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用设计变量来明确给出的。在给定设计变量值的情况下，通过结构分析、流体力学分析、热力学分析等实际/计算实验得到目标函数的值。通常，这些实验是相当昂贵的。为了使这些实验的次数尽可能少，优化与预测目标函数的形式并行进行。响应面法（RSM）在这方面是众所周知的。本研究提出了径向基函数网络（RBFN）和支持向量机（SVM）等几种RSM方法。在这种方法中，最重要的任务之一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，通过添加全局信息来更好地逼近目标函数，同时添加局部信息来更精确地逼近最优解，从而选择额外的样本数据。本研究特别在多目标优化（MOP）和目标规划（GP）的基础上，提出了一种新的支持向量回归（SVR），称为μ-v-SVR。对几种方法进行了比较，并结合实际桥梁实例进行了分析。

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.