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Title: Combinatorial spanning tree representations for evolutionary algorithms
Author: Paulden, Timothy John
ISNI:       0000 0001 3479 1013
Awarding Body: University of Exeter
Current Institution: University of Exeter
Date of Award: 2007
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The research presented in this thesis lies at the interface between two distinct' fields: combinatorial mathematics and evolutionary algorithm design. We examine a number of combinatorial spanning tree representations, and develop theoretical and empirical results to quantify the intrinsic properties of each representation, focusing on properties that encapsulate the representation's suitability for evolutionary search. In Part I of the thesis, we focus on a selectIon of Cayley codes - namely, the Priifer Code, the Blob Code, and the family of Dandelion-like codes (which includes the Dandelion Code, Happy Code, MHappy Code, and Theta Code). Each of these representations is bijective, and so the efficacy of evolutionary search primarily depends on the representation's locality. We develop a number of results which demonstrate that Dandelion-like codes possess highly desirable locality properties (including bounded locality), while those of the Blob Code and Priifer. Code are inferior. We also present linear-time decoding and'encoding algorithms for the various codes, many of which have not previously appeared in the evolutionary algorithms literature. In Part II, the Theta Code is adapted to give bijective spanning tree representations on graph topologies other than the complete graph. These extended representations retain the desirable properties of the Thet'a Code, including its high locality. We then formulate general principles for developing extended representations of this kind. Finally, in Part III, we study the Edge-Window-Decoder (EWD) representation. We find that the EWD representation has several desirable properties for evolutionary search ( bounded locality), but possesses an intrinsic bi~ towards path-like trees. We also present a number of theoretical advances, including the first method for generating EWD strings uniformly at random, and a new technique for characterising representational bias using the Wiener index.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available