ＧＰを用いた非劣解からの設計情報の抽出

抄録

In this study, we conducted a Multi-Objective Design Exploration (MODE) using Genetic Programming (GP) for extracting design information from non-dominated solutions. Tree-based Genetic Programming is applied to non-dominated solutions and to discover design information between objective function and design parameters as expressions in symbolic form without prior knowledge of the problem. The unique feature of GP is that it finds not only the linear relationship between parameters, but also the nonlinear relationship automatically. In MODE, GP can be used as a symbolic regression technique to extract the relationship between objective functions and design parameters as symbolic equations.
We addressed two problems. First one is a test problem in which the relationship between objective function and design parameters of data set is given as a symbolic equation which includes nonlinear terms. Objective functions of tree-based GP are minimization of the number of nodes for simplicity of equation and mean absolute error for accuracy of equation. As the result, various optimal equations which include from simple equations with large residual to complex equations with small residual are obtained. These optimal equations are called ``Non-dominated equations'' here. Nonlinear terms included in data set can be extracted by analyzing the trend of non-dominated equations. In practical problem, the relationship between objective function and design parameters of non-dominated solutions is unknown. Second one is the multi-objective aerodynamic design optimization problem of flapping airfoil motion. Objective functions for optimization are maximization of the time-averaged lift(C_L,ave) and the time-averaged thrust(C_T,ave), and minimization of the time-averaged required power(C_PR,ave). The objective values are evaluated using a two-dimensional incompressible Navier-Stokes solver and a multi-objective evolutionary algorithm code is used to obtain non-dominated solutions. Tree-based GP is applied to each objective function for optimization separately. As the result of analyzing non-dominated equations, pitch offset and frequency have large effect on C_L,ave and C_T,ave. Furthermore frequency and the square of frequency significantly affect C_PR,ave.