A theoretical analysis of the HIFF problem

Nicholas Freitag McPhee, Ellery Fussell Crane

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    2 Scopus citations

    Abstract

    We present a theoretical analysis of Watson's Hierarchical-if-and-only-if (HIFF) problem using a variety of tools. These include schema theory and course graining, the concept of effective fitness, and statistical analysis. We first review the use of Stephen's exact schema equations and schema basis to compute the changes in population distributions over time. We then use the tools described above to solve for the limit distributions of the 2 and 4-bit HIFF problems, and show that these limit distributions are essentially one-dimensional. We also show that a combination of fitness and the number of break points (a rough measure of distance in crossover space) in a string can be used to almost completely explain the limit distribution in the 4-bit HIFF problem.

    Original languageEnglish (US)
    Title of host publicationGECCO 2005 - Genetic and Evolutionary Computation Conference
    EditorsH.G. Beyer, U.M. O'Reilly, D. Arnold, W. Banzhaf, C. Blum, E.W. Bonabeau, E. Cantu-Paz, D. Dasgupta, K. Deb, al et al
    Pages1153-1160
    Number of pages8
    DOIs
    StatePublished - 2005
    EventGECCO 2005 - Genetic and Evolutionary Computation Conference - Washington, D.C., United States
    Duration: Jun 25 2005Jun 29 2005

    Publication series

    NameGECCO 2005 - Genetic and Evolutionary Computation Conference

    Conference

    ConferenceGECCO 2005 - Genetic and Evolutionary Computation Conference
    CountryUnited States
    CityWashington, D.C.
    Period6/25/056/29/05

    Keywords

    • Distance Metrics
    • Evolutionary Computation
    • Hierarchical-if-and-only-if (HIFF) Problem
    • Limit Distributions
    • Schema Theory

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