Application of genetic programming and response surface methodology to optimization and inverse problems

Abstract

Response surface methodology is a method of constructing approximations of the system behavior using results of the response analysis calculated at a series of points in the variable space. The approximation functions are obtained by the least-squares method. One of the main problems in the application of such techniques is the necessity to select a structure of the approximation function. Genetic Programming methodology is used for the creation of approximation functions in the solution of optimization and inverse problems. Genetic Programming is a relatively new form of Artificial Intelligence, and is based on the ideas of Darwinian evolution and genetics. Two important aspects of the problem are addressed: the choice of the plan of experiments and the model tuning using the least-squares response surface fitting. A test example is presented where the technique is applied to a simple optimization problem.