Function approximations by superimposing genetic
programming trees:with applications to engineering
problems
Information Sciences, 122 (2-4):
259--280 (2000)DOI: doi:10.1016/S0020-0255(99)00121-8
Abstract
This paper concerns fundamental issues regarding
genetic programming (GP) as 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 techniques 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
matrixes in small size, each of which is responsible
for determining the value for different small portions
of the whole parameter. This approach can significantly
reduce computational cost, and a reasonably accurate
value for parameters can be obtained. Due to the fact
that the GP algorithm is likely to fall into a local
minimum, the GP algorithm often fails to generate the
functional tree with the desired accuracy. This
motivates us to devise a group of additive genetic
programming trees(GAGPT) which consists of a primary
tree and a set of auxiliary trees. The output of the
GAGPT 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 learning
and generalization capability of the GAGPT, since the
auxiliary tree evolves toward refining the quality of
the GAGPT by optimizing its fitness function. The
effectiveness of our approach is verified by applying
the GAGPT to the estimation of the principal dimensions
of a bulk cargo ship and engine torque of a passenger
car.
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