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44
Multiple Sink Network Design Problem
 In: Proc. of 1 st Int. Conf. on Communications (ICC). (2004
, 2004
"... Abstract — The battery resource of the sensor nodes should be managed efficiently, in order to prolong network lifetime in wireless sensor networks. Moreover, in largescale networks with a large number of sensor nodes, multiple sink nodes should be deployed, not only to increase the manageability o ..."
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Cited by 40 (0 self)
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Abstract — The battery resource of the sensor nodes should be managed efficiently, in order to prolong network lifetime in wireless sensor networks. Moreover, in largescale networks with a large number of sensor nodes, multiple sink nodes should be deployed, not only to increase the manageability of the network, but also to reduce the energy dissipation at each node. In this paper, we focus on the multiple sink location problems in largescale wireless sensor networks. Different problems depending on the design criteria are presented. We consider locating sink nodes to the sensor environment, where we are given a time constraint that states the minimum required operational time for the sensor network. We use simulation techniques to evaluate the quality of our solution. Keywords—wireless sensor networks; power efficiency; multiple sink. I.
Capacitated minimum spanning trees: Algorithms using intelligent search
, 1996
"... In this paper a survey on existing algorithms for the capacitated minimum spanning tree problem (CMST) is given. The algorithms are classified providing some insights into their fundamental principles. Reporting the literature, comparisons of the solution quality are given. As one result of the expl ..."
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Cited by 28 (2 self)
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In this paper a survey on existing algorithms for the capacitated minimum spanning tree problem (CMST) is given. The algorithms are classified providing some insights into their fundamental principles. Reporting the literature, comparisons of the solution quality are given. As one result of the exploration it is observed that heuristic procedures for the CMST in general consider arcs when generating or transforming a solution. Contrary to this we develop an improvement procedure which is based on partitioning nodes into subsets thus focusing more on the combinatorial nature of the CMST. Given a feasible solution the attained node assignment is altered by a local search process based on shifts and node exchanges. To overcome local optimality simulated annealing and tabu search are investigated. Computations on some benchmark test problems are reported and improvements over the wellknown EsauWilliams solution are presented. Some new best solutions are obtained.
An Approximation Algorithm for MinimumCost Network Design
 Institute of Science, Rehovot
, 1998
"... This paper considers the problem of designing a minimum cost network meeting a given set of traffic requirements between n sites, using one type of channels of a given capacity, with varying setup costs for different vertex pairs (comprised of a fixed part plus a part dependent on the pair). An ..."
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Cited by 22 (1 self)
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This paper considers the problem of designing a minimum cost network meeting a given set of traffic requirements between n sites, using one type of channels of a given capacity, with varying setup costs for different vertex pairs (comprised of a fixed part plus a part dependent on the pair). An approximation algorithm is proposed for this problem, guaranteeing a solution whose cost is greater than the optimum by a factor of at most O(log n) (or constant in the Euclidean case). The algorithm is based on the use of a lightweight distancepreserving spanner. 1 Introduction The network design problem has been intensively studied at least since the 70's [KC74, BF77, GFCE74]. A number of heuristics have been developed for it, and various solutions were given for specific cases of the problem, or for specific subproblems (see [K93] and the references therein). The goal of the current note is to give a simple approximation algorithm for the general problem. The minimum cost network d...
Algorithms and software for convex mixed integer nonlinear programs, IMA Volumes
"... Abstract. This paper provides a survey of recent progress and software for solving convex mixed integer nonlinear programs (MINLP)s, where the objective and constraints are defined by convex functions and integrality restrictions are imposed on a subset of the decision variables. Convex MINLPs have ..."
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Cited by 11 (2 self)
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Abstract. This paper provides a survey of recent progress and software for solving convex mixed integer nonlinear programs (MINLP)s, where the objective and constraints are defined by convex functions and integrality restrictions are imposed on a subset of the decision variables. Convex MINLPs have received sustained attention in recent years. By exploiting analogies to wellknown techniques for solving mixed integer linear programs and incorporating these techniques into software, significant improvements have been made in the ability to solve these problems. Key words. Mixed Integer Nonlinear Programming; Branch and Bound; AMS(MOS) subject classifications.
Valid inequalities and facets of the capacitated plant location problem
 Mathematical Programming
, 1989
"... Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitate ..."
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Cited by 9 (1 self)
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Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitated plant location problem. Our purpose is to identify facets and valid inequalities for a wide range of capacitated fixed charge problems that contain this prototype problem as a substructure. The first part of the paper introduces a family of facets for a version of the capacitated plant location problem with constant capacity K for all plants. These facet inequalities depend on K and thus differ fundamentally from the valid inequalities for the uncapacitated version of the problem. We also introduce a second formulation for a model with indivisible customer demand and show that it is equivalent to a vertex packing problem on a derived graph. We identify facets and valid inequalities for this version of the problem by applying known results for the vertex packing polytope.
2010. Perspective reformulations of mixed integer nonlinear programs with indicator variables
 Math. Program
"... Abstract. We study mixed integer nonlinear programs (MINLP)s 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 fixed values, ..."
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Cited by 7 (1 self)
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Abstract. We study mixed integer nonlinear programs (MINLP)s 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 fixed values, and, when it is “turned on”, forces them to belong to a convex set. Many practical MINLPs contain integer variables 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, and a convex hull description of this set is derived. We then extend this result 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 secondorder cone programming. Our work is closely related with the earlier work of Ceria and Soares (1999) as well as recent work by Frangioni and Gentile (2006) and, Aktürk, Atamtürk and Gürel (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 computational results for three applications – quadratic facility location, network design with congestion, and portfolio optimization with buyin thresholds – that show the power of the reformulation technique. Key words. Mixedinteger nonlinear programming – perspective functions 1.
Approximation Algorithms for the Capacitated Minimum Spanning Tree Problem and its Variants in Network Design
, 2004
"... Given an undirected graph G = (V, E) with nonnegative costs on its edges, a root node r V with demand v D wishing to route w(v) units of flow (weight) to r, and a positive number k, the Capacitated Minimum Steiner Tree (CMStT) problem asks for a minimum Steiner tree, rooted at r, spannin ..."
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Cited by 7 (4 self)
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Given an undirected graph G = (V, E) with nonnegative costs on its edges, a root node r V with demand v D wishing to route w(v) units of flow (weight) to r, and a positive number k, the Capacitated Minimum Steiner Tree (CMStT) problem asks for a minimum Steiner tree, rooted at r, spanning the vertices in D in which the sum of the vertex weights in every subtree hanging o# r is at most k. When D = V , this problem is known as the Capacitated Minimum Spanning Tree (CMST) problem. Both CMStT and CMST problems are NPhard. In this paper, we present approximation algorithms for these problems and several of their variants in network design. Our main results are the following.
Designing Reliable Communication Networks with a Genetic Algorithm Using a Repair Heuristic
, 2003
"... This paper investigates GA approaches for solving the reliable communication network design problem. For solving this problem a graph with minimum cost must be found that satisfies a given network reliability constraint. To consider the additional reliability constraint different approaches are poss ..."
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Cited by 5 (1 self)
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This paper investigates GA approaches for solving the reliable communication network design problem. For solving this problem a graph with minimum cost must be found that satisfies a given network reliability constraint. To consider the additional reliability constraint different approaches are possible. We show that existing approaches using penalty functions can result in invalid solutions and are therefore not appropriate for solving this problem. To overcome these problems we present a repair heuristic, which is based on the number of spanning trees in a graph. This heuristic always generates a valid solution, which when compared to a greedy cheapest repair heuristic shows that the new approach finds better solutions with less computational effort.
Effective separation of disjunctive cuts for convex mixed integer nonlinear programs
, 2010
"... We describe a computationally effective method for generating disjunctive inequalities for convex mixedinteger nonlinear programs (MINLPs). The method relies on solving a sequence of cutgenerating linear programs, and in the limit will generate an inequality as strong as can be produced by the cut ..."
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Cited by 4 (1 self)
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We describe a computationally effective method for generating disjunctive inequalities for convex mixedinteger nonlinear programs (MINLPs). The method relies on solving a sequence of cutgenerating linear programs, and in the limit will generate an inequality as strong as can be produced by the cutgenerating nonlinear program suggested by Stubbs and Mehrotra. Using this procedure, we are able to approximately optimize over the rank one simple disjunctive closure for a wide range of convex MINLP instances. The results indicate that disjunctive inequalities have the potential to close a significant portion of the integrality gap for convex MINLPs. In addition, we find that using this procedure within a branchandcut solver for convex MINLPs yields significant savings in total solution time for many instances. Overall, these results suggest that with an effective separation routine, like the one proposed here, disjunctive inequalities may be as effective for solving convex MINLPs as they have been for solving mixedinteger linear programs. 1
2008. Perspective relaxation of MINLPs with indicator variables
 Proceedings 13 th IPCO, Lecture Notes in Computer Science
"... ABSTRACT. 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, ..."
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Cited by 4 (0 self)
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ABSTRACT. 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 secondorder cone programming. Our work is closely related