Question

In a typical genetic algorithm, is there any guideline for estimating the generations required to converge given the amount of entropy in the description of an individual in the population?

Also, I suppose it is reasonable to also require the number of offspring per generation and rate of mutation, but adjustment of those parameters is of less interest to me at the moment.

Answer 1

Well, there are not any concrete guidelines in the form of mathematical models, but there are several concepts that people use to communicate about parameter settings and advice on how to choose them. One of these concepts is diversity, which would be similar to the entropy that you mentioned. The other concept is called selection pressure and determines the chance an individual has to be selected based on its relative fitness.

Diversity and selection pressure can be computed for each generation, but the change between generations is very difficult to estimate. You would also need models that predict the expected quality of your crossover and mutation operator in order to estimate the fitness distribution in the next generation.

There have been work published on these topics very recently:
* Chicano and Alba. 2011. Exact Computation of the Expectation Curves of the Bit-Flip Mutation using Landscapes Theory
* Chicano, Whitley, and Alba. 2012. Exact computation of the expectation curves for uniform crossover

Is your question resulting from a general research interest or do you seek practical guidence?