On the Mean Convergence Time of Multi-parent Genetic Algorithms Without Selection

Abstract. This paper investigates genetic drift in multi-parent genetic algorithms (MPGAs). An exact model based on Markov chains is pro-posed to formulate the variation of gene frequency. This model iden-tifies the correlation between the adopted number of parents and the mean convergence time. Moreover, it reveals the pairwise equivalence phenomenon in the number of parents and indicates the acceleration of genetic drift in MPGAs. The good fit between theoretical and experi-mental results further verifies the capability of this model.

Simple Markov models of the genetic algorithm in classifier systems: multi-step tasks

Abstract Michigan-style Classifier Systems use Genetic Algorithms to facilitate rule discovery. This paper presents a simple Markov model of the algorithm in such systems, with the aim of examining the effects of different types of interdependence between niches in multi-step tasks. Using the model it is shown that the existence of, what is here termed, partner rule variance can have significant and detrimental effects on the Genetic Algorithm's expected behaviour. Suggestions are made as to how to reduce these effects, making..

Hyperschema Theory for GP with One-Point Crossover, Building Blocks, and Some New Results in GA Theory

Two main weaknesses of GA and GP schema theorems axe that they provide only information on the expected value of the number of instances of a given schema at the next generation E[m(H,t + 1)], and they can only give a lower bound for such a quantity. This paper presents new theoretical results on GP and GA schemata which laxgely overcome these weaknesses. Firsfly, unlike previous results which concentrated on schema survival and disruption, our results extend to GP recent work on GA theory by Stephens and Waelbroeck, and make the effects and the mechanisms of schema creation explicit. This allows us to give an exact formulation (rather than a lower bound) for the expected number of instances of a schema at the next generation. Thanks to this formulation we are then able to provide in improved version for an eaxlier GP schema theorem in which some schema creation events axe accounted for, thus obtaining a tighter bound for E[m(H, t + 1)]. This bound is a function of the selection probabilities of the schema itself and of a set of lower-order schemata which one-point crossover uses to build instances of the schema. This result supports the existence of building blocks in GP which, however, axe not necessaxily all short, low-order or highly fit. Building on eaxlier work, we show how Stephens and Waelbroeck 's GA results and the new GP results described in the paper can be used to evaluate schema vaxiance, signal-to-noise ratio and, in general, the probability distribution of re(H, t + 1). In addition, we show how the expectation operator can be removed from the schema theorem so as to predict with a known probability whether re(H, t + 1) (rather than Elm(H, t + 1)]) is going to be above a given threshold

Markov modelling and parameterisation of genetic evolutionary test generations

Genetic algorithm, Parameter selection, Markov model, Hardware design verification,