Contents lists available at ScienceDirect Advanced Engineering Informatics journal homepage: www.elsevier.com/locate/aei Stream flow predictions using nature-inspired Firefly Algorithms and a Multiple Model strategy – Directions of innovation towards next generation practices R. Khatibi a, ⁎ , M.A. Ghorbani b , F. Akhoni Pourhosseini c a GTEV-ReX Limited, Swindon, UK b Water Engineering Department, University of Tabriz and Engineering Faculty; also Near East University, 99138 Nicosia, North Cyprus, Mersin 10, Turkey c Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran ARTICLE INFO Keywords: Backpropagation Firefly Algorithm (FFA) Multi-Layer Perceptron (MLP) Multiple Modelling Prediction Stream Flow ABSTRACT Stream flow prediction is studied by Artificial Intelligence (AI) in this paper using Artificial Neural Network (ANN) as a hybrid of Multi-Layer Perceptron (MLP) with the Levenberg–Marquardt (LM) backpropagation learning algorithm (MLP-LM) and (ii) MLP integrated with the Fire-Fly Algorithm (MLP-FFA). Monthly stream flow records used in this prediction problem comprise two stations at Bear River, the U.S.A., for the period of 1961–2012. Six different model structures are investigated for both MLP-LM and MLP-FFA models and their results were analysed using a number of performance measures including Correlation Coefficients (CC) and the Taylor diagram. The results indicate a significant improvement is likely in predicting downstream flows by MLP- FFA over that by MLP-LM, attributed to identifying the global minimum. In addition, an emerging multiple model (ensemble) strategy is employed to treat the outputs of the two MLP-LM and MLP-FFA models as inputs to an ANN model. The results show yet another further possible improvement. These two avenues for improve- ments identify possible directions towards next generation research activities. 1. Introduction Stream flow prediction based on deriving correlations between modelled results and recorded time-series is often one of testing grounds for newly emerging data-driven techniques. This is evidenced indirectly by Sivakumar and Berndtsson [44] presenting the outcome of an internet search on the number of hydrological publications using Artificial Neural Networks ANN) during 1990–2010. This paper is fo- cussed on investigating the integration of the Fire-Fly Algorithms FFA) developed by Yang [50] with the well-established feedforward Multi- Layer Perceptrons (MLP). Whilst ANN is quite well established in stream flow forecasting, MLP-FFA is yet to be applied. The capability for predicting flows has undergone a radical devel- opment over the years since 1960, of which one class of techniques use a type of transfer function by seeking correlation and autocorrelation between flow values at one or more sections of the same river. Whilst prediction techniques based on distributed models are precluded in this paper (from hydrological routing to those based on the Saint-Venant equations), bottom-up data-driven (or data mining) techniques have emerged over the years since the 1960s. Up to 1990, the focus was on such modelling strategies as: traditional transfer functions regression analysis or statistical methods such as ARIMA models of Auto- Regressive Integrated Moving Averages, see Box and Jenkins [3] and Makridakis and Hibon [29]. Data-driven modelling techniques have undergone a radical shift since the late 1980s as further techniques emerged based on Artificial Intelligence (AI). These include: ANN models, see Thirumalaiah [47], Eğrioğlu et al. [7], Rojas [38] ASCE TF [1]; Genetic Programming, see Koza [27], Savic [42] and Kostić et al. [25]; Genetic Expression Pro- gramming (GEP), see Ferreira [11], Khatibi et al. [20]; and fuzzy logic, see Kothari et al. [26]; as well as machine learning techniques such as SVM, see Vapnik [48] and Ghorbani [13]. Applications of these techniques for single or more stations to predict hourly, daily or monthly stream flows have been investigated and successful results have been reported. http://dx.doi.org/10.1016/j.aei.2017.10.002 Received 25 March 2017; Received in revised form 29 August 2017; Accepted 3 October 2017 ⁎ Corresponding author. E-mail addresses: gtev.rex@gmail.com (R. Khatibi), ghorbani@tabrizu.ac.ir (M.A. Ghorbani), F.Akhonipor93@ms.tabrizu.ac.ir (F.A. Pourhosseini). Abbreviations: AI, Artificial Intelligence; ANN, Artificial Neural Networks; D, downstream station; FFA, Fire-Fly Algorithm; GA, Genetic Algorithm; GEP, gene expression programming; LM, Levenberg-Marquardt algorithm; MLP, Multi-Layer Perceptron; MLP-FFA, MLP synthesised with FFA; MLP-LM, MLP synthesised with the LM algorithm; MM, Multiple Models; MM- ANN, Multiple Models, in which lower order models are driven by ANN; MM-SA, Multiple Models, in which lower order models are driven by Simple Average; MM-SVM, Multiple Models, in which lower order models are driven by SVM; R 2 , Correlation Coefficient; RMSE, Root Mean Square Error; SA, Simple Averaging; SD, Standard Deviation; MAE, Mean Absolute Error; SVM, Support Vector Machine; U, upstream station; XOR, exclusive OR gate Advanced Engineering Informatics 34 (2017) 80–89 1474-0346/ © 2017 Elsevier Ltd. All rights reserved. MARK