Robust multi-objective optimization with multi-scenario coupling
Spatial equilibrium-based water resources allocation in the upper and middle reaches of the Huaihe River Basin
Jitao Zhang (Hohai University)
Jinyu Meng (Hohai University)
Zengchuan Dong (Hohai University)
Dimitri Solomatine (TU Delft - Civil Engineering & Geosciences, Water Problems Institute of Russian Academy of Sciences, IHE Delft Institute for Water Education)
Hui Xu (Hohai University)
Wenzhuo Wang (Hohai University)
Daoli Wang (Hohai University)
Tianyan Zhang (Hohai University)
Guang Yang (Nanjing Hydraulic Research Institute)
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Abstract
Optimized water resource allocation is critical for promoting sustainable regional development. However, the intensification of climate change impacts has increased the variability of water availability, thereby compounding uncertainty and complexity in water allocation decision-making. Meanwhile, mismatches in the spatial distribution of water supply and demand have also become an essential constraint to effectiveness and fairness of water allocation. Prior studies show weak correspondence between modeling frameworks to real world conditions and insufficiently describe regional balance, as well as the dynamic interaction between water inflow and demand under varying hydrological regimes. To address these challenges, this study develops a multi-objective water resource allocation model guided by spatial equilibrium principles, ensuring not only fair inter-regional allocation but also balanced co-development among water, socio-economic, and ecological subsystems. Regional balance is quantified with the Gini coefficient. Subsystem co-development is enforced via the coupling coordination degree. To address uncertainty, a nested multi-scenario robust optimization framework is proposed. It applies copula function to generate realistic encounter scenarios and applies a multi-objective probabilistic robustness evaluation to test solution stability and adaptability across scenarios. Applied to the upper and middle reaches of the Huaihe River Basin (HRB), the approach reduces the water-deficit rate by 45.42 % under extreme dry scenarios, lifts the coordination index to > 0.75, and increases reliability by 45.3 % compared with a traditional robust optimization baseline, demonstrating effectively optimize complex water resource systems while keeping both fairness and stability. This research offers a theoretical and practical framework for optimizing water resource allocation in complex and uncertain environments, contributing to the advancement of resilient and equitable water governance.