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The dissertation presents innovative Evolutionary Search (ES) methods for the reduction in computational expense associated with the optimisation of highly dimensional design spaces. The objective is to develop a semi-automated system which successfully negotiates complex search spaces. Such a system would be highly desirable to a human designer by providing optimised design solutions in realistic time. The design domain represents a real-world industrial problem concerning the optimal material distribution on the underside of a flat roof tile with varying load and support conditions. The designs utilise a large number of design variables (circa 400). Due to the high computational expense associated with analysis such as finite element for detailed evaluation, in order to produce "good" design solutions within an acceptable period of time, the number of calls to the evaluation model must be kept to a minimum. The objective therefore is to minimise the number of calls required to the analysis tool whilst also achieving an optimal design solution. To minimise the number of model evaluations for detailed shape optimisation several evolutionary algorithms are investigated. The better performing algorithms are combined with multi-level search techniques which have been developed to further reduce the number of evaluations and improve quality of design solutions. Multi-level techniques utilise a number of levels of design representation. The solutions of the coarse representations are injected into the more detailed designs for fine grained refinement. The techniques developed include Dynamic Shape Refinement (DSR), Modified Injection Island Genetic Algorithm (MiiGA) and Dynamic Injection Island Genetic Algorithm (DiiGA). The multi-level techniques are able to handle large numbers of design variables (i.e. > 100). Based on the performance characteristics of the individual algorithms and multi-level search techniques, distributed search techniques are proposed. These techniques utilise different evolutionary strategies in a multi-level environment and were developed as a way of further reducing computational expense and improve design solutions. The results indicate a considerable potential for a significant reduction in the number of evaluation calls during evolutionary search. In general this allows a more efficient integration with computationally intensive analytical techniques during detailed design and contribute significantly to those preliminary stages of the design process where a greater degree of analysis is required to validate results from more simplistic preliminary design models.

After introducing the nonlinear evolution equations of interest: the finite depth fluid (FDF), the Kadomtsev-Petviashvili (KP), the Classical and the ordinary Boussinesq equations, formal asymptotic derivations of the KP and the FDF equations are given for the description of surface and interfacial waves. The N-soliton solution of the FDF equation is reconstructed as a finite sum of Wronskian type determinants. This solution is then shown to reduce to the solutions of the KdV and the Benjamin - Ono equations under specific limiting conditions. Interactions between two solitons of the FDF equation are studied and their interaction properties are shown to reduce to those of the KdV and the Benjamin - Ono equations. Computer plots of the interactions of two-soliton solutions of the FDF and the Benjamin - Ono equations are given. Resonance phenomena in solitons are studied with reference to the KP equation. After discussion of the basic concepts of these phenomena, the N-soliton solution is shown to reduce to the Wronskian of N/2 functions (N-even), each of which represents a triad of solitons when the solitons resonate in pairs. Asymptotic behaviour of the interactions between a triad and a soliton and between two triads are examined and the phase shifts of the triads are obtained directly from the Wronskian representation. The interactions are analysed in detail with reference to numerical computations of the full solutions. After showing that the Classical Boussinesq equations are obtained from Whitham's shallow water wave equations, the basic concept of Hirota's pq=c reduction of the first modified KP hierarchy is outlined. The Classical Boussinesq equations are shown as the pq=O reduction of the same hierarchy. The solution of the hierarchy is manipulated to incorporate the pq=O reduction. As a result of these limiting procedures applied to the problem, Wronskian solutions of the Classical Boussinesq equations in terms of rational functions are produced. Finally the pq=c reduction of the KP hierarchy is applied to the ordinary Boussinesq equation. Using this, the N-soliton solution is expressed as a finite sum of Wronskian type determinants. Analytic verification made for the two-soliton solution shows that a number of Wronskian identities are needed for this purpose. The reason for this behaviour is examined.