Retraining of metamodels for the optimisation of water distribution systems

This paper proposes the use of online retrained metamodels for the optimisation of water distribution system (WDS) design, in which artificial neural networks (ANNs) are used to replace the full hydraulic and water quality simulation models and differential evolution (DE) is utilized to carry out the optimisation. The ANNs in the proposed online DE-ANN model are retrained periodically during the optimisation in order to improve their approximation to the appropriate portion of the search space. In addition, a local search strategy is employed to further polish the final solution obtained by the online retrained DE-ANN model. Two WDS case studies are used to verify the effectiveness of the proposed online retrained DE-ANN model, for which both hydraulic and water quality constraints are considered. In order to enable a performance comparison, a model in which a DE is combined with a full hydraulic and water quality simulation model (DEEPANET2.0), and an offline DE-ANN model (ANNs are trained only once at the beginning of optimisation) are established and applied to each case study. The results show that the proposed online retrained DE-ANN model consistently outperforms the offline DE-ANN model for each case study in terms of efficiency and quality of the solution. Compared to the DE-EPANET2.0 model, the proposed online DE-ANN model exhibits a substantial improvement in efficiency, while still producing reasonably good quality solutions.Weiwei Bi, Graeme C. Dand