Multiple control levels in structured genetic alogorithms
Angelos Molfetas · 2006
This work examines the impact that genes with activation relationships have on Genetic Algorithms (GAs). These activation relationships allow genes to control whether other associated genes get expressed in the phenotype. More specifically, this thesis investigates the effect that the incorporation of control levels (tiers of genes which determine the activation of lower genes) have on GAs which are used to generate feedforward Artificial Neural Networks (ANNs). In order to evaluate the performance of different levelled Structured Genetic Algorithms (SGAs; they are GAs which possess control levels), numerous experiments were conducted, utilising the four input XOR, Mackey-Glass and Breast Cancer data sets. In addition, the thesis derives four mathematical models which describe how SGA redundancy changes as more control levels are incorporated. This thesis also presented and implemented a novel four level Structurally Evolved Neural Network Algorithm (SENNGA). Furthermore, it demonstrated the novel implementation of a three level SENNGA. Both of these SENNGAs were tested against the above mentioned experiments. Two of the redundancy models in this thesis made three assumptions: The activation probability spread is homogeneous; corresponding activation probabilities between different levelled encoding schemes are the same; and activation probabilities are not equal to unity. Under these assumptions, the number of redundant genes always increases when control levels are added. Furthermore, when the number of top level genes is fixed, the incorporation of control levels always increases the redundancy ratio. If on other hand, the number of bottom level genes is kept fixed, then the redundancy ratio is not guaranteed to increase. Two more mathematical models were employed that assumed instead a heterogeneous probability spread and the possibility that corresponding activation probabilities between different encoding schemes may not be equal. Under these assumptions the redundancy ratio cannot be guaranteed to increase, irrespective of whether the genes on the top or the bottom level are kept fixed. The experiments showed that the optimum number of control levels varied according to the target problem and on the maximum hidden neuron limit. The optimal number of control levels for a simple problem, the four input XOR (with a small hidden neuron limit) was two, whereas the optimal number of gene levels for a more complicated problem, the Mackey-Glass, was at least four. In addition, large hidden neuron conditions encouraged a higher optimum number of control levels.