Tuning hyperparameters of a SVM-based water demand forecasting system through parallel global optimization

Recently, the number of machine learning based water demand forecasting solutions has been significantly increasing. Different case studies have already reported practical results proving that accurate forecasts may support optimization of operations in Water Distribution Networks (WDN). However, tuning the hyper-parameters of machine leaning algorithms is still an open problem. This paper proposes a parallel global optimization model to optimize the hyperparameters of Support Vector Machine (SVM) regression trained to provide accurate water demand forecasts in the short-time horizon (i.e. 24 h). Every SVM has the first 6 hourly water consumptions as input features and a specific hourly water demand as target to be predicted, among the remaining 18. The Mean Average Percentage Error (MAPE), computed on leave-one-out validation, is the black-box objective function optimized. Moreover, a preliminary time-series clustering has been applied in order to evaluate if this can improve the accuracy of the forecasting mechanism. Time-series clustering implies that the overall number of SVMs, whose hyperparameters are optimized through parallel global optimization, increases, with a SVM trained for each cluster identified and for each hourly water demand to be predicted, making even more critical a quick tuning of the hyperparameters. Results on the urban water demand data in Milan prove that forecasting error is significantly low and that preliminary clustering allows for further reducing error while also improving computational performances.