Investigation on labyrinth spillway multi-objective optimization with an emphasis on predicting discharge coefficient through different artificial neural networks

Abstract

Calculating a precise discharge capacity (Q) in a Labyrinth Spillway (LS) is of supreme importance. Discharge coefficient (Cd) plays the most critical role in LS discharge calculations. In this study, Radial Basis Function Neural Network (RBFNN), Multi-Layer Perceptron trained by Levenberg-Marquardt algorithm (MLP-LM), and hybrid MLP-Firefly-Algorithm (MLP-FA) are employed to estimate the Cd through eight predicting models. Such models are built by scrutinizing parameters affecting Cd. In addition to the standard testing approach a novel approach for assessing the interpolation accuracy of the applied Artificial Neural Networks (ANN) is presented. Comparing the outcomes of the eight models from three ANNs reveals that however MLP-LM and MLP-FA demonstrated higher performance in training and testing stages, RBFNN achieved better results in terms of interpolation accuracy, when ANNs are employed to estimate intermediate data which are not similar to either training or testing data. The best model through three ANNs is adopted for Q calculations in a Multi-objective Optimization Problem (MOP) solved by the Non-dominated Sorting Genetic Algorithm (NSGA-III). Discharge capacity and the LS concrete volume were considered as two objective functions, and the Ute dam LS was investigated as the case study. Despite higher confidence of MLP-LM in the testing stage, it reports unrealistic Q; on average, 350 m3/s and 280 m3/s higher than RBFNN and MLP-FA, respectively. Applying MOP to the Ute labyrinth spillway leads to a set of optimal designs that all are dominating Ute LS original design.