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Abstract
Shape optimization refers to the process of identifying a shape with optimum performance. Such performance measures could include minimization of drag, maximization of lift, minimization of electromagnetic signatures etc. In recent years, optimization methods are increasingly being used to uncover novel shapes with good functional performance. The performance of a shape optimization approach is dependent on three key factors, i.e., shape representation scheme, the morphing scheme (i.e., means to perturb shapes), and finally their effective use within an efficient optimization algorithm. While there is a number of reports on domain specific applications of shape optimization, there is very little understanding about "what is limiting the efficiency?" and "how it can be improved?”
The work reported in this thesis is restricted to boundaries of two-dimensional (2D) shapes and bounding surface of three-dimensional (3D) shapes. In order to offer a common platform for objective evaluation of various shape optimization approaches, the problems have been formulated as shape matching problems. In shape matching, the optimum shape is the target shape and the efficiency of an approach is defined by the number of function evaluations it takes to deliver the optimum shape. In this work, the shape matching similarity measure is based on Euclidean and Hausdorff distance. The shapes/surfaces are represented using B-splines which are known for their flexibility and local controllability. B-splines are defined using control points and the optimum location of such control points is usually identified using an optimization algorithm. In this thesis, an approach of repair is introduced in the context of 2D shape optimization, which essentially identifies the sequence of control points based on convex-hull properties. The method is extended via a sort-repair strategy (i.e., sort based on stations followed by repair) to deal with 3D shape optimization problems. The repair and the sort-repair strategy have been embedded within a hybrid memetic algorithm. The algorithm is a multi-feature hybrid that combines the strength of a real-coded genetic algorithm, differential evolution and a local search. In order to objectively evaluate the performance of the approach, a number of 2D and 3D numerical examples of shape matching have been solved. The benefits offered by the repair and sort-repair strategies have been analyzed. In most cases, the computational savings are phenomenal.