A theoretical analysis of the HIFF problem

Nicholas Freitag McPhee; Ellery Fussell Crane

doi:10.1145/1068009.1068201

A theoretical analysis of the HIFF problem

Nicholas Freitag McPhee, Ellery Fussell Crane

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	GECCO 2005 - Genetic and Evolutionary Computation Conference
Editors	H.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
Pages	1153-1160
Number of pages	8
DOIs	https://doi.org/10.1145/1068009.1068201
State	Published - 2005
Event	GECCO 2005 - Genetic and Evolutionary Computation Conference - Washington, D.C., United States Duration: Jun 25 2005 → Jun 29 2005

Publication series

Name	GECCO 2005 - Genetic and Evolutionary Computation Conference

Conference

Conference	GECCO 2005 - Genetic and Evolutionary Computation Conference
Country/Territory	United States
City	Washington, D.C.
Period	6/25/05 → 6/29/05

Keywords

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

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10.1145/1068009.1068201

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McPhee, N. F., & Crane, E. F. (2005). A theoretical analysis of the HIFF problem. In H. G. Beyer, U. M. O'Reilly, D. Arnold, W. Banzhaf, C. Blum, E. W. Bonabeau, E. Cantu-Paz, D. Dasgupta, K. Deb, & A. et al (Eds.), GECCO 2005 - Genetic and Evolutionary Computation Conference (pp. 1153-1160). (GECCO 2005 - Genetic and Evolutionary Computation Conference). https://doi.org/10.1145/1068009.1068201

A theoretical analysis of the HIFF problem. / McPhee, Nicholas Freitag; Crane, Ellery Fussell.
GECCO 2005 - Genetic and Evolutionary Computation Conference. ed. / H.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. 2005. p. 1153-1160 (GECCO 2005 - Genetic and Evolutionary Computation Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

McPhee, NF & Crane, EF 2005, A theoretical analysis of the HIFF problem. in HG Beyer, UM O'Reilly, D Arnold, W Banzhaf, C Blum, EW Bonabeau, E Cantu-Paz, D Dasgupta, K Deb & A et al (eds), GECCO 2005 - Genetic and Evolutionary Computation Conference. GECCO 2005 - Genetic and Evolutionary Computation Conference, pp. 1153-1160, GECCO 2005 - Genetic and Evolutionary Computation Conference, Washington, D.C., United States, 6/25/05. https://doi.org/10.1145/1068009.1068201

McPhee, Nicholas Freitag ; Crane, Ellery Fussell. / A theoretical analysis of the HIFF problem. GECCO 2005 - Genetic and Evolutionary Computation Conference. editor / H.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. 2005. pp. 1153-1160 (GECCO 2005 - Genetic and Evolutionary Computation Conference).

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A theoretical analysis of the HIFF problem

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Keywords

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