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

Abstract

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.

Learning Automata Based Contention Aware Data Forwarding Scheme for Safety Applications in Vehicular Ad Hoc Networks

“…Granelli et al [30] have proposed a routing scheme based upon the motion of the vehicles. LA has also been widely used in many engineering applications to solve real world problems in all domains efficiently [31][32][33][34][35][36][37]. LA operates on the individual vehicle and collaborates with the other vehicles also for information sharing.…”

“…It is an optimization technique that can be applied in various domains to solve a given problem. Moreover, the machine has the capability of learning from its environment so that it can choose the desired action from a finite set of allowed actions through repeated steps [31][32][33][34][35][36][37]. The initial action chosen is random in nature, but by taking input from the environment in terms of reinforcement signal, after finite number of steps, the solution converges and produces the desired output.…”

“…The initial action chosen is random in nature, but by taking input from the environment in terms of reinforcement signal, after finite number of steps, the solution converges and produces the desired output. are the finite set of responses received from the environment, and Q P Q → × : δ maps the current state and input from the environment to the next state of the automaton and ω is a function which maps the current state and response from the environment to the state of the automaton [31][32][33][34][35][36][37].…”

LLACA: An adaptive localized clustering algorithm for wireless ad hoc networks

“…Learning automaton has been shown to perform well in graph theory [21,23,25,26,28], networking [18,20,22,24,27,29,30,31], and some other areas. 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.…”

Solving maximum clique problem in stochastic graphs using learning automata

“…To evaluate the performance of the proposed algorithm, experiments are accomplished on the following stochastic graphs [15][16][17], which details of them are listed in table 1 to 2, and are demonstrated in figure 2 to 3. These graph model a real communication networks, which the weight of activity/availability of vertices to be random variables.…”