Efficient k-means clustering and greedy selection-based reduction of nodal search space for optimization of sensor placement in the water distribution networks

Monitoring of water distribution network (WDN) requires placement of sensors at strategic locations to detect maximum contamination events at the earliest. The multi-objective optimization (MOO) of sensor placement is a complicated problem owing to its combinatorial nature, interconnected and large WDN sizes, and temporal flows producing complex outcomes for a given set of contamination events. In this study, a new method is proposed to reduce the complexity of the problem by condensing the nodal search space. This method first segregates the nodes based on intrusion events detected, using k-means clustering, followed by selecting nodes from each group based on the improvement observed in the objectives, namely, contamination event detection, expected detection time, and affected population. The selected nodes formed the decision variable space for the MOO study. The developed strategy was tested on two benchmark networks: BWSN Network1 and C-town network, and its performance is compared with the traditional method in terms of hypervolume contribution rate (CR) indicator and the number of Pareto points. The optimal subset of nodes generated twice the number of Pareto points than the complete set of nodes set for placing 20 sensors and had 10% more than CR indicator than the traditional method. For the placement of 5 sensors, the proposed solutions were better at the higher detection likelihood values, which is required to achieve maximum detection. The proposed sensor placement algorithm can be easily scaled to large WDNs. It is expected to provide a better optimal sensor placement solution irrespective of network size as compared to the traditional approach.