Grey box optimization

灰盒优化

• 批准号: RGPIN-2020-04448
• 负责人: Audet, Charles
• 金额: $ 3.13万
• 依托单位: École Polytechnique de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=739700
• 关键词: Grey; box; optimization

The breadth of the optimization field is wide. At one extremity, there are optimization problems for which the structure is well-known and exploitable: linear programming, or convex optimization with explicit algebraic formulations for example. This is not the target class of problems of my research. At the opposite extremity, blackbox optimization (BBO) refers to situations in which the structure of the objective function and of the constraints are unknown and cannot be exploited during the optimization process. These situations frequently arise when the functions defining the problem are computed through a time-consuming simulation.  These are the problems at the center of this research project. One of the most useful tools for solving optimization problems is the derivative. Indeed, the gradient vector is the steepest ascent direction and can be followed in a maximization context. Derivative-free optimization (DFO) refers to the situation where the derivatives of the functions are unavailable, or potentially difficult to estimate. A subtle distinction between DFO and BBO is that in the latter there is no reason to believe that derivatives even exist, and in the former they might exist but their expression is not available. Prior to the 1990's, only punctual developments were made in the DFO and BBO fields. But since then, there has been a steady increase in the interest devoted to these research areas. These are among the most rapidly expanding areas of nonlinear optimization research. This may be explained in part by the fact that computers are now able to simulate complex engineering processes in reasonable time, and by the successful utilization of algorithms on real engineering problems in industrial environments. The research project described in this proposal builds on my prior NSERC-funded work on direct search algorithms for DFO and BBO problems. The objective of this project is to explore the grey zone in the wide optimization field: problems for which part of the structure, but not all, is available. For example, previous work has focused on situations where the objective function is the sum of the squares of blackbox functions, and where crude information with respect to the monotonicity of some constraints with respect to certain variables was explicitly known. The present project will study other types of grey box optimization problems in which high-level qualitative or quantitative information about the constraints, the nature of the problem and the surrogates are available. All developments in the projects outlined in this proposal will be tested on real engineering test problems and will be analyzed using tools from nonsmooth calculus for a rigorous convergence analysis. The outcome of this research is useful to our industrial collaborators in Canada.  We plan to continue to apply our work in areas such as hydrological sciences, pharmaceutical and bioinformatic industry, alloy design, metamaterial design and aeronautics.

优化场的广度很广。在一个末端，存在优化问题，结构是众所周知的和可利用的：线性编程或以显式代数公式的凸优化。这不是我研究的目标问题。在相反的末端，黑框优化（BBO）是指目标函数和约束的结构未知的情况，并且在优化过程中无法利用。当通过耗时的模拟计算定义问题的函数时，经常出现这些情况。这些是该研究项目中心的问题。解决优化问题的最有用的工具之一是导数。实际上，梯度向量是蒸汽的上升方向，可以在最大环境中遵循。无衍生化优化（DFO）是指无法估计或可能难以估计的函数衍生物的情况。 DFO和BBO之间的微妙区别是，在后者中，没有理由相信衍生物甚至存在，而在前者中，它们可能存在，但它们的表达不可用。在1990年代之前，仅在DFO和BBO领域进行了注射性发展。但是从那以后，专门致力于这些研究领域的有趣的有趣的增长。这些是非线性优化研究最快扩展的领域之一。这可以部分通过以下事实来解释：计算机现在能够在合理的时间内模拟复杂的工程流程，以及成功地利用了工业环境中实际工程问题的算法。该提案中描述的研究项目是基于我以前由NSERC资助的DFO和BBO问题的直接搜索算法的工作。该项目的目的是探索广泛优化领域的灰色区域：结构中哪一部分但不是全部的问题。例如，以前的工作集中在目标函数是黑框函数正方形的总和以及有关某些约束相对于某些变量的单调性的粗略信息的情况。本项目将研究其他类型的灰色框优化问题，其中有关约束的高级定性或定量信息，本提案中概述的项目中的所有发展的性质将在实际工程测试问题上进行测试，并将使用非平滑的计算中的工具来分析严格的一致性合并分析。这项研究的结果对我们在加拿大的工业合作者有用。我们计划继续将我们的工作应用于氢科学，药物和生物信息学工业，合金设计，超材料设计和航空技术。