数据驱动的贝叶斯SVR自适应建模及昂贵约束多目标代理优化

实际工程中的多目标优化问题往往具有黑箱特性且需要耗时的功能性评估,采用传统的进化优化方法求解,存在计算成本高昂且难以实现的问题.考虑代理优化方法在处理需要功能性评估工程设计问题中的高效性,提出一种小样本数据驱动下的贝叶斯SVR自适应建模及昂贵约束多目标代理优化方法.该方法在实现过程中选取贝叶斯SVR模型以减少功能性评估过程的昂贵仿真成本,利用最大化约束期望改进矩阵聚合策略进行新设计方案选取,并通过小样本信息的不断更新实现数据驱动下的贝叶斯SVR模型自适应更新和逐步优化.贝叶斯SVR模型具有强的边界刻画能力及预测不确定性度量功能,可为新样本挑选提供预测精度保障及潜在的改进方向.所提出的切比雪夫距离和曼哈顿距离聚合策略从样本填充的改进范围考虑,使其具有较强的改进边界探索能力,在多变量优化问题中具有计算复杂度低、适用性强的特点.测试函数及工程实例结果表明:1)所提出的方法可在小样本条件下有效减少昂贵仿真成本,提升昂贵约束多目标问题的优化效率;2)获取昂贵约束多目标问题的Pareto前沿在收敛性、多样性及空间分布性方面均具有一定优势.

Data-driven Bayesian SVR adaptive modeling and expensive constrained multi-objective surrogate-based optimization

In practical engineering, there are many challenges when solving multi-objective optimization problems, such as the black box characteristics and time-consuming evaluation. The traditional evolutionary optimization method is usually limited due to the expensive cost and the difficulty in obtaining solutions. To modify the deficiency, a data-driven Bayesian SVR adaptive modeling technique and a constrained multi-objective surrogate-based optimization method is proposed in the context of the small sample. The Bayesian SVR model is first utilized to replace the complex computer model, thus reducing the expensive cost of every call to the actual performance function. Then, the new design by maximizing the aggregation strategy of the constrained expected improvement matrix is chosen. Next, the sample information and the data-driven Bayesian SVR model is adaptively updated, and the optimization is fulfilled step by step. The superior characteristic of the Bayesian SVR model, that is, the powerful ability to explore the boundary and the measurement of the prediction uncertainty, ensures the prediction accuracy and provides an improvement direction for selecting the new sample. In addition, the proposed Chebyshev distance and Manhattan distance aggregation strategy has the advantages of low computational complexity and good applicability for multivariable optimization problems. Test functions and engineering examples show that: 1) The proposed method can effectively reduce expensive simulation costs and improve optimization efficiency for expensive constrained multi-objective problems in the context of the small sample; 2) The Pareto frontier of surrogate-based multi-objective optimization has a certain degree of superiority in convergence, diversity, and space dispersion.