The Dynamics of a Genetic Algorithm for a Simple Learning Problem

A formalism for describing the dynamics of Genetic Algorithms (GAs) using methods from statistical mechanics is applied to the problem of generalization in a perceptron with binary weights. The dynamics are solved for the case where a new batch of training patterns is presented to each population member each generation, which considerably simplifies the calculation. The theory is shown to agree closely to simulations of a real GA averaged over many runs, accurately predicting the mean best solution found. For weak selection and large problem size the difference equations describing the dynamics can be expressed analytically and we find that the effects of noise due to the finite size of each training batch can be removed by increasing the population size appropriately. If this population resizing is used, one can deduce the most computationally efficient size of training batch each generation. For independent patterns this choice also gives the minimum total number of training patterns used. Although using independent patterns is a very inefficient use of training patterns in general, this work may also prove useful for determining the optimum batch size in the case where patterns are recycled.Comment: 28 pages, 4 Postscript figures. Latex using IOP macros ioplppt and iopl12 which are included. To appear in Journal of Physics A. Also available at ftp://ftp.cs.man.ac.uk/pub/ai/jls/GAlearn.ps.gz and http://www.cs.man.ac.uk/~jl

An experimental comparative study for interactive evolutionary computation problems

Proceeding of: EvoWorkshops 2006: EvoBIO, EvoCOMNET, EvoHOT, EvoIASP, EvoINTERACTION, EvoMUSART, and EvoSTOC, Budapest, Hungary, April 10-12, 2006This paper presents an objective experimental comparative study between four algorithms: the Genetic Algorithm, the Fitness Prediction Genetic Algorithm, the Population Based Incremental Learning algorithm and the purposed method based on the Chromosome Appearance Probability Matrix. The comparative is done with a non subjective evaluation function. The main objective is to validate the efficiency of several methods in Interactive Evolutionary Computation environments. The most important constraint of working within those environments is the user interaction, which affects the results adding time restrictions for the experimentation stage and subjectivity to the validation. The experiments done in this paper replace user interaction with several approaches avoiding user limitations. So far, the results show the efficiency of the purposed algorithm in terms of quality of solutions and convergence speed, two known keys to decrease the user fatigue.This article has been financed by the Spanish founded research MCyT project OPLINK, Ref: TIN2006-08818-C04-02