TY - GEN

T1 - A theoretical analysis of the HIFF problem

AU - McPhee, Nicholas Freitag

AU - Crane, Ellery Fussell

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - Distance Metrics

KW - Evolutionary Computation

KW - Hierarchical-if-and-only-if (HIFF) Problem

KW - Limit Distributions

KW - Schema Theory

UR - http://www.scopus.com/inward/record.url?scp=32444443636&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=32444443636&partnerID=8YFLogxK

U2 - 10.1145/1068009.1068201

DO - 10.1145/1068009.1068201

M3 - Conference contribution

AN - SCOPUS:32444443636

SN - 1595930108

SN - 9781595930101

T3 - GECCO 2005 - Genetic and Evolutionary Computation Conference

SP - 1153

EP - 1160

BT - GECCO 2005 - Genetic and Evolutionary Computation Conference

A2 - Beyer, H.G.

A2 - O'Reilly, U.M.

A2 - Arnold, D.

A2 - Banzhaf, W.

A2 - Blum, C.

A2 - Bonabeau, E.W.

A2 - Cantu-Paz, E.

A2 - Dasgupta, D.

A2 - Deb, K.

A2 - et al, al

T2 - GECCO 2005 - Genetic and Evolutionary Computation Conference

Y2 - 25 June 2005 through 29 June 2005

ER -