[Executive Summary]This project explores the integration of advanced shape optimization techniques within river engineering to address the dual challenges of flood risk management and ecological preservation. As climate change intensifies extreme weather events, traditional hydraulic designs often fall short. Our research leverages computational fluid dynamics (CFD) and mathematical optimization to derive river geometries that maximize discharge capacity while minimizing environmental disruption. [Key Research Topics]Adjoint-Based and Heuristic Optimization: Utilizing the adjoint method and genetic algorithms to automatically determine the ideal cross-sectional profiles of low-water channels and floodplains to mitigate water level rise and prevent local scouring. [Conclusion] Shape optimization represents the frontier where civil engineering, computational science, and ecology meet. This project aims to bridge the gap between theoretical fluid mechanics and practical river management, offering a sophisticated toolkit for the next generation of resilient infrastructure.