Created by W.Langdon from gp-bibliography.bib Revision:1.7758
a new methodology for representing Discrete-Time Dynamic Systems (DDS) as expression trees. The objective is the state space specification of DDSs: the behaviour of a system for a time instant t_0 is completely accounted for given the inputs to the system and also a set of quantities which specify the state of the system. This means that the proposed method must incorporate a form of memory that will handle this information.
For this purpose a number of node types and associated data structures are defined. These will allow for the implementation of local and time recursion and also other specific functions, such as the sigmoid commonly encountered in neural networks. An example is given by representing a recurrent NN as an expression tree.
a new approach to the channel equalisation problem. A survey of existing methods for channel equalisation reveals that the main shortcoming of these techniques is that they rely on the assumption of a particular structure or model for the system addressed. This implies that knowledge about the system is available; otherwise the solution obtained will have a poor performance because it was not well matched to the problem.
This gives a main motivation for applying GP to channel equalisation, which is done in this work for the first time. Firstly, to provide a unified technique for a wide class of problems, including those which are poorly understood; and secondly, to find alternative solutions to those problems which have been successfully addressed by existing techniques.
In particular, in the equalisation of nonlinear channels, which have been mainly addressed with Neural Networks and various adaptation algorithms, the proposed GP approach presents itself as an interesting alternative.",
The motivation for a parameterised GP is addressed, together with an overview of how it has been addressed by other authors. The drawbacks of these methods are highlighted: there is no established way of determining the number of parameters to use and their placement; further, unused parameters can be unnecessarily adapted while, on the other hand, useful ones might be eliminated. The way in which node gains overcome these problems is explained. An extra advantage is the possibility of expressing complex systems in a compact way, which is labelled {"}compacting effect{"} of node gains.
The costs of node gains are also pointed out: increase in the degrees of freedom and increased complexity. This, in theory, results in an increase of computational expense, due to the handling of more complex nodes and to the fact that an extra multiplication is needed per node. These costs, however, are expected to be of, at most, the same order of magnitude as those of the alternatives.
Experimental analysis shows that random node gains may not be able to achieve all the potential benefits expected. It is conjectured that optimisation of the values is needed in order to attain the full benefits of node gains, which brings along the next contribution.
a mathematical model is given for an adaptive GP. As concluded from the previous point, adaptation of the values of the node gains is needed in order to take full advantage of them. A Simulated Annealing (SA) algorithm is introduced as the adaptation algorithm. This is put in the context of an analogy: the adaptation of the gains by SA is equivalent to the learning process of an individual during its lifetime.
This analogy gives way to the introduction of two learning schemes, labelled Lamarckian and Darwinian, which refer to the possibility of inheriting the learned gains.
The Darwinian and Lamarckian learning schemes for GP are compared to the standard GP technique and also to GP with random node gains. Statistical analysis, done for both fixed and time-varying environments, shows the superiority of both learning methods over the non-learning ones, although it is not possible at this stage to determine which of the two provides a better performance.
a number of interesting results in the channel equalisation problem. These are compared to those obtained by other techniques and it is concluded that the proposed method obtains better or similar performance when extreme values (maximum fitness or minimum error) are considered.",
Genetic Programming entries for Anna Esparcia-Alcazar