Optimizing black-box objective functions using computational intelligence and its application to seismic reinforcement of cable stayed bridges

在许多实际工程设计问题中，目标函数的形式并不是以设计变量的形式明确给出的。给定设计变量的值，在这种情况下，目标函数的值是通过结构分析、流体力学分析、热力学分析等真实的/计算实验来获得的，这些实验通常是相当昂贵的。为了使这些实验的数量尽可能少，优化与预测目标函数的形式并行执行。响应面方法（RSM）是沿着被广泛使用的方法，本研究提出了几种响应面方法，如径向基函数网络（RBFN）和支持向量机（SVM）。该方法的一个重要任务是适度地寻找有效的样本数据，以使实验次数尽可能少。在所提出的方法中，以这样的方式选择额外的样本数据：既添加了用于更好地逼近目标函数的全局信息，又添加了用于更精确地逼近最优解的局部信息。在这项研究中，特别是，沿着多目标优化（MOP）和目标规划（GP）的思路，提出了一种新的支持向量回归机（SVR），称为μ-v-SVR通过试验问题和真实的桥梁算例对几种方法进行了沿着比较。

In many practical engineering design problems, the form of objective functions is not given explicitly in terms of design variables. Given the value of design variables, under this circumstance, the value of objective functions is obtained by real/computational experiments such as structural analysis, fluidmechanic analysis, thermodynamic analysis, and so on.Usually, these experiments are considerably expensive. In order to make the number of these experiments as few as possible, optimization is performed in parallel with predicting the form of objective functions. Response Surface Methods (RSM) are well known along this approach.This research proposes several approaches to RSM such as Radial Basis Function Networks (RBFN) and Support Vector Machines (SVM). One of the most important tasks in this approach is to find effective sample data moderately in order to make the number of experiments as small as possible. In the proposed methods, additional sample data are selected in such a way that both global information for better approximation of objective function and local information for more precise approximation of optimal solution are added.In this research, in particular, a new type of support vector regression (SVR) called μ-v-SVR is proposed along the line of multi-objective optimization (MOP) and goal programming (GP).Several methods are compared along with not only test problems but also real bridge examples.