A Retrospective Diagnostic Framework for Multi-Objective Rule Curve Optimization of a Two-Tier Hydropower Reservoir System in Lao PDR

Multi-objective rule-curve optimization with metaheuristic algorithms is widely used to improve reservoir release decisions, yet the correctness of the underlying problem formulation is rarely verified retrospectively against actual operation. This study selected the Nam Mang 3 hydropower system in the Lao People’s Democratic Republic (Lao PDR), which pairs a main reservoir for energy production with a regulating pond that controls downstream releases. The operation model was reconstructed and verified on the design-plan operation year, on which the water balance closes with zero residual and the energy relation holds exactly, and the penalty term was recovered identically from both recorded objectives, and the problem formulation was diagnosed with a six-tool protocol, applied to the solutions of seven metaheuristic algorithms and cross-checked against the design plan and actual production records. The protocol identifies the structural conditions that must be improved before the newly developed rule curves are adopted as actual operating rules. The two tiers exhibit symmetrically opposite characteristics: the main tier is over-determined (energy spans only 0.165%, and the existing policy lies outside the search bounds at 20 of 24 positions), while the pond tier is under-determined (without constraints or a mass balance). The study proposes a complete two-tier formulation that restores the pond mass balance, release coupling, and constraints, together with six improvement criteria with verifiable numerical targets, as the basis for the subsequent optimization of regulating pond operation.