Optimal and Phasing Design of Water Distribution Networks in View of Demand Uncertainty

Water distribution networks (WDNs) are critical infrastructure systems that must balance cost-efficiency and reliability while adapting to evolving water demand. A significant challenge in designing WDNs lies in addressing future demand uncertainties caused by factors such as population growth, urbanization, and climate change. This study presents a single-objective optimization framework focused on minimizing the investment cost of network pipes while ensuring system reliability, measured by the Network Resilience Index. A penalty function is integrated into the objective function to validate feasibility by satisfying minimum head requirements at all nodes.

A key feature of the proposed approach is the incorporation of phasing design, which allows for the gradual expansion of the network in alignment with projected demand growth. Phasing design ensures that infrastructure investments are staged strategically, reducing upfront costs and preventing overdesign in the early stages. This approach also provides flexibility, enabling network upgrades to be planned and executed in response to evolving demand patterns. By optimizing each phase, engineers can design a system that balances immediate needs with long-term goals, ultimately minimizing costs while maintaining reliable service.

To address demand uncertainty, a probabilistic model is employed, representing growth rates as discrete random variables with assigned probabilities. This approach enables the consideration of multiple demand scenarios across all phases of the network's lifecycle. By evaluating a range of potential future conditions, the methodology ensures robust performance under various scenarios, enhancing the network's adaptability.

Optimization is conducted using advanced algorithms, specifically Differential Evolution (DE) which is well-suited for complex nonlinear problems. The framework is validated using two benchmark problems: the Two-Loop Network (TLN). Results demonstrate that the phasing design approach, coupled with probabilistic demand modeling and advanced optimization techniques, produces cost-effective and reliable solutions.

This study highlights the critical role of phasing design in ensuring efficient resource allocation, flexibility in network development, and robustness against future uncertainties. By incorporating demand uncertainty and leveraging optimization techniques, the proposed framework supports the sustainable development of WDNs, providing a practical tool for engineers to address the dual challenges of cost minimization and reliability in real-world applications.

Keywords: Water distribution network; Phasing design; Differential evolution; Demand uncertainty; Network Resilience Index