On the convergence rate of the elitist genetic algorithm based on mutation probability

Abstract

The Markov chain approach to the elitist genetic algorithm enables not only to prove its convergence to an equilibrium distribution, but also to establish its convergence rate. These convergence rates are based on the transition matrix of the Markov chain which models the algorithm. This paper improves existing estimates of the convergence rates of the elitist genetic algorithm and presents new ones based only on the mutation probability. Experimental results illustrate that, for a fixed mutation probability, the algorithm’s mean convergence time tends to remain unchanged as the crossover probability varies. On the other hand, the reciprocal is not observed.

KEYWORDS And phrases:

• Non-homogeneous Markov Chain
• Doeblin type condition
• Convergence rate
• Dobrushin’s delta

AMS 2010 subject classifications::

• Primary 60J10
• 65C50, Secondary 60J20