Evaluating Learn-to-Optimize Frameworks for Complex Water Resources Allocation: A Comparison Between Meta-Learning, Reinforcement Learning, and Classical Solvers

Water resources management is fundamentally concerned with ensuring reliable water supply while simultaneously protecting society from water-related hazards. In recent decades, water resources systems have faced increasing challenges due to growing human water demand and escalating hydrologic uncertainty driven by climate change and socio-economic development. Under these conditions, optimizing the operation of existing water resources system has become essential for achieving efficient and adaptive water allocation strategies capable of meeting both present and future demands. Traditional optimization approaches, including classical mathematical programming and evolutionary algorithms, have been widely applied in water resources system analysis. However, their convergence efficiency often be argued when confronted with high-dimensional, nonlinear, and strongly constrained real-world problems. Recent advances in artificial intelligence and machine learning have introduced the Learn-to-Optimize (L2O) paradigm, in which a meta-optimizer trains neural networks to learn optimization update rules rather than directly optimizing decision variables. This framework offers the potential to enhance optimization performance, particularly for complex systems. Accordingly, this study evaluates the effectiveness of three optimization frameworks: (1) a classical quasi-Newton solver, (2) a long short-term memory (LSTM)-based L2O optimizer, and (3) an L2O framework integrated with a reinforcement learning agent. Their performance is systematically compared in terms of convergence behavior, solution quality, and computational efficiency. To assess robustness across different levels of problem complexity, the three methods are tested on a simple Trid benchmark, the nonlinear Rosenbrock function, as well as a large-scale water-supply allocation problem representing the Hsinchu regional water resources system in northern Taiwan. Preliminary results indicate that classical algorithms remain highly efficient for smooth, low-dimensional benchmark functions, whereas meta-learning-based optimizers demonstrate promising advantages when addressing nonlinear and highly constrained water resources optimization problems. Ongoing experiments aim to further quantify these performance differences across problem classes in a more rigorous and systematic manner.

 

Keywords: Optimization; Artificial Intelligence; Machine Learning; Learn-to-Optimize; Long-Short-Term Memory; Reinforcement Learning