Reproducible Multi-Objective Metaheuristic Optimisation of a Physics-Informed Surrogate for Grid-Coupled PEM Electrolysers: NSGA-II Pareto Front, Rolling-Horizon Dispatch, and Conformal Uncertainty Quantification

Operating-point recommendations for proton exchange membrane (PEM) water electrolysers under variable renewable input require reproducibility evidence sufficient for project finance and dispatch latencies compatible with rolling-horizon control. Existing surrogate-driven optimisation pipelines satisfy neither requirement consistently: scalarised single-algorithm metaheuristics return solutions whose reproducibility cannot be assessed across the individual decision-objective components, and deterministic surrogate evaluations expose recommendations to heteroscedastic prediction error in the sparsely-trained operating envelope without uncertainty discounting. This paper develops a unified surrogate-driven optimisation, dispatch, and uncertainty-quantification pipeline that addresses both shortcomings simultaneously. A voltage-targeted physics-informed neural network (PINN) trained on 1,200 PEM operating records serves as the inner-loop surrogate. Five population-based metaheuristics — particle swarm optimisation (PSO), grey wolf optimiser (GWO), whale optimisation algorithm (WOA), honey badger algorithm (HBA), and NSGA-II — are compared on the bi-objective (𝐻2 , SEC) problem. The NSGA-II non-dominated set collapses to two points along an SEC-saturated 𝐻2 ridge at the surrogate’s lower-voltage feasibility bound, exposing a structural feature of the trained surrogate that any deployment must account for. A per-component coefficient of variation (CV) reproducibility diagnostic is introduced and shown to detect algorithm-dependent multimodality that the scalarobjective CV does not: under a 24-hour rolling-horizon dispatch case study driven by measured NASA POWER irradiance for Walvis Bay (Erongo Region, Namibia) on 15 January 2025, the per-component CV(𝐻2 ) crosses 10% at 58 of 96 dispatch intervals (60%), with the per-algorithm exceedance counts ranging from 2 (NSGA-II) to 58 (GWO), while the scalar-objective CV remains below 1% throughout for PSO, WOA, and NSGA-II. A sensitivity analysis on the scalarisation weights (𝑤SEC, 𝑤𝐻2 ) over a 9 × 9 grid identifies the narrow weight band 𝑤𝐻2 ∈ [0.5, 0.6] as operationally robust at the 5% threshold. Split-conformal prediction wrappers calibrated on the validation partition produce 90% prediction intervals (𝑞𝛼 = 0.249 V, mean locally-weighted width 0.510 V) with empirical coverage 0.911 on the held-out test set. The conformal-discounted optimisation reroutes the WOA recommendation from the deterministic boundary point (𝑗, 𝑇 ) = (1.23 A cm−2 , 403 K) to a non-saturating interior point (1.80 A cm−2 , 314 K) that simultaneously increases nominal hydrogen production by 47% and reduces the worst-case voltage uncertainty by 85% — a strict Paretoimprovement that turns the conformal extension into a corrective for boundary-saturated deterministic optima. The combined pipeline is identified as the methodologically defensible approach for surrogatedriven PEM dispatch under variable renewables, with direct application to hyper-scale projects in Namibia and other renewable-rich African settings targeting levelised hydrogen costs of USD 1.50– 2.00 per kilogram.