Optimization of Water Quantity Allocation in Multi-Source Urban Water Supply Systems Using Graph Theory

The optimization of urban multi-source water supply systems is essential for addressing the growing challenges of water allocation, cost management, and system resilience in modern cities. This study introduces a graph-theory-based optimization model to analyze the structural and operational dynamics of urban water supply systems, incorporating constraints such as water quality, pressure, and system connectivity. Using Lishui City as a case study, the model evaluates three water allocation plans to meet the projected 2030 water demand. Advanced algorithms, including Floyd’s shortest path algorithm and the GA-COA-SA hybrid optimization algorithm, were employed to address constraints such as pipeline pressure, water quality attenuation, and nonlinear flow dynamics. Results indicate a 1.4% improvement in cost-effectiveness compared to the current allocation strategy, highlighting the model’s capability to enhance efficiency. Among the evaluated options, Plan 2 emerges as the most cost-effective solution, achieving a supply capacity of 4.5920 × 105 m3/d with the lowest annual cost of 5.7015 × 107 yuan, highlighting the model’s capability to improve both efficiency and resilience. This study prioritizes cost-efficiency tailored to regional challenges, distinguishing itself from prior research that emphasized redundancy and water quality analysis. The findings demonstrate the potential of graph-theoretic approaches combined with advanced optimization techniques to enhance decision-making for sustainable urban water management.