Evolutionary Optimized Tensor Product Bernstein Polynomials versus Backpropagation Networks

In this paper a new approach for approximation problems involving only few input and output parameters is presented and compared to traditional Backpropagation Neural Networks (BPNs). The basic model is a Tensor Product Bernstein Polynomial (TPBP) for which suitable control points need to be found. It is shown that a TPBP can also be interpreted as a special class of feed-forward neural networks where control point coordinates are represented by input weights. Although optimal control points for a TPBP leading to the smallest possible approximation errors can be determined by the Method of Least Squares (MLS), this approach has only poor generalization capabilities. Instead, the usage of a (μ, λ)-Evolution Strategy is proposed. Experiments with different sets of test data indicate that the solutions obtained by the TPBP/ES approach generalize very well without exhibiting large approximation errors. When comparing this technique to BPNs, similar approximation and generalization errors were observed. One major advantage of the TPBP/ES approximation model over others such as BPNs is the possibility for humans to better understand a found approximation and to manually post-process it in a very intuitive way to achieve specific changes. Another benefit is that any error function might be used as optimization goal.