Optimal design of artificial neural networks by a multi-objective strategy: groundwater level predictions

Abstract

Currently, environmental modelling is frequently conducted with the aid of artificial neural networks (ANNs) in an effort to achieve greater accuracy in simulation and forecasting beyond that typically obtained when using solely linear models. For the design of an ANN, modellers must contend with two key issues: (a) the selection of model input and (b) the determination of the number of hidden neurons. A novel approach is introduced to address the optimal design of ANNs based on a multi-objective strategy that enables the user to find a set of feasible ANNs, determined as optimal trade-off solutions between model simplicity and accuracy. This is achieved in a multi-objective fashion by simultaneously minimizing three different cost functions: the model input dimension, the hidden neuron number and the generalization error computed on a validation set of data. The multi-objective approach is based on the Pareto dominance criterion and an evolutionary strategy has been employed to solve the combinatorial optimization problem. From a theoretical perspective, the choice of a multi-objective approach marks an attempt to account for, and overcome, the "curse of dimensionality" and to circumvent the drawbacks of "overfitting" that are inherent in ANNs. Moreover, it is demonstrated that the strategy renders the choice of the ANN more robust, as is evident by "unseen data" in the testing stage, since structure determination is not merely based on the statistical evaluation of the generalization performance. The methodology is tested and the results are reported in a case study relating groundwater level predictions to total monthly rainfall.

Hydrological hysteresis and its value for assessing process consistency in catchment conceptual models

“…The value of such multivariable and/or multiobjective evaluation strategies has been demonstrated in the past, for example using groundwater levels (e.g. Fenicia et al, 2008;Molénat et al, 2005, Giustolisi andSimeone, 2006;Freer et al, 2004;Seibert, 2000;Lamb et al, 1998), soil moisture (Kampf and Burges, 2007;Parajka et al, 2006), saturated-area extension (Franks et al, 1998), snow cover patterns (e.g. Nester et al, 2012), remotely sensed evaporation, (e.g.…”

Metaheuristic design of feedforward neural networks: A review of two decades of research

“…Apart from the discussed objective in this section, some interesting dimensions in multiobjective treatment to FNN can be noted in [309], in which authors proposed to apply NSGA-II for the simultaneous optimization of three objectives: input-dimension, training error, and network complexity. Hence, an optimized a network that performs well on the minimal set of input dimension was obtained.…”

Inferring groundwater system dynamics from hydrological time-series data

“…The studied groundwater system is the shallow unconfined aquifer of Brindisi (Ricchetti & Polemio, 1996;Spizzico et al, 2006;Giustolisi & Simeone, 2006, located in the northern part of the Salento Peninsula (Apulia, southern Italy). The aquifer is situated in the wide structural tectonic depression between two large calcareous blocks of the Apulian foreland calcareous platform: Murge and Salento.…”

“…(3) The availability of a set of non-dominated models (Van Veldhuizen & Lamont, 2000) in the space of possible structures defined by EPR, allows the analysis of the differences among them, thus bringing into prominence the main differences as well as the most recurring terms. The latter are more likely to be associated with the underlying physical information rather than reproducing only short-term effects (Giustolisi & Simeone, 2006;Giustolisi & Savic, 2009). …”