Optimization Techniques for Problems Arising in Design and Other Engineering Applications

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The objectives of this research are to contribute to the advancement of optimization as applied to engineering design and other engineering applications. Specifically, three main goals will be targeted: (1) Work will be pursued to enhance a previously introduced tradeoff exploration methodology, by borrowing from utility theory and information-based design theory; and to enhance a software environment implementing this methodology. (2) Efforts will be devoted to developing and analyzing highly effective optimization algorithms with the property that all iterates, that is, all successive approximate solutions generated by the algorithms, satisfy the prescribed constraints--a crucial property in many engineering contexts. (3) The resulting algorithms will be implemented, tested and validated on test benches pertaining to various engineering disciplines. If successful, these efforts should have a significant impact on engineering design. It is important that all iterates satisfy the prescribed constraints in many engineering applications. There is a lack of fast, effective optimization algorithms that enjoy this property. If the present effort is successful, the work per iteration will be substantially reduced, especially for large problems. An important side effect of reducing the amount of computation per iteration is a resulting gain in accuracy. Failures in the solution of optimization problems can often be traced to insufficient computational accuracy. Also, tradeoff exploration is ubiquitously needed in engineering design, where the complexity and number of competing design specifications make it challenging to identify an appropriate utility function. Effective tools aimed at capturing the designer's underlying preferences can give him/her a definite edge.