基于多属性空间分割的高维代理模型全局优化方法研究

Expensive black-box problems are always found in the field of engineering design, and the efficient approach to solve these problems is surrogate-based global optimization (SBGO) method, which is also a hot research area in the field of engineering optimization. But there are still some deficiencies of the current SBGO methods when dealing with high-dimensional problems. Such as, low efficiency to get a uniform sample through design of experiment (DOE)), time-consuming to construct the surrogate model (SM), low prediction accuracy of the SM and high difficulty to find the global optimum. Therefore, we propose to study on the SBGO method based on multiple attribute space division in this project. Parallel stochastic optimization algorithm and symmetric space mapping technology will be used to improve the efficiency of uniform sampling in high dimensional space. Then, dimension reduction techniques are used to construct RBF-HDMR and Kriging SM efficiently with a better accuracy, which can express important information of high dimensional space. Besides, space division is adopted to reduce the degree of nonlinearity of the problem. Next, multiple attribute decision making is used to search for good solutions in the subspaces in parallel and update the sample set. It is expected to significantly improve the efficiency and capacity of the optimization. Afterwards, a high-dimensional expensive black-box global optimization system is constructed, and the method is verified through a high-fidelity shape optimization design of blended-wing-body underwater glider (BWBUG). The results of this research will further enrich the high-dimensional global optimization theory, and improve its practicality in engineering design, which have vital theoretical significance and application value in engineering.

贵重黑箱问题广泛存在于工程设计中，代理模型全局优化是解决该类问题的有效途径。目前代理模型全局优化方法在高维贵重黑箱问题上存在以下不足：实验设计均匀采样效率低、代理模型建模效率和预测精度下降、优化方法难以搜寻到全局最优解。为此，本项目提出开展基于多属性空间分割的高维代理模型全局优化方法研究。拟运用并行随机优化算法和对称空间映射技术提高高维空间均匀采样效率；利用降维技术构造可表达高维空间重要信息的RBF-HDMR与Kriging模型，提高代理模型高维建模效率和精度；利用多属性空间分割技术进行设计空间划分，降低问题的非线性程度，通过多属性决策在多个子空间中自适应地并行寻找有益解并更新样本集，有望大幅提高优化效率和寻优能力，并以翼身融合水下滑翔机高精度外形优化设计为例进行实验验证。研究成果将进一步丰富和完善高维全局优化设计理论，并提高其工程实用性，具有重要的理论意义和工程应用价值。

本项目面向高维贵重黑箱优化问题，将降维思想和多属性空间分割思想引入到高维全局优化过程中，提出了基于多属性空间分割的高维代理模型全局优化方法，主要使用高维模型表示建模理论、降维理论、组合代理模型方法以及多属性空间分割方法，开展针对高维贵重黑箱问题的代理模型建模方法及全局优化方法研究。完成的主要内容和取得的重要结果如下：.（1）开展了高维空间中的快速采样方法研究。将高维设计空间分为两个子空间，建立了多种群并行策略实现子空间快速均匀采样，提出了一种高维映射机制实现了整个高维空间的快速均匀采样。.（2）开展了基于组合策略的HDMR代理模型方法。建立了PRS、RBF以及Kriging三种代理模型的预测信息融合机制，提出了一种基于交叉验证的代理模型权重系数计算方法，提高了HDMR代理模型方法的稳定性和效率。.（3）开展了高维Kriging模型的数学建模研究。提出了一种基于最大信息系数的高维Kriging建模方法，实现了模型超参数的快速预估，提高了Kriging模型的建模效率。此外，还提出了一种基于预估校正思想的高维Kriging建模方法，进一步提升了建模精度和建模效率。.（4）开展了基于空间缩减的高维全局优化方法。提出了一种打分补点策略筛选贵重新增样本，建立了设计空间缩减机制实现了算法局部收敛性能的加速，建立了子代理模型的选择机制，提升了高维代理模型全局优化的稳健性和效率。此外，提出了新的代理辅助进化算法，提高了进化算法处理高维贵重优化问题的效率。.（5）完成了基于多属性空间分割的高维代理模型全局优化系统构建，建立了翼身融合水下滑翔机高精度外形优化设计自动化计算框架，实现了翼身融合水下滑翔机外形优化的应用验证。.研究结果表明本项目提出的方法可有效解决高维贵重黑箱优化问题中面临的实验设计均匀采样效率低、代理模型建模效率和预测精度低、优化方法难以搜寻到全局最优解等科学问题，对进一步丰富和完善高维全局优化设计理论，并提高其工程实用性，具有重要的理论意义和应用价值。