Evolving Neural and Fuzzy Systems - Computational Intelligence in Time Series Forecasting - page 305

by Stork et al . (1990). A series of improvements followed, the most interesting of
them being the achievement of Hwang et al . (1997) in evolving the network
topology, connection weights, and the node transfer function simultaneously.
8.1.1.6 Application Examples
Evolved neural networks have found a wide application in time series forecasting,
because the network evolutionary process has contributed the network structure
and the network parameters (connecting weights, activation functions, hidden
nodes, etc .) that are optimal. The only difficulty that accompanies the application
of such networks is the selection of the optimal initial population that will
guarantee the shortest search time. To reduce it's influence on the problem at hand,
Prudencio and Ludermir (2001) have advocated using the case initialized genetic
algorithm (Louis and Johnson, 1999), based on experience in optimizing the
solution of some similar problems. The solution concept was applied to the
problem of river flow prediction, where the time series models NARX (Nonlinear
Auto-Regressive model with eXogenous variables and the NARMAX (Nonlinear
Auto-Regressive Moving Average model with eXogenous variables) have been
employed. In the models, the following parameters have been optimized: length of
time window, length of context layer, and the number of hidden layers. The
network was trained with the Levenberg-Marquardt method (Marquardt, 1963).
The objective of the case study was to forecast the monthly river flow of a
hydrographic reservoir, based on 144 available flow values acquired within a
period of 12 years. During the experiments, about 20 neural network architectures
were developed in order to find the best one. The software system developed,
although tailored for forecasting purposes, is suitable for application in other
problem classes.
8.1.2 Evolving Fuzzy Logic Systems
In evolving fuzzy logic systems, two principal decisions should be made:
x selection of the fuzzy rule base that could be considered as the most
promising one to solve optimally the given problem and the selection of
strategy for their genetic encoding
x definition of membership function parameters.
Optimal definition of membership functions to be used in the process of systems
evolution is also a crucial problem here that, to be well-solved, needs much skill
and computational efforts. This is because the performance of the system to be
developed is very sensitive to the shapes of the membership functions. The early
proposals on how to manage these problems (Shao, 1988) did not bring a
significant success in performance improvement, until it was recognized that for
solving this problem the optimal parameter tuning of membership function shape
should be used, for instance by being carried out using an evolutionary algorithm.
Tettamanzi (1995) has proven that the integration of evolutionary algorithms and
fuzzy logic could cover the following application fields: