Novel Spanning-Tree Matrix Approach to Model and Optimize Large-Scale Tree-Shaped Water Distribution Networks

This study introduces the Spanning-Tree Matrix Approach, a novel computational method for modeling large-scale, tree-shaped water distribution networks. The method focuses on minimizing network cost while satisfying hydraulic design constraints. A case study demonstrated the integration of this approach with the Honey-Bee Mating Optimization algorithm to determine the optimal combination of pipe diameters. Results confirm the model’s effectiveness and scalability for tree-shaped network configurations. The Spanning-Tree Matrix Approach is also versatile—it can accommodate various governing equations and design criteria, and can be easily embedded in modern stochastic optimization algorithms such as Genetic Algorithms, Simulated Annealing, and Ant-Colony Optimization. Due to its adaptability and simplicity, further research is encouraged to apply this approach to other spanning-tree hydraulic systems, including waster water networks, river or groundwater networks.