Error thresholds and optimal mutation rates in genetic algorithms

Declaration I hereby declare that this thesis has not been submitted, either in the same or different form, to this or any other university for a degree. Acknowledgements I am very grateful to my supervisors Hilary Buxton and Inman Harvey for their constant guidance and support. They followed the whole process very closely and suggested useful ideas and insights all the way long. The frequent and stimulating discussions we had at our regular meetings made it all happen. Many thanks to both of you. Many thanks to my examiners Adrian Thompson and Terry Fogarty for their very useful comments and critical reading. I am also grateful to my husband, Andy, who not only gave me constant emotional support and love, but also encouraged me to pursue this goal in the first place. He was patient and understanding enough to overcome the difficult period of separation in the first stage of my DPhil. For him the deepest thoughts and love. I specially want to thank Margarita Sordo for her constant friendship, encouragement and help throughout the whole DPhil. She was really generous in her attitude to help in many ways, and also carefully and critically read a good part of this document. Finally, many thanks to my parents Marta and Hernan, my brothers, my beloved grandmother Teodora and my aunt Gisela; for their unconditional love and support, and for being so kind whenever I was back home. Summary When applying a genetic algorithm to solve a given problem, the designer faces a large number of choices, with little theoretical guidance and few rules of thumb about how to proceed. Among these choices, the setting of evolutionary parameters (e.g. mutation rate, recombination rate, population size and selection parameters) is important since their values determine the performance of the algorithm to a great extent. However, finding a good combination of parameters is not an easy task since they interact with one another non-linearly and cannot be optimised one at a time. Moreover, 'optimal' parameter settings are believed to be problem-dependent. The mutation rate is acknowledged as one of the most sensitive parameters, so good heuristics for setting the mutation rate are welcomed. This thesis brings the fundamental notion of the error thresholds of replication from molecular evolution into the field of evolutionary computation. Error thresholds are intuitively related to the idea of an optimal balance between exploration and exploitation in genetic search. So, …