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23
Variable neighborhood search for the bounded diameter minimum spanning tree problem
 Proceedings of the 18th Mini Euro Conference on Variable Neighborhood Search
, 2005
"... The bounded diameter minimum spanning tree problem is an NPhard combinatorial optimization problem with applications in various fields like communication network design. We propose a general variable neighborhood search approach for it, utilizing four different types of neighborhoods. They were d ..."
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Cited by 14 (9 self)
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The bounded diameter minimum spanning tree problem is an NPhard combinatorial optimization problem with applications in various fields like communication network design. We propose a general variable neighborhood search approach for it, utilizing four different types of neighborhoods. They were designed in a way enabling an efficient incremental evaluation and search for the best neighboring solution. An experimental comparison on instances with complete graphs with up to 1000 nodes indicates that this approach consistently outperforms the so far leading evolutionary algorithms with respect to solution quality and computation time.
A new 0–1 ILP approach for the bounded diameter minimum spanning tree problem
 Proceedings of the 2nd International Network Optimization Conference
, 2005
"... The bounded diameter minimum spanning tree (BDMST) problem is NPhard and appears e.g. in communication network design when considering certain quality of service requirements. Prior exact approaches for the BDMST problem mostly rely on network flowbased mixed integer linear programming and Miller ..."
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Cited by 13 (7 self)
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The bounded diameter minimum spanning tree (BDMST) problem is NPhard and appears e.g. in communication network design when considering certain quality of service requirements. Prior exact approaches for the BDMST problem mostly rely on network flowbased mixed integer linear programming and MillerTuckerZemlinbased formulations. This article presents a new, compact 0–1 integer linear programming model, which is further strengthened by dynamically adding violated connection and cycle elimination constraints within a branchandcut environment. The proposed approach is empirically compared to two recently published formulations. It turns out to work well in particular on dense instances with tight diameter bounds.
Experimental Analysis of Practically Efficient Algorithms for BoundedHop Accumulation
 in AdHoc Wireless Networks, In Proc. of the IEEE IPDPSWMAN
"... The paper studies the problem of computing a minimal energycost range assignment in an adhoc wireless network which allows a set S of stations located in the 2dimensional Euclidean space to perform accumulation (alltoone) operations towards some root station b in at most h hops (2Dim Min hAcc ..."
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Cited by 12 (5 self)
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The paper studies the problem of computing a minimal energycost range assignment in an adhoc wireless network which allows a set S of stations located in the 2dimensional Euclidean space to perform accumulation (alltoone) operations towards some root station b in at most h hops (2Dim Min hAccumulation Range Assignment problem). We experimentally investigate the behavior of fast and easytoimplement heuristics for the 2Dim Min hAccumulation Range Assignment problem on instances obtained by choosing at random n points in a square of side length L. We compare the performance of an easytoimplement, very fast heuristic with those of three simple heuristics based on classical greedy algorithms (Prim’s and Kruskal’s ones) defined for the Minimum Spanning Tree problem. The comparison is carried out over thousands of random instances in several different situations depending on: the distribution of the stations in the plane, their density, the energy cost function. 1
A PermutationCoded Evolutionary Algorithm for the BoundedDiameter Minimum Spanning Tree Problem
 in 2003 Genetic and Evolutionary Computation Conference’s Workshops Proceedings, Workshop on Analysis and Desgn of Representations
, 2003
"... The diameter of a tree is the largest number of edges on any path between two vertices in it. Given a weighted, connected, undirected graph G and a bound D 2, the boundeddiameter minimum spanning tree problem seeks a spanning tree on G of minimum weight whose diameter does not exceed D. ..."
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Cited by 10 (3 self)
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The diameter of a tree is the largest number of edges on any path between two vertices in it. Given a weighted, connected, undirected graph G and a bound D 2, the boundeddiameter minimum spanning tree problem seeks a spanning tree on G of minimum weight whose diameter does not exceed D. An evolutionary algorithm for this NPhard problem encodes candidate trees as permutations of their vertices. The first vertex (if D is even) or the first two vertices (if D is odd) form the center of the tree a permutation represents. A greedy heuristic appends the remaining vertices to the tree in their listed order, as economically as possible, while maintaining the diameter bound. In tests on 25 Euclidean problem instances, this EA identifies shorter trees on average than does an EA that encodes trees as sets of their edges, though it takes longer.
Multiobjective EA approach for improved quality of solutions for spanning tree problem
 in: Proc. Internat. Conf. Evolutionary MultiCriterion Optimization (EMO), Lecture Notes in Computer Science
, 2005
"... Abstract. The problem of computing spanning trees along with specific constraints is mostly NPhard. Many approximation and stochastic algorithms which yield a single solution, have been proposed. In this paper, we formulate the generic multiobjective spanning tree (MOST) problem and consider edge ..."
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Cited by 5 (0 self)
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Abstract. The problem of computing spanning trees along with specific constraints is mostly NPhard. Many approximation and stochastic algorithms which yield a single solution, have been proposed. In this paper, we formulate the generic multiobjective spanning tree (MOST) problem and consider edgecost and diameter as the two objectives. Since the problem is hard, and the Paretofront is unknown, the main issue in such probleminstances is how to assess the convergence. We use a multiobjective evolutionary algorithm (MOEA) that produces diverse solutions without needing a priori knowledge of the solution space, and generate solutions from multiple tribes in order to assess movement of the solution front. Since no experimental results are available for MOST, we consider three well known diameterconstrained minimum spanning tree (dcMST) algorithms including randomized greedy heuristics (RGH) which represents the current state of the art on the dcMST, and modify them to yield a (near) optimal solutionfronts. We quantify the obtained solution fronts for comparison. We observe that MOEA provides superior solutions in the entirerange of the Paretofront, which none of the existing algorithms could individually do. 1
Multiobjective network design for realistic traffic models
 In Proceedings of generic and evolutionary computation conference (GECCO’07
, 2007
"... Network topology design problems find application in several real life scenarios. However, most designs in the past either optimize for a single criterion like delay or assume simplistic traffic models like Poisson. Such assumptions make the solutions inapplicable in the practical world. In this pap ..."
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Cited by 5 (0 self)
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Network topology design problems find application in several real life scenarios. However, most designs in the past either optimize for a single criterion like delay or assume simplistic traffic models like Poisson. Such assumptions make the solutions inapplicable in the practical world. In this paper, we formulate and solve a multiobjective network topology design problem for a realistic Internet traffic model which is assumed to be self similar. We optimize for the average packet delivery delay and network layout cost to construct realistic network topologies. We present a multiobjective evolutionary algorithm (MOEA) to obtain the diverse nearoptimal network topologies. For fair comparison, we design a multiobjective deterministic heuristic based on branch exchange – we call the heuristic Pareto Branch Exchange (PBE). We empirically show that the MOEA used performs well for real networks of various sizes, and generated topologies are quite different with significantly larger delays for the self similar traffic model.
Neighbourhood Searches for the Bounded Diameter . . .
, 2006
"... We consider the Bounded Diameter Minimum Spanning Tree problem and describe four neighbourhood searches for it. They are used as local improvement strategies within a variable neighbourhood search (VNS), an evolutionary algorithm (EA) utilising a new encoding of solutions, and an ant colony optimisa ..."
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Cited by 4 (0 self)
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We consider the Bounded Diameter Minimum Spanning Tree problem and describe four neighbourhood searches for it. They are used as local improvement strategies within a variable neighbourhood search (VNS), an evolutionary algorithm (EA) utilising a new encoding of solutions, and an ant colony optimisation (ACO). We compare the performance in terms of effectiveness between these three hybrid methods on a suite of popular benchmark instances, which contains instances too large to solve by current exact methods. Our results show that the EA and the ACO outperform the VNS on almost all used benchmark instances. Furthermore, the ACO yields most of the time better solutions than the EA in longterm runs, whereas the EA dominates when the computation time is strongly restricted.
Codings and operators in two genetic algorithms for the leafconstrained minimum spanning tree problem
 International Journal of Applied Mathematics and Computer Science
, 2004
"... The features of an evolutionary algorithm that most determine its performance are the coding by which its chromosomes represent candidate solutions to its target problem and the operators that act on that coding. Also, when a problem involves constraints, a coding that represents only valid solution ..."
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Cited by 2 (1 self)
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The features of an evolutionary algorithm that most determine its performance are the coding by which its chromosomes represent candidate solutions to its target problem and the operators that act on that coding. Also, when a problem involves constraints, a coding that represents only valid solutions and operators that preserve that validity represent a smaller search space and result in a more effective search. Two genetic algorithms for the leafconstrained minimum spanning tree problem illustrate these observations. Given a connected, weighted, undirected graph G with n vertices and a bound ℓ, this problem seeks a spanning tree on G with at least ℓ leaves and minimum weight among all such trees. A greedy heuristic for the problem begins with an unconstrained minimum spanning tree on G, then economically turns interior vertices into leaves until their number reaches ℓ. One genetic algorithm encodes candidate trees with Prüfer strings decoded via the Blob Code. The second GA uses strings of length n−ℓ that specify trees ’ interior vertices. Both GAs apply operators that generate only valid chromosomes. The latter represents and searches a much smaller space. In tests on 65 instances of the problem, both Euclidean and with weights chosen randomly, the BlobCoded GA cannot compete with the greedy heuristic, but the subsetcoded GA consistently identifies leafconstrained spanning trees of lower weight than the greedy heuristic does, particularly on the random instances.
A Distributed Protocol for the BoundedHops Convergecast in AdHoc Networks
 In Proc. of AdHoc Now
, 2006
"... Abstract. Given a set S of points (stations) located in the ddim. Euclidean space and a root b ∈ S, the hhops Convergecast problem asks to find for a minimal energycost range assignment which allows to perform the convergecast primitive (i.e. node accumulation) towards b in at most h hops. For t ..."
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Cited by 1 (0 self)
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Abstract. Given a set S of points (stations) located in the ddim. Euclidean space and a root b ∈ S, the hhops Convergecast problem asks to find for a minimal energycost range assignment which allows to perform the convergecast primitive (i.e. node accumulation) towards b in at most h hops. For this problem no polynomial time algorithm is known even for h = 2. The main goal of this work is the design of an efficient distributed heuristic (i.e. protocol) and the analysis (both theoretical and experimental) of its expected solution cost. In particular, we introduce an efficient parameterized randomized protocol for hhops Convergecast and we analyze it on random instances created by placing n points uniformly at random in a dcube of side length L. We prove that for h = 2, its expected approximation ratio is bounded by some constant factor. Finally, for h = 3,..., 8, we provide a wide experimental study showing that our protocol has very good performances when compared with previously introduced (centralized) heuristics. 1
Constructing LowLatency Overlay Networks: Tree vs. Mesh Algorithms
"... Abstract—Distributed interactive applications may have stringent latency requirements and dynamic user groups. These applications may benefit from a group communication system, and to improve the system support for such applications, we investigate graph algorithms that construct lowlatency overlay ..."
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Cited by 1 (0 self)
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Abstract—Distributed interactive applications may have stringent latency requirements and dynamic user groups. These applications may benefit from a group communication system, and to improve the system support for such applications, we investigate graph algorithms that construct lowlatency overlay networks for applicationlayer multicast. In particular, we focus on reducing the diameter and the pairwise latencies in the overlay. The overlay construction time is also considered, as it is often timedependent in our dynamic target applications. Here, we have implemented and experimentally analyzed spanningtree heuristics and mesh construction heuristics, and compared their performance and applicability to distributed interactive applications. We found that trees are faster to construct and save considerable amounts of resources in the network. Meshes, on the other hand, yield lower pairwise latencies and increases the fault tolerance, but at the expense of increased resource consumption. I.