Adaptation of population sizes by competing subpopulations

Abstract|We present a competiton scheme which dynamically allocates the number of trials given to di erent search strategies. The competition scheme changes the sizes of the subgroups, but also the size of the whole population. The competition scheme is able to combine the strengths of individual search strategies in a synergetic way. This claim is demonstrated by numerical experiments with two di cult functions to be optimized. KeyW ords|breeder genetic algorithm, population dynamics, competition, consumption factor, variable population size I

Predictive Models for the Breeder Genetic Algorithm -- I. Continuous Parameter Optimization

In this paper a new genetic algorithm called the Breeder Genetic Algorithm (BGA) is introduced. The BGA is based on artificial selection similar to that used by human breeders. A predictive model for the BGA is presented which is derived from quantitative genetics. The model is used to predict the behavior of the BGA for simple test functions. Different mutation schemes are compared by computing the expected progress to the solution. The numerical performance of the BGA is demonstrated on a test suite of multimodal functions. The number of function evaluations needed to locate the optimum scales only as n ln(n) where n is the number of parameters. Results up to n = 1000 are reported

Optimal Interaction of Mutation and Crossover in the Breeder Genetic Algorithm

The dynamic behavior of mutation and crossover is investigated with the Breeder Genetic Algorithm. The main emphasis is on binary functions. The genetic operators are compared near their optimal performance. It is shown that mutation is most efficient in small populations. Crossover critically depends on the size of the population. Mutation is the more robust search operator. But the BGA combines the two operators in such a way that the performance is better than that of a single operator. For the DECEPTION function it is shown that increasing the size of the population above a certain number decreases the quality of the solutions obtained

Adaptation of Population Sizes by Competing Subpopulations

We present a competiton scheme which dynamically allocates the number of trials given to different search strategies. The competition scheme changes the sizes of the subgroups, but also the size of the whole population. The competition scheme is able to combine the strengths of individual search strategies in a synergetic way. This claim is demonstrated by numerical experiments with two difficult functions to be optimized. KeyWords---breeder genetic algorithm, population dynamics, competition, consumption factor, variable population size I. Introduction Most evolutionary algorithms depend on a set of control parameters. Often the optimal setting of the parameters depends on the particular application. Moreover the optimal control parameters may vary for different stages of the search. There are two basic ways of adapting the parameters. The first is to use some externally specified schedule [7] [5]. The second applies the mechanisms of evolution itself. This approach is successfully..

Analysis of selection, mutation and recombination in genetic algorithms

Genetic algorithms have been applied fairly successful to a number of optimization problems. Nevertheless, a common theory why and when they work is still missing. In this paper a theory is outlined which is based on the science of plant and animal breeding. A central part of the theory is the response to selection equation and the concept of heritability. A fundamental theorem states that the heritability is equal to the regression coe cient of parent to o spring. The theory is applied to analyze selection, mutation and recombination. The results are used in the Breeder Genetic Algorithm whose performance is shown to be superior to other genetic algorithms

The Science of Breeding and its Application to the Breeder Genetic Algorithm BGA

The Breeder Genetic Algorithm BGA models artificial selection as performed by human breeders. The science of breeding is based on advanced statistical methods. In this paper a connection between genetic algorithm theory and the science of breeding is made. We show how the response to selection equation and the concept of heritability can be applied to predict the behavior of the BGA. Selection, recombination and mutation are analyzed within this framework. It is shown that recombination and mutation are complementary search operators. The theoretical results are obtained under the assumption of additive gene effects. For general fitness landscapes regression techniques for estimating the heritability are used to analyze and control the BGA. The method of decomposing the genetic variance into an additive and a nonadditive part connects the case of additive fitness functions with the general case

The Response to Selection Equation for Skew Fitness Distributions

The equation for the response to selection is a powerful analysis and modeling tool for genetic algorithms. In this paper we extend the classical analysis which is restricted to a normal distribution to skew fitness distributions. We show that for a small number of variables the Gamma distribution fits the distribution of the fitness values better than a normal distribution. We compute the selection intensities for the Gamma distribution. It is shown that with these values the prediction for the mean fitness of the population is very accurate. Finally we show that multi-modal functions may lead to fitness distributions having several modal values. I. Introduction Let an optimization problem be given on a domain G ae R n f = f(x ) = min x2G f(x); G ae R n : (1) We make no assumptions concerning the convexity and differentiability of the function f(x). For the minimization a number of algorithms have been proposed. In this paper we apply the Breeder Genetic Algorithm BGA [6..

Strategy Adaptation by Competing Subpopulations

Abstract. The breeder genetic algorithm BGA depends on a set of control parameters and genetic operators. In this paper it is shown that strategy adaptation by competing subpopulations makes the BGA more robust and more e cient. Each subpopulation uses a di erent strategy which competes with other subpopulations. Numerical results are presented for a number of test functions