Sequential Approximate Optimization

Abstract

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 some analysis such as structural analysis, fluid mechanic analysis, and thermodynamic analysis. Usually, these analyses are considerably time consuming to obtain a value of objective functions. In order to make the number of analyses as few as possible, sequential approximate optimization method has been suggested [69, 139, 151] (1) first, predicting the form of objective functions by techniques of machine learning (e.g., SVR, RBFN) and (2) optimizing the predicted objective function. A major problem in those methods is how to get a good approximation of the objective function based on as few sample data as possible. In addition, if the current solution is not satisfactory, it is needed to improve the approximation of the objective function by adding some additional data. The form of objective functions is revised by relearning on the basis of additional data step by step. Then, how to choose such additional data effectively becomes an important issue. In this section, we introduce several methods how to choose additional data, focusing on design of incremental experiments.