Use of surrogates in derivative-free optimization

本提案中描述的研究项目涉及无导数优化（DFO）。更确切地说，它专注于黑盒优化，当工程优化问题的目标和约束由被视为黑盒的计算机代码获得时，就会发生这种情况。有几个特性使得这些代码对于优化来说不切实际：它们可能评估起来很昂贵，被噪声污染，或者无法返回值。没有衍生信息是可用的，甚至近似值也不能用于优化。在这种情况下，不能使用基于导数的方法，可以考虑DFO方法。本提案讨论了网格自适应直接搜索（MADS）方法的扩展，特别是使用代理人，以提高其efficiency.My研究分为三个类别：算法的发展，优化软件设计，和应用。本申请提出了第一类中的六个项目。这六个项目大多数涉及在直接搜索框架内使用代理人。每个项目，在目标和时间框架方面，已专门为硕士或博士生定义。因此，大约86%的预算用于研究生的工资。

The research project described in this proposal concerns derivative-free optimization (DFO). More precisely, it focuses on blackbox optimization, which occurs when the objective(s) and constraints of an engineering optimization problem are obtained by a computer code seen as a blackbox. Several characteristics make these codes impractical for optimization: they may be expensive to evaluate, be contaminated with noise, or fail to return a value. No derivative information is available and even approximations can not be exploited for the optimization. In this context, derivative-based methods cannot be used, and DFO methods may be considered. The present proposal discusses extensions of the mesh adaptive direct search (MADS) method, and in particular the use of surrogates to improve its efficiency.My research is equally divided into three categories: algorithmic developments, optimization software design, and applications. The present application proposes six projects in the first category. Support for the two other categories has been requested from other organizations.Most of these six projects concern the use of surrogates within a direct search framework. Each project, in terms of objectives and time frame, has been specifically defined for an MSc or PhD student. As a consequence, approximately 86% of the requested budget is devoted to graduate-student salaries.