An Improved Ant-Based Algorithm for the Degree-Constrained Minimum Spanning Tree Problem

Bui, Tuan Anh; Deng, Xianghua; Zrncic, C. M.

doi:10.1109/tevc.2011.2125971

Cited by 28 publications

(8 citation statements)

References 22 publications

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“…Mathematical Problems in Engineering 9 By comparing multicolony ant algorithm with single colony ant algorithm [2], multicolony ant algorithm is obviously more effective in solution optimization which proves that multicolony ant algorithm shows greater advantages in DCMST optimal searching. Conditions under = 2 and = 3 are selected here to illustrate the proposed opinion.…”

Section: Experimental Results and Analysismentioning

confidence: 99%

“…Many DCNST problems are solved by ant colony algorithm [1][2][3][4][5]; these applications adopt ant colony algorithm with single colony. It comes with shortcomings of long search time and stagnation.…”

Section: Introductionmentioning

confidence: 99%

“…A typical example was given in [2] to solve DCMST by an improved ant colony algorithm. In this example, a group of ants were asked to explore the given graph; then a group of signed edge set which is related to the pheromone on paths was selected as a candidate set.…”

Section: Introductionmentioning

confidence: 99%

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Novel Degree Constrained Minimum Spanning Tree Algorithm Based on an Improved Multicolony Ant Algorithm

Sun

Chang

et al. 2015

Mathematical Problems in Engineering

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Degree constrained minimum spanning tree (DCMST) refers to constructing a spanning tree of minimum weight in a complete graph with weights on edges while the degree of each node in the spanning tree is no more thand(d≥ 2). The paper proposes an improved multicolony ant algorithm for degree constrained minimum spanning tree searching which enables independent search for optimal solutions among various colonies and achieving information exchanges between different colonies by information entropy. Local optimal algorithm is introduced to improve constructed spanning tree. Meanwhile, algorithm strategies in dynamic ant, random perturbations ant colony, and max-min ant system are adapted in this paper to optimize the proposed algorithm. Finally, multiple groups of experimental data show the superiority of the improved algorithm in solving the problems of degree constrained minimum spanning tree.

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Section: Experimental Results and Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Novel Degree Constrained Minimum Spanning Tree Algorithm Based on an Improved Multicolony Ant Algorithm

Sun

Chang

et al. 2015

Mathematical Problems in Engineering

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“…For this reason, a large number of heuristics have been applied in the literature. For example, Krishnamoorthy et al (2001) compare simulated annealing and genetic algorithms, whereas tabu search is used in Wamiliana (2004), and Bui et al (2012) propose an ant-based colony algorithm.…”

Section: Methodsmentioning

confidence: 99%

Dendritic and Axonal Wiring Optimization of Cortical GABAergic Interneurons

et al. 2016

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The way in which a neuronal tree expands plays an important role in its functional and computational characteristics. We aimed to study the existence of an optimal neuronal design for different types of cortical GABAergic neurons. To do this, we hypothesized that both the axonal and dendritic trees of individual neurons optimize brain connectivity in terms of wiring length. We took the branching points of real three-dimensional neuronal reconstructions of the axonal and dendritic trees of different types of cortical interneurons and searched for the minimal wiring arborization structure that respects the branching points. We compared the minimal wiring arborization with real axonal and dendritic trees. We tested this optimization problem using a new approach based on graph theory and evolutionary computation techniques. We concluded that neuronal wiring is near-optimal in most of the tested neurons, although the wiring length of dendritic trees is generally nearer to the optimum. Therefore, wiring economy is related to the way in which neuronal arborizations grow irrespective of the marked differences in the morphology of the examined interneurons.Electronic Supplementary MaterialThe online version of this article (doi:10.1007/s12021-016-9309-6) contains supplementary material, which is available to authorized users.

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“…Due to the NP-hardness of the DCMST problem, the exact solutions can only be applied to the relatively small problem instances, whereasvery large graphs often arise in real-world applications. Therefore, several heuristics such as genetic algorithms (GAs; Zhou et al 1996;Raidl and Julstrom 2000;Zeng and Wang 2003;Soak et al 2004;Han et al 2005;Hanr and Wang 2006;Pereira et al 2009), local search (Ribeiro and Souza 2002;Zeng and Wang 2003;de Souza and Martins 2008;Martins and de Souza 2009), ant colony optimization (ACO; Bui and Zrncic 2006;Doan 2007;Bau et al 2005Bau et al , 2008Bui et al 2011), particle swarm optimization (PSO; Goldbarg et al 2006;Binh and Nguyen 2008;Guo et al 2009;Ernst 2010), evolutionary computation (Knowles and Corne 2000;Raidl 2000), Lagrangian approach (Volgenant 1989;Andrade et al 2006;Ernst 2010) have been proposed to solve the problem.…”

Section: Introductionmentioning

confidence: 99%

Degree-Constrained Minimum Spanning Tree Problem in Stochastic Graph

Torkestani

2012

Cybernetics and Systems

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A degree-constrained minimum spanning tree (DCMST) problem is an NP-hard combinatorial optimization problem in graph theory seeking the minimum cost spanning tree with the additional constraint on the vertex degree. Several different approaches have been proposed in the literature to solve this problem using a deterministic graph. However, to the best of the author's knowlege, no work has been performed on solving the problem using stochastic edgeweighted graphs. In this article, a learning automata-based algorithm is proposed to find a near optimal solution of the DCMST problem using a stochastic graph, where the cost associated with the graph edge is a random variable with a priori unknown probability distribution. The convergence of the proposed algorithm to the optimal solution is theoretically proved based on the Martingale theorem. To show the performance of the proposed algorithm, several simulation experiments are conducted on stochastic Euclidean graph instances. Numerical results are compared with those of the standard sampling method (SSM). The numerical results confirm the superiority of the proposed sampling technique over the SSM both in terms of the sampling rate and solution optimality.

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An Improved Ant-Based Algorithm for the Degree-Constrained Minimum Spanning Tree Problem

Cited by 28 publications

References 22 publications

Novel Degree Constrained Minimum Spanning Tree Algorithm Based on an Improved Multicolony Ant Algorithm

Novel Degree Constrained Minimum Spanning Tree Algorithm Based on an Improved Multicolony Ant Algorithm

Dendritic and Axonal Wiring Optimization of Cortical GABAergic Interneurons

Degree-Constrained Minimum Spanning Tree Problem in Stochastic Graph

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