A Discipline of Evolutionary Programming

Genetic fitness optimization using small populations or small population updates across generations generally suffers from randomly diverging evolutions. We propose a notion of highly probable fitness optimization through feasible evolutionary computing runs on small size populations. Based on rapidly mixing Markov chains, the approach pertains to most types of evolutionary genetic algorithms, genetic programming and the like. We establish that for systems having associated rapidly mixing Markov chains and appropriate stationary distributions the new method finds optimal programs (individuals) with probability almost 1. To make the method useful would require a structured design methodology where the development of the program and the guarantee of the rapidly mixing property go hand in hand. We analyze a simple example to show that the method is implementable. More significant examples require theoretical advances, for example with respect to the Metropolis filter.