The paper discusses three major issues. First, it discusses why it makes sense to approach problems in a hierarchical fashion. It defines the class of hierarchically decomposable functions that can be used to test the algorithms that approach problems in this fashion. Finally, the Bayesian optimization algorithm (BOA) is extended in order to solve the proposed class of problems.

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An adaptive niching scheme called coevolutionary shared niching (CSN) is proposed, implemented, analyzed and tested. The scheme overcomes the limitations of fixed sharing schemes by permitting the locations and radii of niches to adapt to complex landscapes, thereby permitting a better distribution of solutions in problems with many badly spaced optima. The scheme takes its inspiration from the model of monopolistic competition in economics and utilizes two populations, a population of businessmen and a population of customers, where the locations of the businessmen correspond to niche locations and the locations of customers correspond to solutions. Initial results on straightforward test functions validate the distributional effectiveness of the basic scheme, although tests on a massively multimodal function do not find the best niches in the allotted time. This result spurs the design of an imprint mechanism that turns the best customers into businessmen, thereby making better use o...

Adding a sharing method to a genetic algorithm promotes the formation and maintenance of stable subpopulations. This paper explores the limits of sharing by deriving closed-form expressions for the expected time to disappearance of a subpopulation. The time to disappearance is shown to be an exponential function of population size, with relative subpopulation fitnesses determining the base of the exponential. However, disappearance time decreases rapidly as the number of subpopulations increases. Both theoretical and experimental illustrations are given of genetic drift in sharing. I. Introduction Given a problem with multiple solutions, the traditional genetic algorithm (GA) will at best, ultimately converge to a population containing only one of those solutions [1]. The culprit, known as genetic drift, can be defined as the convergence of a finite population in the absence of selection pressure, due to variance in the selection process. To combat genetic drift, GAs were developed t...

this paper, an approximation for the Pareto set of optimal solutions is obtained by using a genetic algorithm (GA). The first objective function is the drag coefficient. As a constraint, it is required that the lift coefficient is above a given value. The CFD analysis solver is based on the finite volume discretization of the inviscid Euler equations. The second objective function is equivalent to the integral of the transverse magnetic radar cross section (RCS) over a given sector. The computational electromagnetics (CEM) wave field analysis requires the solution of a two-dimensional Helmholtz equation which is obtained using a fictitious domain method. Numerical experiments illustrate the above evolutionary methodology on an IBM SP2 parallel computer. c fl ??? John Wiley & Sons, Inc.

The paper shows that there is a key dividing line between two types of symmetrical problems: problems for which a genetic algorithm (GA) benefits from the fact that genetic drift chooses between equally good partial solutions, and problems for which all equally good partial solutions have to be preserved to find an optimum. By analyzing in detail the search process of a selectorecombinative GA optimizing a TwoMax and comparing this search process with that of a onedimensional Ising model, the paper investigates the difference between these two types of symmetrical problems. For the first type of problems, naively adding a niching technique to the genetic algorithm makes the problem harder to solve. For the last type of problems, niching is necessary to find an optimum. 1

Sharing methods promote the formation and maintenance of stable subpopulations or niches in genetic algorithms. This paper derives, for various models of sharing, lower bounds on the population size required to maintain, with probability fl, a fixed number of niches. The first model assumes all niches are equivalent with respect to fitness and that crossover is minimally disruptive. The next two models allow niches to differ with respect to fitness. The final model takes into account the disruptive effects of crossover. GAs with sharing are run on seven test problems in optimization and classification, using population sizes derived from the models. 1 Introduction The simple genetic algorithm (GA), when confronted with a problem having multiple solutions, will converge, in the best case, to a population containing only one of those solutions (Goldberg & Segrest, 1987). This behavior prompted the development of GAs capable of forming and maintaining stable subpopulations or niches. GA...

. Evolutionary Computation focuses on probabilistic search and optimization methods gleaned from the model of organic evolution. Genetic algorithms, evolution strategies and evolutionary programming are three independently developed representatives of this class of algorithms, with genetic programming and classifier systems as additional paradigms in the field. This paper focuses on the link between evolutionary computation and DNA-based computing by discussing the relevant aspects of evolutionary computation both from a practical and a theoretical point of view. In particular, theoretical results concerning the calculation of convergence velocities and the derivation of optimal schedules for mutation rates respectively steps sizes are presented. The potential for cross-fertilization between the fields of DNA-based computing and evolutionary computation is outlined both from a principal point of view and by means of an experimental investigation concerning the NP-hard maximum clique pr...

This paper analyzes the impact of using noisy data sets in Pittsburgh-style learning classifier systems. This study was done using a particular kind of learning classifier system based on multiobjective selection. Our goal was to characterize the behavior of this kind of algorithms when dealing with noisy domains. For this reason, we developed a theoretical model for predicting the minimal achievable error in noisy domains. Combining this theoretical model for crisp learners with graphical representations of the evolved hypotheses through multiobjective techniques, we are able to bound the behavior of a learning classifier system. This kind of modeling lets us identify relevant characteristics of the evolved hypotheses, such as over fitting conditions that lead to hypotheses that generalize the concept to be learned poorly.