No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

Decision making under uncertainty presents major challenges from both modelling and solution methods perspectives. The need for stochastic optimisation methods is widely recognised; however, compromises typically have to be made in order to develop computationally tractable models. Robust optimisation is a practical alternative to stochastic optimisation approaches, particularly suited for problems in which parameter values are unknown and variable. In this thesis, we review robust optimisation, in which parameter uncertainty is defined by budgeted polyhedral uncertainty sets as opposed to ellipsoidal sets, and consider its application to portfolio selection. The modelling of parameter uncertainty within a robust optimisation framework, in terms of structure and scale, and the use of uncertainty sets is examined in detail. We investigate the effect of different definitions of the bounds on the uncertainty sets. An interpretation of the robust counterpart from a min-max perspective, as applied to portfolio selection, is given. We propose an extension of the robust portfolio selection model, which includes a buy-in threshold and an upper limit on cardinality. We investigate the application of robust optimisation to portfolio selection through an extensive empirical investigation of cost, robustness and performance with respect to risk-adjusted return measures and worst case portfolio returns. We present new insights into modelling uncertainty and the properties of robust optimal decisions and model parameters. Our experimental results, in the application of portfolio selection, show that robust solutions come at a cost, but in exchange for a guaranteed probability of optimality on the objective function value, significantly greater achieved robustness, and generally better realisations under worst case scenarios.

Most decision tree induction methods used for extracting knowledge in classification problems are unable to deal with uncertainties embedded within the data, associated with human thinking and perception. This thesis describes the development of a novel tree induction algorithm which improves the classification accuracy of decision trees in non-deterministic domains. A novel algorithm, Fuzzy CIA, is presented which applies the principles of fuzzy theory to decision tree algorithms in order to soften the sharp decision boundaries which are inherent in these induction techniques. Fuzzy CIA extrapolates rules from a crisply induced tree, fuzzifies the decision nodes and combines membership grades using fuzzy inference. A novel approach is also proposed to manage the defuzzification of regression trees. The application of fuzzy logic to decision trees can represent classification of knowledge more naturally and in-line with human thinking and creates more robust trees when it comes to handling imprecise, missing or conflicting information. A series of experiments, using real world datasets, were performed to compare the performance of Fuzzy CIA with crisp trees. The results have shown that Fuzzy CIA can significantly improve the classification / prediction performance when compared to crisp trees. The amount of improvement is found to be dependant upon the data domain, the method in which fuzzification is applied and the fuzzy inference technique used to combine information from the tree.

Population-based stochastic global search/optimisation algorithms often generate solutions with low accuracy. However, they cover the search space well; a property we refer to as exploration. In contrast, local optimisation algorithms, largely deterministic, find solutions with high accuracy when left to run long enough; they have the property we refer to as exploitation. Local optimisation algorithms, by their very nature, do not cover well the search space. It is also well known that some are more computationally demanding than others. It is, therefore, attractive to try and design algorithms which are good both at exploration and exploitation, but also have reasonable computing demands. A popular way to achieving this is to hybridise algorithms which have the desired properties. In this thesis, we consider the hybidisation of Adaptive Differential Evolution and Particle Swarm Optimisation algorithms with local search algorithms namely the Broyden-Fletcher-Goldfard-Shanno algorithm, the Steepest-Descent algorithm and the Nelder-Mead Simplex algorithm. Three combinations have been investigated. • Adaptive Differential Evolution with an Expensive Local Search Method, referred to as Hybridization of Adaptive Differential Evolution with an Expensive Local Search Method; it combines a variant of Differential Evolution, Adaptive Differential Evolution with Optional External Archive, with the Broydon-Fletcher-Goldfarb-Shanno updating method, as the local search method. • Adaptive Differential Evolution and two local search algorithms, one expensive represented by Broydon-Fletcher-Goldfarb-Shanno, and the other comparatively cheap, represented by the Steepest Descent with a restart strategy; this is referred to as Hybridization of Adaptive Differential Evolution and Two Local Search Techniques with a Restart Strategy. • Particle Swarm Optimization algorithm with the Nelder-Mead Simplex algorithm, which is derivative-free, unlike the other two local search algorithms. This is referred to as A Hybridization of Particle Swarm Optimization with the Nelder-Mead Simplex Algorithm. These hybrid algorithms are then applied to unconstrained nonlinear optimization problems. Tests are carried out on well known problems from the Congress on Evolutionary Computation 2005(CEC2005) as well as those of the Congress on Evolutionary Computation 2010(CEC2010) test suits. Results show that improvements can be gained, but still at a cost. The thesis also contains an extensive review of the literature concerned with hybridization, particularly of evolutionary type algorithms with both classical and novel optimization approaches.