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Applications of Group Theory to Representation for Computational Intelligence

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dc.contributor.advisor Ashlock, Daniel
dc.contributor.advisor Pereira, Rajesh Gilbert, Jeremy Alexander 2022-01-13T17:30:45Z 2022-01-13T17:30:45Z 2022-01 2021-12-15
dc.description.abstract Representations Arising From Group Theory. This thesis introduces a novel approach to developing representations for evolutionary computation, using group theory as a foundation. The goal is to develop new representations which are better suited for navigating treacherous fitness landscapes, yielding improvements to algorithm performance over traditional methods. To construct such a representation, a selection of elements from a group are specified and used as generators to form a subgroup. The representation takes the form of words over the set of generators. An evolutionary algorithm is then able to search the space of words, which is a standard form of evolutionary algorithm. Multiple new representations are presented, built from additive vector groups, bijections of the unit interval, and affine transformations on Euclidean space. These representations can be used in a variety of applications, including real optimization, data normalization, image generation and modification, and point packing generation. Some can also be used to discretize a continuous search space, allowing the use of algorithms such as Monte Carlo Tree Search. The discrete nature of these representations also allows for use of a dictionary of previous optimal solutions. This permits an algorithm to find a diverse set of best fit solutions, by using the dictionary to exclude parts of the search space near solutions that have already been found, realized as prefixes of stored words. A parameter study is performed for each representation, and they are compared to conventional methods on a variety of test problems. en_US
dc.description.sponsorship Natural Sciences and Engineering Research Council of Canada en_US
dc.language.iso en en_US
dc.publisher University of Guelph en
dc.subject Evolutionary Computation en_US
dc.subject Evolutionary Algorithms en_US
dc.subject Representation for Evolutionary Computation en_US
dc.subject The Representation Problem en_US
dc.subject Point Packing en_US
dc.subject Population Initialization en_US
dc.subject Generalized Julia Set en_US
dc.subject Real Optimization en_US
dc.subject Data Normalization en_US
dc.subject Finding approximate cumulative distribution function en_US
dc.subject Group Theory Applications en_US
dc.title Applications of Group Theory to Representation for Computational Intelligence en_US
dc.type Thesis en_US Mathematics and Statistics en_US Doctor of Philosophy en_US Department of Mathematics and Statistics en_US
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dcterms.relation D. Ashlock and J. Gilbert. A discrete representation for real optimization with unique search properties. In Proceedings of the IEEE Symposium on the Foundations of Computational Intelligence, pages 54–61, 2014. DOI: 10.1109/FOCI.2014.7007807 en_US
dcterms.relation J. Gilbert and D. Ashlock. Evolvable warps for data normalization. In Proceedings of the IEEE 2016 Congress on Evolutionary Computation, pages 1562–1569, 2016. DOI: 10.1109/CEC.2016.7743975 en_US
dcterms.relation D. Ashlock and J. Gilbert. A greedy, generative, lattice representation for point packing. In Proceedings of the 2019 IEEE Congress on Evolutionary Computation, pages 3181– 3188, 2019. DOI: 10.1109/CEC.2019.8790058 en_US University of Guelph en

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