Function approximations by superimposing genetic programming trees: with applications to engineering problems

This paper concerns fundamental issues regarding genetic programming (GP) a s a tool for real-valued function approximations. Standard GP suffers from the lack of estimation techniques for numerical parameters of a functional tree. Unlike other research activities, where non-linear optimization techn iques are employed, we adopt the use of a linear associative memory for the estimation of these parameters under the GP algorithm. Instead of dealing with a large associative matrix, we present the method of building several associative matrices in small size, each of which is responsible for determ ining the value for different small portions of the whole parameter. This a pproach can significantly reduce computational cost, and a reasonably accur ate value for parameters can be obtained. Due to the fact that the GP algor ithm is likely to fall into a local minimum, the GP algorithm often fails t o generate the functional tree with the desired accuracy. This motivates us to devise a group of additive genetic programming trees (GAGPT) which cons ists of a primary tree and a set of auxiliary trees. The output of the GAGP T is the summation of outputs of the primary tree and all auxiliary trees. The addition of auxiliary trees makes it possible to improve both the learn ing and generalization capability of the GAGPT, since the auxiliary tree ev olves towards refining the quality of the GAGPT by optimizing its fitness f unction. The effectiveness of our approach is verified by applying the GAGP T to the estimation of the principal dimensions of a bulk cargo ship and en gine torque of a passenger car. (C) 2000 Elsevier Science Inc. All rights r eserved.