Convergence of teams and hierarchies of learning automata in connectionist systems

2011

Applied Soft Computing

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.

Section: Stochastic Graphmentioning

confidence: 99%

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

2011

Applied Soft Computing

“…A learning automaton [15][16][17][18][19][20][21] is an adaptive decision-making unit that improves its performance by learning how to choose the optimal action from a finite set of allowed actions through repeated interactions with a random environment. The action is chosen at random based on a probability distribution kept over the action-set and at each instant the given action is served as the input to the random environment.…”

Section: Learning Automatamentioning

confidence: 99%

“…The environment can be described by a triple Learning automata can be classified into two main families [15][16][17][18][19][20]: fixed structure learning automata and variable structure learning automata. Variable structure learning automata are represented by a triple…”

Section: Learning Automatamentioning

confidence: 99%

Clustering the wireless Ad Hoc networks: A distributed learning automata approach

Journal of Parallel and Distributed Computing

2010

In Ad-Hoc networks, the performance is significantly degraded as the size of the network grows. The network clustering by which the nodes are hierarchically organized on the basis of the proximity relieves this performance degradation. Finding the weakly connected dominating set (WCDS) is a promising approach for clustering the wireless Ad-Hoc networks. Finding the minimum WCDS in the unit disk graph is an NP-Hard problem, and a host of approximation algorithms have been proposed. In this paper, we first proposed a centralized approximation algorithm called DLA-CC based on distributed learning automata (DLA) for finding a near optimal solution to the minimum WCDS problem. Then, we propose a DLAbased clustering algorithm called DLA-DC for clustering the wireless Ad-Hoc networks. The proposed cluster formation algorithm is a distributed implementation of DLA-CC, in which the dominator nodes and their closed neighbors assume the role of the cluster-heads and cluster members, respectively. In this paper, we compute the worst case running time and message complexity of the clustering algorithm for finding a near optimal cluster-head set. We argue that by a proper choice of the learning rate of the clustering algorithm, a trade-off between the running time and message complexity of algorithm with the cluster-head set size (clustering optimality) can be made. The simulation results show the superiority of the proposed algorithms over the existing methods.KEYWORDS Wireless Ad-Hoc networks, clustering, weakly connected dominating set, distributed learning automata INTRODUCTIONA wireless Ad-Hoc network is a multi hop wireless communication network supporting a collection of mobile hosts. There is no fixed infrastructure and no central administration and the mobile hosts can form a temporary network infrastructure in an Ad-Hoc fashion. Two hosts can directly communicate when they are within transmission range of each other, and indirectly through relaying by the intermediate hosts.In an Ad-Hoc network, each host assumes the role of a router and relays the packets toward the final destinations, if a source can not directly send the packets to a final destination due to the limitation of the radio transmission range. Since the wireless Ad-Hoc networks exhibit severe resource constraints such as the bandwidth and power limitations, network topology changes, and the lack of the fixed infrastructures and consequently,

“…A learning automaton [32][33][34][35][36][37][38] is an adaptive decision-making unit that improves its performance by learning how to choose the optimal action from a finite set of allowed actions through repeated interactions with a random environment. The action is chosen at random based on a probability distribution kept over the action set and at each instant the given action is served as the input to the random environment.…”

Section: Learning Automatamentioning

confidence: 99%

Learning Automata-Based Algorithms for Finding Minimum Weakly Connected Dominating Set in Stochastic Graphs

Int. J. Unc. Fuzz. Knowl. Based Syst.

2010

A weakly connected dominating set (WCDS) of graph G is a subset of G so that the vertex set of the given subset and all vertices with at least one endpoint in the subset induce a connected sub-graph of G. The minimum WCDS (MWCDS) problem is known to be NP-hard, and several approximation algorithms have been proposed for solving MWCDS in deterministic graphs. However, to the best of our knowledge no work has been done on finding the WCDS in stochastic graphs. In this paper, a definition of the MWCDS problem in a stochastic graph is first presented and then several learning automata-based algorithms are proposed for solving the stochastic MWCDS problem where the probability distribution function of the weight associated with the graph vertices is unknown. The proposed algorithms significantly reduce the number of samples needs to be taken from the vertices of the stochastic graph. It is shown that by a proper choice of the parameters of the proposed algorithms, the probability of finding the MWCDS is as close to unity as possible. Experimental results show the major superiority of the proposed algorithms over the standard sampling method in terms of the sampling rate.