Derivative-free and blackbox optimization for engineering problems

针对工程问题的无导数和黑盒优化

• 批准号: RGPIN-2015-05311
• 负责人: Audet, Charles
• 金额: $ 2.48万
• 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: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=644301
• 关键词: Derivative; free; blackbox; optimization; engineering

This research project is the continuation of my prior work funded by NSERC on the development of the Mesh Adaptive Direct Search algorithm (MADS) for derivative-free and blackbox optimization problems.  In many engineering optimization problems, the objective and constraint functions are nonsmooth and evaluated through a computer simulation. The outputs of these codes are often of limited precision, contaminated with numerical noise, expensive to evaluate, and sometimes the code fails to return a value. ***There has been an important amount of work in developing models to improve the efficiency of direct search optimization methods.  Quadratic models, Gaussian processes, kriging interpolation as well as radial basis functions are such examples.  There has also been work on expanding the capabilities to integer, categorical and periodic variables, on efficient treatment of constraints, on bi- and multi objective problems.  In the present proposal we plan to pursue the development of MADS methods in many ways.***The current MADS algorithm generates trial points on a discretization of the space of variables called the mesh.  Several engineers that have applied MADS to practical problems complained that a consequence of the way that the mesh size parameter is updated leads to modifications in the values of the variables below a reasonable granularity.  We plan to alter the way that the mesh size parameter is updated, which is at the heart of the MADS algorithm, and the cornerstone of the nonsmooth convergence analysis.  ****Some constraints return a binary value indicating if it is satisfied or not, e.g., a flag indicating if the simulation failed or not.  Such a binary constraint is difficult to model using the above-mentioned modelling techniques.  We plan to import classification methods and data mining tools from the machine learning community to model them.  We proposed the BiMADS algorithm for biobjective blackbox constrained optimization.  For such problems, BiMADS returns a finite list of trade-off solutions, with respect to two conflicting objectives.  We plan to once again use classification tools to analyze the nature of the list of trade-off solutions, and to create representative solutions.***Surrogates are used by MADS as an inexpensive substitute of the true simulation.  MADS uses them by sampling the surrogate several times before deciding where to launch the true simulation.  Our numerical experiments systematically show that surrogates considerably help in finding better solutions.  We plan to devise a generic framework to handle surrogates with parametrizable precision, and to build additional models to dynamically estimate the difference between the true and surrogate functions.   ***All the projects outlined in this proposal will be rigorously analyzed using nonsmooth calculus.**

该研究项目是NSERC资助的关于网格自适应直接搜索算法（MADS）的先前工作的延续。在许多工程优化问题中，目标和约束功能是非平滑的，并通过计算机模拟进行了评估。这些代码的输出通常受到限制的精度，被数值噪声污染，评估昂贵，有时代码无法返回值。 ***在开发模型以提高直接搜索优化方法的效率时，已经有很多重要的工作。这些例子就是二次模型，高斯过程，克里格插值以及径向基础函数。还在研究将功能扩展到整数，分类和周期性变量，有效地处理约束和多目标问题。在本提案中，我们计划以许多方式追求MADS方法的开发。几位对实际问题应用疯狂的工程师抱怨说，更新网格大小参数的方式导致变量值以下的变量值的修改。我们计划改变网格大小参数更新的方式，这是MADS算法的核心，也是非平滑收敛分析的基石。 ****一些约束返回二进制值，指示是否满足，例如，标志指示模拟是否失败。这种二进制约束很难使用上述建模技术进行建模。我们计划将分类方法和数据挖掘工具从机器学习社区导入，以对其进行建模。我们提出了用于生物原始黑框的BIMADS算法约束优化。对于此类问题，Bimads就两个相互矛盾的目标返回了权衡解决方案的有限列表。我们计划再次使用分类工具来分析权衡解决方案列表的性质，并创建代表性的解决方案。 MADS通过在决定启动真正的模拟的位置之前多次对代理人采样来使用它们。我们的数值实验系统地表明，代替代有助于找到更好的解决方案。我们计划设计一个通用框架来处理具有可参数精度的替代物，并构建其他模型以动态估计真实和替代功能之间的差异。**