Robust multi-objective wind farm layout optimisation under per-turbine cost uncertainty

Per-turbine construction and O&M costs are universally treated as deterministic in wind farm layout optimisation (WFLO), despite documented UK onshore LCOE uncertainty of GBP 35–62/MWh and turbine fatigue load variation of up to 25% across positions. This paper addresses that gap by proposing a multi-objective robust WFLO framework applied to the Kelmarsh Wind Farm (UK) as a wind resource and turbine characterisation data source. A Gaussian Mixture Model (GMM) with BIC-optimal K = 4 component selection characterises 6 years (2016–2021) of SCADA wind climatology; Gaussian Process (GP) regression with statistical outlier removal constructs wake-corrected power curves validated across all six Senvion MM92 turbines (R 2 = 0.977–0.994). Box and Ellipsoid uncertainty sets are embedded within an NSGA-II Pareto backbone and benchmarked against classical GA and deterministic NSGA-II on identical inputs. On an 81-position design domain, the robust Box model (ε = 0.10, Γ = 2) selects 57 turbines and achieves a mean AEP improvement of 5.28% ± 0.66% over NSGA-II at identical cost (USD 3.3 × 10 7 ), confirmed statistically significant at p < 0.01 (Wilcoxon signed-rank test, 10 independent runs; W = 0) which corresponding to approximately 1.0–1.2 GWh/year additional generation and an indicative LCOE reduction of GBP 2.3/MWh against the Arup/DESNZ 2024 UK baseline. The AEP gain is non-monotone in the conservatism budget Γ, with a site-specific interior optimum at Γ = 2. The Box formulation achieves this within the same O(N·M 2 ) scalability as standard NSGA-II at only 1.3× computational overhead, offering a tractable path to deployment on large offshore wind farms.