Finite population models of dynamic optimization with stochastically alternating fitness functions

We present a stochastic, finite population model of genetic algorithms in dynamic environments. In this model, fitness functions alternate stochastically over time. The limit behavior of these systems can be utilized to express predictions of expected behavior and measurements of performance for the algorithm and its parameter choices. We provide methods to analyze and study the limit behavior and performance measures for these systems. We also show how the stochastic and deterministic environment models can be applied to study the influence of the system´s parameters - rate of mutations, rate of changes in the environment, population size and selective pressure - on the long run performance of GAs in the respective environments. A comparison of these conclusions between static and dynamic environments is given.