxonomy of Hybrid Metaheuristics

Hybrid metaheuristics have received considerable interest these recent years in the field of combinatorial optimization. A wide variety of hybrid approaches have been proposed in the literature. In this paper, a taxonomy of hybrid metaheuristics is presented in an attempt to provide a common terminology and classification mechanisms. The taxonomy, while presented in terms of metaheuristics, is also applicable to most types of heuristics and exact optimization algorithms.As an illustration of the usefulness of the taxonomy an annoted bibliography is given which classifies a large number of hybrid approaches according to the taxonomy.     

一种自适应Dai-Liao共轭梯度法

共轭梯度法是一种解决大规模无约束优化问题的重要方法.本文对Dai-Liao(DL)共轭梯度法的参数进行了研究,提出了一种新的自适应DL共轭梯度法.在适当的条件下,证明了该方法的全局收敛性.数值结果表明,我们的方法对给定的测试问题是有效的.     

Nested Partitions Method for Stochastic Optimization

The nested partitions (NP) method is a recently proposed new alternative for global optimization. Primarily aimed at problems with large but finite feasible regions, the method employs a global sampling strategy that is continuously adapted via a partitioning of the feasible region. In this paper we adapt the original NP method to stochastic optimization where the performance is estimated using simulation. We prove asymptotic convergence of the new method and present a numerical example to illustrate its potential.     

一个自适应Dai-Liao共轭梯度法

共轭梯度法是求解大规模无约束优化问题的经典方法之一.基于搜索方向矩阵的谱条件数,给出了一个Dai-Liao(DL)共轭梯度法中参数的自适应形式,提出一种自适应DL共轭梯度算法.在适当的条件下,对于一致凸的目标函数证明了该方法具有全局收敛性.数值结果表明,提出的方法是可行的.     

Pareto Simulated Annealing for Fuzzy Multi-Objective Combinatorial Optimization

The paper presents a metaheuristic method for solving fuzzy multi-objective combinatorial optimization problems. It extends the Pareto simulated annealing (PSA) method proposed originally for the crisp multi-objective combinatorial (MOCO) problems and is called fuzzy Pareto simulated annealing (FPSA). The method does not transform the original fuzzy MOCO problem to an auxiliary deterministic problem but works in the original fuzzy objective space. Its goal is to find a set of approximately efficient solutions being a good approximation of the whole set of efficient solutions defined in the fuzzy objective space. The extension of PSA to FPSA requires the definition of the dominance in the fuzzy objective space, modification of rules for calculating probability of accepting a new solution and application of a defuzzification operator for updating the average position of a solution in the objective space. The use of the FPSA method is illustrated by its application to an agricultural multi-objective project scheduling problem.     

分布式数据流处理系统管理中负载均衡问题建模与求解

对分布式数据流处理系统管理中,处理节点负载均衡问题进行了研究。阐述了分布式数据流处理系统的运行机理以及节点负载不均衡的成因,并提出了对系统负载均衡调整的优化方案;对提出的优化方案建立模型,并对模型的适用条件进行理论分析;然后采用蚁群算法对模型进行求解,并针对分布式数据流处理系统实时性的需求对算法进行改进;最后用实验证明本文所建立的模型及其求解方法对于解决分布式数据流处理系统管理中节点负载均衡问题的有效性。     

An Iteration Method for Reliability Evaluation of a Fleet System

The fleet system considered here consists of n identical units (members) which are operated together under an operational program which specifies the schedule of the operation of the system and maintenance performed on the units in the system. Introduction of this operational program makes the reliability evaluation of the fleet system more realistic but complicated. A conventional Markov approach is effective only when a fleet system consists of a few units. This paper presents a new method for the reliability evaluation of a fleet system. This method reduces the problem of the reliability evaluation of the system to that of each unit by introducing a ‘utilization factor’. Therefore, the size of the problem is irrelevant to the number of the units in the system. An iteration method is used to obtain the unique solution of the problem.     

Resource Constrained Shortest Path Problems in Path Planning for Fleet Management

In the management and control of a vehicle fleet on a road network, the problem arises of finding the best route in relation to the mission of the fleet and to the typology of freight or users. Sometimes the route has to be adapted not only to current traffic conditions, but also to the physical, geometric and functional attributes of the roads, related to their urban location and environmental characteristics. This problem is approached here through an extension of the classic Shortest Path problem, named Resource Constrained Shortest Path problem (RCSP), where the resources are related to the road link attributes, assumed as relevant to the specific planning problem. A classification scheme of these attributes is first proposed and RCSP is described and reviewed. Next, a General Resource Constrained Shortest Path problem (GRCSP) is defined, which can be found in all cases where it is necessary to plan, statically or dynamically, the path of a vehicle and to respect a set of constraints expressed in terms of parameters and indices associated with the roads on the network. For this general problem a model has been formulated and a Branch and Cut solution approach is proposed. Computational results obtained on test and real networks during the experimentation of a fleet with low emission vehicles are also given. This revised version was published online in August 2006 with corrections to the Cover Date.     

Derivative-Free Filter Simulated Annealing Method for Constrained Continuous Global Optimization

In this paper, a simulated-annealing-based method called Filter Simulated Annealing (FSA) method is proposed to deal with the constrained global optimization problem. The considered problem is reformulated so as to take the form of optimizing two functions, the objective function and the constraint violation function. Then, the FSA method is applied to solve the reformulated problem. The FSA method invokes a multi-start diversification scheme in order to achieve an efficient exploration process. To deal with the considered problem, a filter-set-based procedure is built in the FSA structure. Finally, an intensification scheme is applied as a final stage of the proposed method in order to overcome the slow convergence of SA-based methods. The computational results obtained by the FSA method are promising and show a superior performance of the proposed method, which is a point-to-point method, against population-based methods.     

On the Convergence of the Cross-Entropy Method

The cross-entropy method is a relatively new method for combinatorial optimization. The idea of this method came from the simulation field and then was successfully applied to different combinatorial optimization problems. The method consists of an iterative stochastic procedure that makes use of the importance sampling technique. In this paper we prove the asymptotical convergence of some modifications of the cross-entropy method.     

An Efficient Algorithm for the Knapsack Sharing Problem

The Knapsack Sharing Problem (KSP) is an NP-Hard combinatorial optimization problem, admitted in numerous real world applications. In the KSP, we have a knapsack of capacity c and a set of n objects, namely N, where each object j, j = 1,...,n, is associated with a profit p _j and a weight w _j. The set of objects N is composed of m different classes of objects J _i, i = 1,...,m, and N = ^m _i=1 J _i. The aim is to determine a subset of objects to be included in the knapsack that realizes a max-min value over all classes.In this article, we solve the KSP using an approximate solution method based upon tabu search. First, we describe a simple local search in which a depthparameter and a tabu list are used. Next, we enhance the algorithm by introducing some intensifying and diversifying strategies. The two versions of the algorithm yield satisfactory results within reasonable computational time. Extensive computational testing on problem instances taken from the literature shows the effectiveness of the proposed approach.     

Probability Distribution of Solution Time in GRASP: An Experimental Investigation

A GRASP (greedy randomized adaptive search procedure) is a multi-start metaheuristic for combinatorial optimization. We study the probability distributions of solution time to a sub-optimal target value in five GRASPs that have appeared in the literature and for which source code is available. The distributions are estimated by running 12,000 independent runs of the heuristic. Standard methodology for graphical analysis is used to compare the empirical and theoretical distributions and estimate the parameters of the distributions. We conclude that the solution time to a sub-optimal target value fits a two-parameter exponential distribution. Hence, it is possible to approximately achieve linear speed-up by implementing GRASP in parallel.     

八硬币集中四坏硬币的最优测试方法

在前人研究成果的基础上,给出用无砝码的天平从8个硬币中搜索4枚坏硬币的最优搜索方法.     

一类非标准球选取的最优过程

本文用组合优化和数学归纳法 ,对外形不可区分的 n个球中之一个非标准者的选取问题 (以无砝码的天平为工具 )进行了详细的讨论 ,得到了最小秤次及选出坏球的具体方法和步骤