Application of a Heuristic Model (PSO—Particle Swarm Optimization) for Optimizing Surface Water Allocation in the Machángara River Basin, Ecuador

Efficient surface water allocation in reservoir-equipped basins is essential for balancing competing demands within the Water–Energy–Food (WEF) nexus. This study investigated the applicability of Particle Swarm Optimization (PSO) for optimizing water distribution in the Machángara River Basin, Ecuador; a complex, constraint-rich hydrological system. Implemented via the Pymoo package in Python, the PSO model was evaluated across calibration, validation, and execution phases, and benchmarked against exact methods, including Linear Programming (LP) and Mixed Integer Linear Programming (MILP). The results revealed that standard PSO struggled to satisfy equality constraints and yielded suboptimal solutions, with elevated penalty costs. Despite incorporating MILP-inspired encoding and repair functions, the algorithm failed to identify feasible solutions that met operational requirements. The execution phase, which includes reservoir construction decisions, resulted in a total penalty exceeding EUR 164.95 billion, with no improvement observed from adding reservoirs. Comparative analysis confirmed that LP and MILP outperformed PSO in constraint compliance and penalty minimization. Nonetheless, the study contributes a reproducible implementation framework and a comprehensive benchmarking strategy, including synthetic test functions, performance metrics, and diagnostic visualizations. These tools can facilitate systematic evaluation of PSO’s behavior in high-dimensional, nonlinear environments and provide a foundation for future hybrid or adaptive heuristic models. The findings underscore the limitations of standard PSO in hydrological optimization but also highlight its potential when enhanced through hybridization. Future research should explore PSO variants that integrate exact solvers, adaptive control mechanisms, or cooperative search strategies to improve feasibility and convergence. This work advances the methodological understanding of metaheuristics in environmental resource management and supports the development of robust optimization tools under the WEF-nexus paradigm.