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共 35 条记录，以下是21-30 订阅

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the stochastic machine replenishment problem

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13th international conference on integer programming and combinatorial optimization

作者： Munagala, Kamesh Shi, Peng Duke Univ Dept Comp Sci Durham NC 27708 USA

ISBN: (纸本)9783540688860

We study the stochastic machine replenishment problem, which is a canonical special case of closed multiclass queuing systems in Markov decision theory. the problem models the scheduling of processor repairs in a multiprocessor system in which one repair can be made at a time and the goal is to maximize system utilization. We analyze the performance of a natural greedy index policy for this problem. We first show that this policy is a 2 approximation by exploring linear queuing structure in the index policy. We then try to exploit more complex queuing structures, but this necessitates solving an infinite-size, non-linear, non-convex, and non-separable function-maximization program. We develop a general technique to solve such programs to arbitrary degree of accuracy, which involves solving a discretized program on the computer and rigorously bounding the error. this proves that the index policy is in fact a 1.51 approximation. the main non-trivial ingredients of the proof are two folds: finding a way to analyze the complex queuing structure of the index policy, and bounding the error in discretization when numerically solving the non-linear function-maximization. We believe that this framework is general enough to be useful in the analysis of index policies in related problems. As far as we are aware, this is one of the first non-trivial approximation analysis of an index policy a multi-class queuing problem, as well as one of the first non-trivial example of an approximation ratio that is rigorously proven by numerical optimization via a computer.

关键词： optimization

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Perspective relaxation of mixed integer nonlinear programs with indicator variables

引用

13th international conference on integer programming and combinatorial optimization

作者： Gunluk, Oktay Linderoth, Jeff IBM Corp Thomas J Watson Res Ctr Dept Math Sci Yorktown Hts NY 10598 USA Univ Wisconsin Madison Dept Ind & Syst Engn Madison WI 53706 USA

ISBN: (纸本)9783540688860

We study mixed integer nonlinear programs (MINLP) that are driven by a collection of indicator variables where each indicator variable controls a subset of the decision variables. An indicator variable, when it is "turned off", forces some of the decision variables to assume a fixed value, and, when it is "turned on", forces them to belong to a convex set. Most of the integer variables in known MINLP problems are of this type. We first study a mixed integer set defined by a single separable quadratic constraint and a collection of variable upper and lower bound constraints. this is an interesting set that appears as a substructure in many applications. We present the convex hull description of this set. We then extend this to produce an explicit characterization of the convex hull of the union of a point and a bounded convex set defined by analytic functions. Further, we show that for many classes of problems, the convex hull can be expressed via conic quadratic constraints, and thus relaxations can be solved via second-order cone programming. Our work is closely related with the earlier work of Ceria and Soares (1996) as well as recent work by Frangioni and Gentile (2006) and, Akturk, Atamturk and Gurel (2007). Finally, we apply our results to develop tight formulations of mixed integer nonlinear programs in which the nonlinear functions are separable and convex and in which indicator variables play an important role. In particular, we present strong computational results with two applications - quadratic facility location and network design with congestion - that show the power of the reformulation technique.

关键词： Second-order cone programming

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Periodic polyhedra

引用

13th international conference on Compiler Construction

作者： Meister, B ICPS LSIIT F-67400 Illkirch Graffenstaden France

ISBN: (纸本)3540212973

this paper presents a new method for computing the integer hull of a parameterized rational polyhedron by introducing the concept of periodic polyhedron. Besides concerning generally parametric combinatorial optimization, the method has many applications for the analysis, optimization and parallelization of loop nests, especially in compilers.

关键词： combinatorial optimization

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Cone-LP's and semidefinite programs: Geometry and a simplex-type method 5th

Cone-LP's and semidefinite programs: Geometry and a simplex-...

引用

5th international conference integer programming and combinatorial optimization, ipco 1996

作者： Pataki, Gábor Department of Combinatorics and Optimization University of Waterloo WaterlooONN2L 3G1 Canada

ISBN: (纸本)3540613102

We consider optimization problems expressed as a linear program with a cone constraint. Cone-LP's subsume ordinary linear programs, and semidefinite programs. We study the notions of basic solutions, nondegeneracy, and feasible directions, and propose a generalization of the simplex method for a large class including LP's and SDP's. One key feature of our approach is considering feasible directions as a sum of two directions. In LP, these correspond to variables leaving and entering the basis, respectively. the resulting algorithm for SDP inherits several important properties of the LP-simplex method, in particular, the linesearch can be done in the current face of the cone, similarly to LP, where the linesearch must determine only the variable leaving the basis. © Springer-Verlag Berlin Heidelberg 1996.

关键词： Linear programming

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the induced disjoint paths problem

引用

13th international conference on integer programming and combinatorial optimization

作者： Kawarabayashi, Ken-ichi Kobayashi, Yusuke Natl Inst Informat Tokyo 1018430 Japan Univ Tokyo Tokyo 1138656 Japan

ISBN: (纸本)9783540688860

For a graph G and a collection of vertex pairs {(s(1), t(1)),..., (s(k), t(k))}, the disjoint paths problem is to find k vertex-disjoint paths P-1,..., P-k, where P-i is a path from s(i) to t(i) for each i = 1,..., k. this problem is one of the classic problems in combinatorial optimization and algorithmic graph theory, and has many applications, for example in transportation networks, VLSI layout, and recently, virtual circuits routing in high-speed networks. As an extension of the disjoint paths problem, we introduce a new problem which we call the induced disjoint paths problem. In this problem we are given a graph G and a collection of vertex pairs {(s(1,) t(1)),..., (s(k), t(k))}. the objective is to find k paths P-i,..., P-k such that Pi is a path from si to ti and P-i and P-j have neither common vertices nor adjacent vertices for any distinct i,j. this problem setting is a generalization of the disjoint paths problem, since if we subdivide each edge, then desired disjoint paths would be induced disjoint paths. the problem is motivated by not only the disjoint paths problem but also the recognition of an induced subgraph. the latter has been developed in the recent years, and this is actually connected to the Strong Perfect Graph theorem [4], and the recognition of the perfect graphs [2]. In this paper, we shall investigate the complexity issues of this problem. the induced disjoint paths problem has several variants depending on whether k is a fixed constant or a part of the input, whether the graph is directed or undirected, and whether the graph is planar or not. We show that the induced disjoint paths problem is (i) solvable in polynomial time when k is fixed and G is a directed planar graph, (ii) solvable in linear time when k is fixed and G is an undirected planar graph, (iii) NP-hard when k = 2 and G is an acyclic directed graph, (iv) NP-hard when k = 2 and G is an undirected general graph. (i) generalizes the result by Schrijver [22], while (ii) genera

关键词： combinatorial optimization

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combinatorial formulation guided local search for inland waterway routing and scheduling

Combinatorial formulation guided local search for inland wat...

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13th IASTED international conference on Control and Applications, CA 2011

作者： Davidović, Tatjana Lazić, Jasmina Maraš, Vladislav Mathematical Institute Serbian Academy of Sciences and Arts Kneza Mihaila 36/III 11001 Belgrade Serbia Faculty of Transport and Traffic Engineering University of Belgrade Vojvode Stepe 305 Belgrade Serbia

ISBN: (纸本)9780889868724

We investigate the optimization of inland transport routes of barge container ships with the objective to maximize the profit of a shipping company. this problem consists of determining the upstream and downstream calling sequence and the number of loaded and empty containers transported between any two ports. We present combinatorial as well as Mixed integer Linear programming (MILP) formulation for this problem. We propose to combine these two approaches with an aim to generate efficient heuristic to solve considered problem. the proposed mixed-formulation Local Search (MIX-LS) represents good basis for implementation of LS-based meta-heuristic methods and we presented Multi-start Local Search (MLS) within this framework. To compare the proposed approach with the state-of-the-art Mixed integer programming (MIP) based heuristics we run all methods within a predefined time limit. It appears that pure local search is comparable with the MIPbased heuristic methods, while MLS outperforms all methods regarding both criteria: solution quality and running time.

关键词： Heuristic methods

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A characterization of seymour graphs 4th

A characterization of seymour graphs

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4th international conference on integer programming and combinatorial optimization, ipco 1995

作者： Ageev, A.A. Kostochka, A.V. Szigeti, Z. Institute of Mathematics Universitetskii pr.4 Novosibirsk630090 Russia Mathematical Institute of the Hungarian Academy of Sciences Reáltanoda u. 13-15 BudapestH-1053 Hungary

ISBN: (纸本)9783540594086

A connected undirected graph G is called a Seymour graph if the maximum number of edge disjoint T-cuts is equal to the cardinality of a minimum T-join for every even subset T of V(G). Several families of graphs have been shown to be subfamilies of Seymour graphs (Seymour [5][6], Gerards [1], Szigeti [7]). In this paper we prove a characterization of Seymour graphs which was conjectured by Seb6 and implies the results mentioned above. © Springer-Verlag Berlin Heidelberg 1995.

关键词： Undirected graphs

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Bounds on the Chvátal Rank of Polytopes in the 0/1-Cube 1

引用

7th international conference on integer programming and combinatorial optimization, ipco 1999

作者： Eisenbrand, Friedrich Schulz, Andreas S. Max-Planck-Institut für Informatik Im Stadtwald SaarbrückenD-66123 Germany MIT Sloan School of Management and Operations Research Center E53-361 CambridgeMA02139 United States

ISBN: (数字)9783540487777

ISBN: (纸本)3540660194

Gomory’s and Chvátal’s cutting-plane procedure proves recursively the validity of linear inequalities for the integer hull of a given polyhedron. the number of rounds needed to obtain all valid inequalities is known as the Chv´ atal rank of the polyhedron. It is well-known that the Chv´ atal rank can be arbitrarily large, even if the polyhedron is bounded, if it is of dimension 2, and if its integer hull is a 0/1-polytope. We prove that the Chvátal rank of polyhedra featured in common relaxations of many combinatorial optimization problems is rather small;in fact, the rank of any polytope contained in the n-dimensional 0/1-cube is at most 3n2lg n. this improves upon a recent result of Bockmayr et al. [6] who obtained an upper bound of O(n3 lgn). Moreover, we refine this result by showing that the rank of any polytope in the 0/1-cube that is defined by inequalities with small coefficients is O(n). the latter observation explains why for most cutting planes derived in polyhedral studies of several popular combinatorial optimization problems only linear growth has been observed (see, e.g., [13]);the coefficients of the corresponding inequalities are usually small. Similar results were only known for monotone polyhedra before. Finally, we provide a family of polytopes contained in the 0/1-cube the Chvátal rank of which is at least (1 + Ε)nfor some Ε > 0;the best known lower bound was n. © Springer-Verlag Berlin Heidelberg 1999.

关键词： combinatorial optimization

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Computing and Combinatorics 13th Annual international conference, COCOON 2007 Proceedings

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13th Annual international Computing and Combinatorics conference, COCOON 2007

ISBN: (纸本)9783540735441

the proceedings contain 53 papers. the topics discussed include: the combinatorics of sequencing the corn genome;online frequency assignment in wireless communication networks;information distance from a question to an answer;a new field splitting algorithm for intensity-modulated radiation therapy;seed-based exclusion method for non-coding RNA gene search;integer programming formulations and computations solving phylogenetic and population genetic problems with missing or genotypic data;improved exact algorithms for counting 3- and 4-colorings;quadratic kernelization for convex recoloring of tress;on the number of cycles in planar graphs;an improved exact algorithm for cubic graph TSP;dimension, halfspaces, and the density of hard sets;isolation concepts for enumerating dense subgraphs;counting minimum weighted dominating sets;volume computation using a direct Monte Carlo method;and improved throughput bounds for interference-aware routing in wireless networks.

关键词： combinatorial optimization

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Models and methods for One-Dimensional Space Allocation Problem with forbidden zones 13

Models and methods for One-Dimensional Space Allocation Prob...

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13th international Scientific and Technical conference on Applied Mechanics and Systems Dynamics, AMSD 2019

作者： Zabudsky, G.G. Veremchuk, N.S. Sobolev Institute of Mathematics Novosibirsk Russia Siberian State Automobile and Highway University Omsk Russia

We consider an extension of the well-known optimization placement problem. the problem is One-Dimensional Space Allocation Problem (ODSAP). the classical formulation of the problem is to place rectangular connected objects on a line with the minimum total cost of connections between them. the extension of the problem is that there are fixed objects (forbidden zones) on the line. the objects are impossible to place in forbidden zones. the placed objects are connected among themselves and with the zones. the configuration of connections between objects is defined by a network. A similar situation arises, for example, when designing the location of technological equipment of petrochemical enterprise. It is necessary to place units of equipment so that the total cost of the pipeline ties was minimal. In this article a review of the models and methods to solve of the classical ODSAP is given. the properties of the problem with the forbidden zones are noted. Models of combinatorial optimization and integer programming for the problem are constructed. Algorithms for finding an approximate solution and branch and bounds are described. Results of computational experiments are reported. © Published under licence by IOP Publishing Ltd.

关键词： integer programming

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