On-Line Packing Sequences of Cubes in the Unit Cube

Almost thirty years ago Meir and Moser proved that every sequence of d -dimensional cubes of total volume 2 ^)d can be packed in the unit cube. We show that if d 5, then this property holds true also for the on-line packing.     

一类带多重核元集在线装箱问题

本文讨论了一类在线变尺寸装箱问题,假定箱子的尺寸可以是不同的.箱子是在线到达的,仅当箱子到达后其尺寸才知道.给定一个带有核元的物品表及其上的核元关系图.我们的目标是要将表中元素装入到达的箱子中,保证任何箱子所装物品不互为核元,即所装物品对应的点所导出的子图是个空图,并使得所用的箱子总长最小.我们证明了该问题是NPHard的,并给出了基于图的点染色、图的团分解和基于背包问题的近似算法,给出了算法的时间复杂度和性能界.     

On the effectiveness of the Harmonic Shelf Algorithm for on-line strip packing

In [J. Csirik, G.J. Woeginger, An on-line algorithm for multidimensional bin packing, Inform. Process. Lett. 63 (1997) 171-175] the authors study the asymptotic worst case ratio between the height of the strip needed to on-line pack a list of boxes by means of the Harmonic Shelf Algorithm and the height of the strip used by an optimal algorithm. In this note we analyze the effectiveness of the former algorithm in terms of the ratio between the unused area inside the strip and the total size of this strip, and we show that the Harmonic Shelf Algorithm is also capable of packing items so that the asymptotic worst case value of this ratio comes arbitrarily close to .     

Packing 1×2×4 bricks in a cubical box

Given a cubical box C_2n+1 of side 2n+1 and a supply of 1×2×4 bricks, it is proved that if n≥2, then

(A1)

one can pack bricks for n odd, and bricks for n even,

(A2)

the capacity of C_2n+1 is , and if n≡1 or 2 (mod4), this upper bound for the capacity can be reduced by 1.

     

Local Search Algorithms for the Bin Packing Problem and Their Relationships to Various Construction Heuristics

The tradeoff between the speed and quality of the solutions obtained by various construction and local search algorithms for the elementary bin packing problem (BPP) are analyzed to obtain useful information for designing algorithms for real-world problems that can be modeled as BPPs. On the basis of intensive computational experiments, we observe that the framework of a solution (i.e., a part of a solution consisting of large items or items with tight constraints) should be constructed in the early stages of a local search. New local search algorithms are proposed as empirical support for the observation.     

约束装箱问题的混合遗传算法求解

本将最佳适应法和遗传算法相结合，提出了一种新的启发式混合遗传算法对具有时间约束的装箱问题进行求解，给出了具体的算法步骤，试算结果表明基于启发式算法的混合遗传算法适合于求解各种约束条件下的大规模装箱问题。     

An Efficient Sampling Algorithm for Network Motif Detection

We propose a sequential importance sampling strategy to estimate subgraph frequencies and detect network motifs. The method is developed by sampling subgraphs sequentially node by node using a carefully chosen proposal distribution. Viewing the subgraphs as rooted trees, we propose a recursive formula that approximates the number of subgraphs containing a particular node or set of nodes. The proposal used to sample nodes is proportional to this estimated number of subgraphs. The method generates subgraphs from a distribution close to uniform, and performs better than competing methods. We apply the method to four real-world networks and demonstrate outstanding performance in practical examples. Supplemental materials for the article are available online.     

An Efficient Genetic Algorithm for the p-Median Problem

We propose a new genetic algorithm for a well-known facility location problem. The algorithm is relatively simple and it generates good solutions quickly. Evolution is facilitated by a greedy heuristic. Computational tests with a total of 80 problems from four different sources with 100 to 1,000 nodes indicate that the best solution generated by the algorithm is within 0.1% of the optimum for 85% of the problems. The coding effort and the computational effort required are minimal, making the algorithm a good choice for practical applications requiring quick solutions, or for upper-bound generation to speed up optimal algorithms.     

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.     

快速三维散乱数据点重建算法

提出了一种快速三维散乱数据点重建算法.我们对包围盒算法进行了改进,减少了建立散乱点近邻关系所需的计算量;同时针对位置相对平坦的数据点,结合最小二乘法给出了一种计算法矢的混合方法.实例表明,该算法是有效的.     

Efficient Heuristics for the Heterogeneous Fleet Multitrip VRP with Application to a Large-Scale Real Case

The basic Vehicle Routing Problem (VRP) consists of computing a set of trips of minimum total cost, to deliver fixed amounts of goods to customers with a fleet of identical vehicles. Few papers address the case with several types of vehicles (heterogeneous fleet). Most of them assume an unlimited number of vehicles of each type, to dimension the fleet from a strategic point of view. This paper tackles the more realistic tactical or operational case, with a fixed number of vehicles of each type, and the optional possibility for each vehicle to perform several trips. It describes several heuristics, including a very efficient one that progressively merges small starting trips, while ensuring that they can be performed by the fleet. This heuristic seeks to minimize the number of required vehicles as a secondary objective. It outperforms classical VRP heuristics, can easily handle various constraints, and gives very good initial solutions for a tabu search method. The real case of a French manufacturer of furniture with 775 destination stores is presented.     

Packing Densities and Simulated Tempering for Hard Core Gibbs Point Processes

Monotonicity and convergence properties of the intensity of hard core Gibbs point processes are investigated and compared to the closest packing density. For such processes simulated tempering is shown to be an efficient alternative to commonly used Markov chain Monte Carlo algorithms. Various spatial characteristics of the pure hard core process are studied based on samples obtained with the simulated tempering algorithm.     

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.     

An Efficient Algorithm for Embedding Nonplanar Graphs in Planes

An efficient multi-step algorithm is presented for embedding a nonplanar graph on the least possible number of planes. In the first step, the graph is drawn on a plane with the smallest possible number of crossings. Then the appropriate crossing edges are selected and moved onto the second plane. This process is repeated introducing subsequent planes until no crossing remains.     

An Efficient Exact Algorithm for Constraint Bipartite Vertex Cover

The constraint bipartite vertex cover problem (CBVC for short) is as follows: given a bipartite graph G with n vertices and two positive integers k₁, k₂, is there a vertex cover taking at most k₁ vertices from one and at most k₂ vertices from the other vertex set of G? CBVC is NP-complete. It formalizes the spare allocation problem for reconfigurable arrays, an important problem from VLSI manufacturing. We provide a nontrivial so-called fixed parameter algorithm for CBVC, running in O(1.3999^{k₁ + k₂} + (k₁ + k₂)n) time. Our algorithm is efficient and practical for small values of k₁ and k₂, as occurring in applications. The analysis of the search tree is based on a novel bonus point system: after the processing of the search tree (which takes time exponential in k), a polynomial-time final analysis follows. Parts of the computation that would be normally done within the search-tree phase can be postponed; nevertheless, knowledge about the size of those parts can be used to reduce the length of the search paths (and hence the depth of the search tree as a whole) by a sort of bonus points.     

基于模拟退火算法的矩形优化排样问题的研究

考虑了一种矩形优化排样系统中遗传算法和模拟退火算法的结合算法.首先建立了该系统的通用数学模型.然后给出了求解该问题的遗传模拟退火算法.最后用VC++6.0模拟算例的结果表明该算法是一种行之有效的方法.     

An Efficient Algorithm for a Sparse k-Edge-Connectivity Certificate

We present an efficient algorithm for finding a sparse k-edge-connectivity certificate of a multigraph G. Our algorithm runs in O((log kn)(log k)²(log n)²) time using O(k(n + m′)) processors on an ARBITRARY CRCW PRAM, where n and m′ stand for the numbers of vertices in G and edges in the simplified graph of G, respectively.     

An Efficient Algorithm for Exact Distribution of Discrete Scan Statistics

Waiting time random variables and related scan statistics have a wide variety of interesting and useful applications. In this paper, exact distribution of discrete scan statistics for the cases of homogeneous two-state Markov dependent trials as well as i.i.d. Bernoulli trials are discussed by utilizing probability generating functions. A simple algorithm has been developed to calculate the distributions. Numerical results show that the algorithm is very efficient and is capable of handling large problems. AMS 2000 Subject Classification 60J22, 60E05, 60J10     

An Efficient Algorithm for Computing the HHSVM and Its Generalizations

The hybrid Huberized support vector machine (HHSVM) has proved its advantages over the ?₁ support vector machine (SVM) in terms of classification and variable selection. Similar to the ?₁ SVM, the HHSVM enjoys a piecewise linear path property and can be computed by a least-angle regression (LARS)-type piecewise linear solution path algorithm. In this article, we propose a generalized coordinate descent (GCD) algorithm for computing the solution path of the HHSVM. The GCD algorithm takes advantage of a majorization–minimization trick to make each coordinatewise update simple and efficient. Extensive numerical experiments show that the GCD algorithm is much faster than the LARS-type path algorithm. We further extend the GCD algorithm to solve a class of elastic net penalized large margin classifiers, demonstrating the generality of the GCD algorithm. We have implemented the GCD algorithm in a publicly available R package gcdnet.