Optimization Techniques for Problems Arising in Design and Other Engineering Applications

本研究的目的是促进优化在工程设计和其他工程应用中的应用。具体而言，将有三个主要目标：(1)将通过借鉴效用理论和基于信息的设计理论，努力加强先前引入的权衡探索方法；并增强实现此方法的软件环境。(2)将致力于开发和分析具有所有迭代性质的高效优化算法，即由算法生成的所有连续近似解都满足规定的约束-这是许多工程环境中的关键性质。(3)所得到的算法将在与各种工程学科相关的试验台上实现、测试和验证。如果成功，这些努力将对工程设计产生重大影响。在许多工程应用中，所有迭代都满足规定的约束是很重要的。缺乏快速、有效的优化算法来享受这一属性。如果当前的工作是成功的，那么每次迭代的工作量将大大减少，特别是对于大型问题。减少每次迭代的计算量的一个重要副作用是精度的提高。求解优化问题的失败通常可以追溯到计算精度不足。此外，权衡探索在工程设计中无处不在，其中竞争设计规范的复杂性和数量使得确定适当的实用功能变得具有挑战性。旨在捕捉设计师潜在偏好的有效工具可以给他/她带来明确的优势。

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.