Bounding Distributions for the Weight of a Minimum Spanning Tree in Stochastic Networks

Hutson, Kevin R.; Shier, Douglas R.

doi:10.1287/opre.1050.0214

Cited by 8 publications

(8 citation statements)

References 7 publications

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“…To study the efficiency of the proposed algorithms, we have conducted three set of simulation experiments on four well-known stochastic benchmark graphs borrowed from [41,42]. The first set of experiments aims to investigate the relationship between the learning rate of Algorithm 1 and the error rate in standard sampling method.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The aim of the third set of experiments (Experiment III) is to investigate the performance of the best proposed algorithm (Algorithm 5) as opposed to multiple edge sensitivity method (MESM) proposed by Hutson and Shier [41]. In Experiment III, in addition to the sparse graphs Alex2 and Alex3, all algorithms are also tested on two complete graphs with 5 and 6 vertices called and [41,42]. The edge weight distribution of complete graphs and can take 4 and 3 states, respectively.…”

Section: Experiments IIImentioning

confidence: 99%

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Learning automata-based algorithms for solving stochastic minimum spanning tree problem

Torkestani

Meybodi

2011

Applied Soft Computing

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Due to the hardness of solving the minimum spanning tree (MST) problem in stochastic environments, the stochastic MST (SMST) problem has not received the attention it merits, specifically when the probability distribution function (PDF) of the edge weight is not a priori known. In this paper, we first propose a learning automata-based sampling algorithm (Algorithm 1) to solve the MST problem in stochastic graphs where the PDF of the edge weight is assumed to be unknown. At each stage of the proposed algorithm, a set of learning automata is randomly activated and determines the graph edges that must be sampled in that stage. As the proposed algorithm proceeds, the sampling process focuses on the spanning tree with the minimum expected weight. Therefore, the proposed sampling method is capable of decreasing the rate of unnecessary samplings and shortening the time required for finding the SMST. The convergence of this algorithm is theoretically proved and it is shown that by a proper choice of the learning rate the spanning tree with the minimum expected weight can be found with a probability close enough to unity. Numerical results show that Algorithm 1 outperforms the standard sampling method. Selecting a proper learning rate is the most challenging issue in learning automata theory by which a good trade off can be achieved between the cost and efficiency of algorithm. To improve the efficiency (i.e., the convergence speed and convergence rate) of Algorithm 1, we also propose four methods to adjust the learning rate in Algorithm 1 and the resultant algorithms are called as Algorithm 2 through Algorithm 5. In these algorithms, the probabilistic distribution parameters of the edge weight are taken into consideration for adjusting the learning rate. Simulation experiments show the superiority of Algorithm 5 over the others. To show the efficiency of Algorithm 5, its results are compared with those of the multiple edge sensitivity method (MESM). The obtained results show that Algorithm 5 performs better than MESM both in terms of the running time and sampling rate.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Experiments IIImentioning

confidence: 99%

Learning automata-based algorithms for solving stochastic minimum spanning tree problem

Torkestani

Meybodi

2011

Applied Soft Computing

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“…The former is solved by the eDLAbased algorithm on the directed stochastic graph, Graph2, taken from [7]. The latter is solved by the eDLA-based algorithm on the undirected stochastic graph Alex1-a taken from [26]. In [7], the authors proposed a DLA-based algorithm to solve the SSPP.…”

Section: Methodsmentioning

confidence: 99%

Extended distributed learning automata

Meybodi

2014

Appl Intell

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In this paper, a new structure for cooperative learning automata called extended learning automata (eDLA) is introduced. Based on the new structure, an iterative randomized heuristic algorithm using sampling is proposed for finding an optimal subgraph in a stochastic edge-weighted graph. Stochastic graphs are graphs in which the weights of edges have an unknown probability distribution. The proposed algorithm uses an eDLA to find a policy that leads to a subgraph that satisfy some restrictions such as minimum or maximum weight (length). At each stage of the proposed algorithm, the eDLA determines which edges should be sampled. The proposed eDLA-based sampling method may reduce unnecessary samples and hence decrease the time required for finding an optimal subgraph. It is shown that the proposed method converges to an optimal solution, the probability of which can be made arbitrarily close to 1 by using a sufficiently small learning parameter. A new variance-aware threshold value is also proposed that can significantly improve the convergence rate of the proposed eDLA-based algorithm. It is further shown that our algorithm is competitive in terms of the quality of the solution.

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“…K. Hutson and D. Shier [20] assumed that the edge weights are independently distributed discrete random variables, and they looked for the distribution of the weight of the minimum spanning tree. They used a classical Hasse diagram to represent the different states of the network.…”

Section: Conference Reportmentioning

confidence: 99%

“…Information related to spanning trees is generally propagated through this diagram and used to deduce a new spanning tree after a change of an edge weight. Hutson and Shier [20] gave a new theorem allowing the propagation of the information even after many simultaneous changes. The running times of the algorithm based on their new propagation method seem to be better than those of previous algorithms.…”

Section: Conference Reportmentioning

confidence: 99%