Maximum Entropy Approach for Water Distribution Network Optimization

In this paper we consider a Deterministic Annealing (DA) framework for optimizing reservoir placement and associated water transport costs in Water Distribution Networks (WDNs). We introduce a capacity-constrained formulation to ensure that each junction in the network serves a limited number of demand points, preventing overload and improving system stability. Moreover, we propose update rules for secondary Lagrange multipliers corresponding to capacity inequality constraints. Finally, we extend the framework to utilize real-world pipe networks and validate our algorithm through a case study on the Modena, Italy network. Experimental results demonstrate that our DA-based method achieves lower operational costs compared to previous approach.