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Greedy Heuristics and an Evolutionary Algorithm for the BoundedDiameter Minimum Spanning Tree Problem
 Proceedings of the 2003 ACM Symposium on Applied Computing
, 2003
"... bound D, the boundeddiameter minimum spanning tree problem seeks a spanning tree on G of lowest weight in which no path between two vertices contains more than D edges. This problem is NPhard for 4 1, where n is the number of vertices in G. An existing greedy heuristic for the problem, called ..."
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bound D, the boundeddiameter minimum spanning tree problem seeks a spanning tree on G of lowest weight in which no path between two vertices contains more than D edges. This problem is NPhard for 4 1, where n is the number of vertices in G. An existing greedy heuristic for the problem, called OTTC, is based on Prim's algorithm. OTTC usually yields poor results on instances in which the triangle inequality approximately holds; it always uses the lowestweight edges that it can, but such edges do not in general connect the interior nodes of lowweight boundeddiameter trees. A new randomized greedy heuristic builds a boundeddiameter spanning tree from its center vertex or vertices. It chooses each next vertex at random but attaches the vertex with the lowestweight eligible edge. This algorithm is faster than OTTC and yields substantially better solutions on Euclidean instances. An evolutionary algorithm encodes spanning trees as lists of their edges, augmented with their center vertices. It applies operators that maintain the diameter bound and always generate valid o#spring trees. These operators are e#cient, so the algorithm scales well to larger problem instances. On 25 Euclidean instances of up to 1 000 vertices, the EA improved substantially on solutions found by the randomized greedy heuristic.
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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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
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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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 New Hybrid Genetic Algorithm for Solving the Bounded Diameter Minimum Spanning Tree Problem
"... Abstract — In this paper, a new hybrid genetic algorithm – known as HGA – is proposed for solving the Bounded Diameter Minimum Spanning Tree (BDMST) problem. We experiment with HGA on two sets of benchmark problem instances, both Euclidean and NonEuclidean. On the Euclidean problem instances, HGA i ..."
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Abstract — In this paper, a new hybrid genetic algorithm – known as HGA – is proposed for solving the Bounded Diameter Minimum Spanning Tree (BDMST) problem. We experiment with HGA on two sets of benchmark problem instances, both Euclidean and NonEuclidean. On the Euclidean problem instances, HGA is shown to outperform the previous best two Genetic Algorithms (GAs) reported in the BDMST literature, while on the NonEuclidean problem instance, HGA performs comparably with these two GAs. T I.
TimeOptimal Algorithm for Computing the Diameter of a Point Set on a Completely Overlapping Network
"... Abstract Given a finite set P of n points in ddimensional Euclidean space, the diameter is defined as the maximum Euclidean distance between any two points in the set P. In this paper, we illustrate a timeoptimal algorithm to compute the diameter of a point set on a theoretical network called a c ..."
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Abstract Given a finite set P of n points in ddimensional Euclidean space, the diameter is defined as the maximum Euclidean distance between any two points in the set P. In this paper, we illustrate a timeoptimal algorithm to compute the diameter of a point set on a theoretical network called a completely overlapping network (CON). This network model has an applicable potential in reallife applications because it is an extension of LANs that are widely used at present. Index Terms computational geometry, diameter, overlapping network, timeoptimal algorithm. I.
BoundedDiameter MST Instances with Hybridization of MultiObjective EA
"... The Bounded Diameter (a.k.a Diameter Constraint) Minimum Spanning Tree (BDMST/DCMST) is a wellknown combinatorial optimization problem. In this paper, we recast a few wellknown heuristics, which are evolved for BDMST problem to a BiObjective Minimum Spanning Tree (BOMST) problem and then obtain P ..."
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The Bounded Diameter (a.k.a Diameter Constraint) Minimum Spanning Tree (BDMST/DCMST) is a wellknown combinatorial optimization problem. In this paper, we recast a few wellknown heuristics, which are evolved for BDMST problem to a BiObjective Minimum Spanning Tree (BOMST) problem and then obtain Pareto fronts. After examining Pareto fronts, it is concluded that none of the heuristics provides the superior solution across the complete range of the diameter. We have used a MultiObjective Evolutionary Algorithm (MOEA) approach, Pareto Converging Genetic Algorithm (PCGA), to improve the Pareto front for BOMST, which in turn provides better solution for BDMST instances. We have considered edgeset encoding to represent MST and then applied recombination operators having strong heritability and mutation operators having negligible complexity to improve the solutions. Analysis of MOEA solutions confirms the improvement of Pareto front solutions across the complete range of the diameter over Pareto front solutions generated from individual heuristics. We have considered multiisland scheme using InterIsland rank histogram and performed multiple run of the algorithm to avoid from trapping into localoptimal solutionset.
Algorithm Designing for Broadcasting in MANET 1
"... There are a lot of advancements going on in radio technologies. With the advent of technologies, we also need to improve our methods for their efficient usage. We face several problems in Broadcasting. The most common of these problems is making efficient BDMSTs to minimize distance between nodes. I ..."
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There are a lot of advancements going on in radio technologies. With the advent of technologies, we also need to improve our methods for their efficient usage. We face several problems in Broadcasting. The most common of these problems is making efficient BDMSTs to minimize distance between nodes. In this paper our focus is on genetic algorithm, which is being considered among the most proficient BDMST algorithms. Genetic algorithm works more efficiently provided its initial population is already processed. Thus, we have taken our initial population from NRGH algorithm. In this paper we have included all our studies and works to make a progressively efficient BDMST. This paper is not for best results but its a combination of enhancements towards better solution.