一种动态聚合策略增强的高效全局优化算法用于求解高维叶轮机械设计问题
A Dynamic Aggregation Strategy Enhanced Efficient Global Optimization Algorithm for Solving High-Dimensional Turbomachinery Design Problems
浏览论文内容
中文总结 AI 辅助
提出DA-EGO算法，通过动态分解高维空间并自适应调整子空间，在有限预算下高效求解高维叶轮机械设计优化问题，并在基准和实际案例中验证有效性。
中文摘要 AI 辅助
为了在预算内解决高维（$d \geq 30$）昂贵的黑箱问题，提出了一种带有动态聚合策略的高效全局优化（EGO）算法，记为DA-EGO。具体而言，DA-EGO将原始高维设计空间分解为一组低维子空间，以进行高效的基于代理模型的优化搜索，并将各子空间的最优解组合为一个精英点用于全局搜索。最重要的是，子空间不是固定的。相反，根据子空间和全空间中的变量交互分析，每次迭代都会更新子空间变量。使用扰动方法和方差分析来检测变量交互。为了进一步加速优化进程，还根据前一次迭代的子空间优化结果分析，自适应调整子空间的搜索范围。在21个基准实例上的测试（包括7个函数在30、60和90维上的测试）表明，DA-EGO在1500次函数评估的预算下，对可分离和部分可分离问题是有效的。其优势取决于具体情况：在不可分离的偏移Rosenbrock函数上，GSGA在60维和90维时表现更好，而30维的结果与IKAEA和GSGA在统计上相当。此外，DA-EGO的优势还体现在对具有28个变量的跨音速转子叶片的气动优化以及具有60个变量的压气机级优化中。综上所述，所提出的DA-EGO的有效性已得到充分证明。
英文摘要
In order to solve the high-dimensional ($d \geq 30$) expensive black-box problems within budget, an efficient global optimization (EGO) algorithm with a dynamic aggregation strategy is proposed, labeled as DA-EGO. Specifically, the DA-EGO decomposes the original high-dimensional design space into a set of low-dimensional subspaces for efficient surrogate-based optimization search, and the optimal solutions of subspaces are combined as an elite point for the global search. Most importantly, the subspaces are not fixed. Instead, the subspace variables are updated in each iteration, according to the variable interaction analyses in the sub- and full-spaces. The perturbation method and the analysis of variance are used to detect variable interactions. To further accelerate the optimization progress, the searching ranges of subspaces are also adaptively adjusted according to the analyses of subspace optimization results of the previous iteration. Tests on 21 benchmark instances, comprising seven functions at 30, 60, and 90 dimensions, show that DA-EGO is effective on separable and partially separable problems under a budget of 1500 function evaluations. Its advantage is case-dependent: on the non-separable shifted Rosenbrock function, GSGA performs better at 60 and 90 dimensions, while the 30-dimensional results are statistically comparable to IKAEA and GSGA. Moreover, the advantage of DA-EGO is also seen in the aerodynamic optimization of a transonic rotor blade with 28 variables as well as the compressor stage optimization with 60 variables. With the above, the effectiveness of the proposed DA-EGO has been well demonstrated.
发表机构
- AVIC Shenyang Engine Design Institute（中国航发沈阳发动机设计研究所）
机构由 AI 辅助整理，请以论文原文为准。
