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A Markov Chain Analysis of Genetic Algorithms with a State Dependent Fitness Function
Dawid H. A Markov Chain Analysis of Genetic Algorithms with a State Dependent Fitness Function. Complex Systems. 1994;8:407-417.Abstract.
We analyze the behavior of a Simple Genetic Algorithm (GA) in systems where the fitness of a string is determined
by a function depending on the state of the whole population. The GA is modeled by a Markov chain and we
conclude that for small mutation probabiliti esthelimit
distribution will put almost all the weight to the
homogeneous states. We derive conditions under which a
homogeneous state will be stable for the dynamics
representing the expected behavior of the GA. Interpreting
the state dependent fitness function as an economic system we prove that any strict economic equilibrium will be a
symptotic all y stable with respect to the expected
behavior of the GA