Theoretical and practical aspects of evolutionary algorithms with application to the partitioning of multivariate self-affine time series

This thesis examines certain aspects of the theory and practice of multiobjective evolutionary algorithms (MOEAs). Firstly a set of theoretical results is developed concerning the operation of ranking schemes under multiobjective tournament selection and the effect on both the development of the rank or fitness distribution. Limiting expressions are shown for the nonsampling probability according to rank, for schemes with and without replacement, with an extension including the effect of elitism. Further limiting expressions under iterated tournament selection for time to convergence and nonsampling probability are also shown. The various effects of varying the tournament size on nonsampling probability, evolution of the rank distribution, and time to convergence are discussed. Next, the practical problem of partitioning a multivariate selfaffine time series with unknown and time-varying joint distribution is considered. The aim is to completely partition the time series, possibly of high dimension, into disjoint, contiguous subseries at one timescale that are similar to subseries at another timescale after application of an affine transformation. The multiobjective combinatorial optimization problem is defined with limited assumptions as a biobjective one, and a specialized MOEA is presented which finds optimal self-affine time series partitionings with a minimum of choice parameters. The MOEA is highly specialized and contains a number of unusual features, including permuted multiobjective tournament selection, in line with the theory developed earlier in the thesis. The algorithm seeks to simultaneously minimize both the similarity in terms of the covariance structures between successive partitions, and also the difference between the partitions defined at one timescale and at another, shorter timescale. The resulting set of Pareto-efficient solution sets provides a rich representation of the self-affine properties of a multivariate time series at different locations and time scales.