On tracking-ability of a stochastic genetic algorithm to changing environments

A stochastic genetic algorithm (StGA) effectively searches an optimal action which maximizes the probability to have reward payoffs in stochastic environments by employing stochastic learning automata and genetic algorithms. This paper discusses the tracking ability of the StGA to environmental changes from theoretical and empirical points of view. In the theoretical investigation, we employ an inhomogeneous Markov chain to formulate state transition of the probability for a population of actions to have an optimal one. We perform theoretical investigations on change of the probability to create an optimal action and of the probability to lose all the optimal ones. Simulation experiments are performed to show the effectiveness of the StGA in changing environments whose penalty probability vectors gradually or suddenly change.