Development of a hybrid genetic programming technique for computationally expensive optimisation problems

The increasing computational power of modern computers has contributed to the advance of nature-inspired algorithms in the fields of optimisation and metamodelling. Genetic programming (GP) is a genetically-inspired technique that can be used for metamodelling purposes. GP main strength is in the ability to infer the mathematical structure of the best model fitting a given data set, relying exclusively on input data and on a set of mathematical functions given by the user. Model inference is based on an iterative or evolutionary process, which returns the model as a symbolic expression (text expression). As a result, model evaluation is inexpensive and the generated expressions can be easily deployed to other users. Despite genetic programming has been used in many different branches of engineering, its diffusion on industrial scale is still limited. The aims of this thesis are to investigate the intrinsic limitations of genetic programming, to provide a comprehensive review of how researchers have tackled genetic programming main weaknesses and to improve genetic programming ability to extract accurate models from data. In particular, research has followed three main directions. The first has been the development of regularisation techniques to improve the generalisation ability of a model of a given mathematical structure, based on the use of a specific tuning algorithm in case sinusoidal functions are among the functions the model is composed of. The second has been the analysis of the influence that prior knowledge regarding the function to approximate may have on genetic programming inference process. The study has led to the introduction of a strategy that allows to use prior knowledge to improve model accuracy. Thirdly, the mathematical structure of the models returned by genetic programming has been systematically analysed and has led to the conclusion that the linear combination is the structure that is mostly returned by genetic programming runs. A strategy has been formulated to reduce the evolutionary advantage of linear combinations and to protect more complex classes of individuals throughout the evolution. The possibility to use genetic programming in industrial optimisation problems has also been assessed with the help of a new genetic programming implementation developed during the research activity. Such implementation is an open source project and is freely downloadable from http://www.personal.leeds.ac.uk/~cnua/mypage.html