An iterative stochastic algorithm based on distributed learning automata for finding the stochastic shortest path in stochastic graphs

In this paper, we study the problem of finding the shortest path in stochastic graphs and propose an iterative algorithm for solving it. This algorithm is based on distributed learning automata (DLA), and its objective is to use a DLA for finding the shortest path from the given source node to the given destination node whose weight is minimal in expected sense. At each stage of this algorithm, DLA specifies edges needed to be sampled. We show that the given algorithm finds the shortest path with minimum expected weight in stochastic graphs with high probability which can be close to unity as much as possible. We compare the given algorithm with some distributed learning automata-based iterative algorithms, a particle swarm optimization-based algorithm, an ant colony-based algorithm, a Q-learning-based algorithm, and an actor–critic-based algorithm for finding the shortest path. Computer experiments show that the proposed algorithm requires fewer edge samples to find the shortest path than the previously introduced DLA-based algorithms.