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M. P. Cuéllar (Universidad de Granada, Spain), Miguel Delgado (Universidad de Granada, Spain) and M. C. Pegalajar (Universidad de Granada, Spain)

DOI: 10.4018/978-1-59904-849-9.ch168

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TopMulti-objective algorithms have become popular in the last years to solve the problem of the simultaneous training and topology optimization of neural networks, because of the innovations they can provide to solve it. Certain authors have addressed this problem through the evolution of single ensembles as for example with DIVACE-II (Chandra et al., 2006), which also implements different levels of coevolution. In other works, the networks are fully evolved and the evolutionary operators are designed to deal with both training and structure optimization. Some authors have addressed the problem of the structure optimization attending to reduce either the number of network neurons or either the number of network connections. In the first methods (Abbass et al., 2001; Delgado et al., 2005; González et al., 2003), the optimization is easier since the codification of a network contains a smaller number of freedom degrees than the last methods; however, they have a disadvantage in the sense that the networks obtained are fully connected. On the other hand, the methods in the second place (Jin et al., 2004; Cuéllar et al, 2007) attempt to reduce the number of connections but it is not ensured that also the number of network nodes is also minimum. Nevertheless, experimental results have shown that the networks obtained with these proposals have a low size (Jin et al, 2004).

Multi-Objective Optimization: Optimization of a problem that involves the satisfacibility or optimization of two or more objectives, sometimes opposed each other.

Dynamical Recurrent Neural Networks: Artificial neural network that include recurrent connections in the network structure. They are capable to process patterns with undetermined size and/or indexed in time. The output in these networks at time t+1 are computed using the network inputs at time t and the network state, provided by the recurrent connections.

Time-Series Prediction: Problem that involves the prediction of the future values of a time series, considering a few values from the data set in the past.

Evolutionary Algorithm: Optimization algorithm based on Darwinian nature evolution.

Regularization: Optimization of both complexity and performance of a neural network following a linear aggregation or a multi-objective algorithm.

Ensembles: Self-containing area of a neural network (neuron, connection, set of a neuron with connections...) that, being combined with other ensembles, is able to build a neural network that solves a problem.

Time-Series: Data sequence indexed in time.

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