Mapping the royal road and other hierarchical functions

Wiles, J. H. and Tonkes, B (2003) Mapping the royal road and other hierarchical functions. Evolutionary Computation, 11 2: 129-149. doi:10.1162/106365603766646807

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Author Wiles, J. H.
Tonkes, B
Title Mapping the royal road and other hierarchical functions
Journal name Evolutionary Computation   Check publisher's open access policy
ISSN 1063-6560
Publication date 2003-01-01
Sub-type Article (original research)
DOI 10.1162/106365603766646807
Open Access Status File (Publisher version)
Volume 11
Issue 2
Start page 129
End page 149
Total pages 22
Editor M. Schoenauer
Place of publication Cambridge, MA, United States
Publisher MIT Press
Language eng
Abstract In this paper we present a technique for visualising hierarchical and symmetric, multimodal fitness functions that have been investigated in the evolutionary computation literature. The focus of this technique is on landscapes in moderate-dimensional, binary spaces (i.e., fitness functions defined over {0, 1}(n), for n less than or equal to 16). The visualisation approach involves an unfolding of the hyperspace into a two-dimensional graph, whose layout represents the topology of the space using a recursive relationship, and whose shading defines the shape of the cost surface defined on the space. Using this technique we present case-study explorations of three fitness functions: royal road, hierarchical-if-and-only-if (H-IFF), and hierarchically decomposable functions (HDF). The visualisation approach provides an insight into the properties of these functions, particularly with respect to the size and shape of the basins of attraction around each of the local optima.
Keyword Computer Science, Artificial Intelligence
Computer Science, Theory & Methods
Royal Road
Hierarchical If-and-only-if
Hierarchically Decomposable Functions
Fitness Landscape
Q-Index Code C1

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Created: Wed, 15 Aug 2007, 11:53:11 EST