An active subspace method for accelerating convergence in Delaunay-based optimization via dimension reduction
An active subspace method for accelerating convergence in Delaunay-based optimization via dimension reduction
复制标题
一种通过降维加速基于 Delaunay 的优化收敛的主动子空间方法
DOI：
10.1109/cdc.2018.8619219
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
T. Bewley
中科院分区：
文献类型：
--
作者：
Muhan Zhao;S. R. Alimo;T. Bewley
基于Delaunay的无导数优化(Δ-DOGES)是一种高效且可证明收敛的全局优化算法，适用于具有计算代价较高的函数计算的问题，包括目标函数的解析表达式可能不可用的情况。Δ-DOWS属于响应面方法家族，存在典型的“维度灾难”，其计算量随着设计参数的增加而迅速增加。因此，Δ-DOGES的设计参数n通常被限制在n≤10。为了提高高维问题的性能，本文提出了一种无导数优化方法和一种激活子空间方法相结合的方法，该方法寻求目标函数的逐次精化代理模型的全局极小值，并优先检测和探索目标函数的最大变异性的方向。其他方向对目标函数的贡献受一个小常量的限制。该算法在函数变异最大的d维活动子空间上迭代地使用Δ-DOWS算法来寻找最小值。逆映射用于将数据从活动子空间投影回全模型，以评估函数值。这项任务是通过解决一个相关的不等式约束问题来完成的。测试结果表明，该策略对少数几个模型优化问题是非常有效的。
Delaunay-based derivative-free optimization (Δ-DOGS) is an efficient and provably-convergent global optimization algorithm for problems with computationally-expensive function evaluations, including cases for which analytical expressions for the objective function may not be available. Δ-DOGS belongs to the family of response surface methods (RSMs), and suffers from the typical “curse of dimensionality”, with the computational cost increasing quickly as the number of design parameters increases. As a result, the number of design parameters n in Δ- DOGS is typically limited to n ≤ 10. To improve performance for higher-dimensional problems, this paper proposes a combination of derivative-free optimization, seeking the global minimizer of a successively-refined surrogate model of the objective function, and an active subspace method, detecting and exploring preferentially the directions of most variability of the objective function. The contribution of other directions to the objective function is bounded by a small constant. This new algorithm iteratively applies Δ-DOGS to seek the minimizer on the d -dimensional active subspace that has most function variation. Inverse mapping is used to project data from the active subspace back to full-model for evaluating function values. This task is accomplished by solving a related inequality constrained problem. Test results indicate that the resulting strategy is highly effective on a handful of model optimization problems.