A Transferable Sensitivity-Analysis Protocol for Evolutionary Multi-Objective Optimisation in Surrogate-Based Engineering Design: Validation on Synthetic Benchmarks and Enclosed Screw Conveyors

Applied engineering studies that use evolutionary multi-objective optimisation (MOO) rarely report confidence bounds on the Pareto-optimal solutions they recommend. This paper presents a four-stage sensitivity-analysis protocol that supplies them: cross-algorithm benchmarking, Friedman and Bonferroni-corrected Wilcoxon testing, hyperparameter sensitivity analysis, and ISO/IEC GUM-compliant uncertainty propagation. The protocol is first validated on the ZDT1, ZDT3 and DTLZ2 benchmarks (n = 2–12 decision variables), then demonstrated on an enclosed screw-conveyor design using Discrete Element Method (DEM) surrogates built by Response Surface Methodology (RSM). On the benchmarks, it correctly identified both algorithmic equivalence (MOGA and NSGA-II indistinguishable on four of five instances) and MOEA/D’s characteristic weakness on the disconnected ZDT3 front, whose hypervolume degraded most with dimensionality. For the engineering case, MOGA matched NSGA-II (p = 0.47–0.79) and remained within 0.5% hypervolume of SMS-EMOA over 12 runs, while hyperparameter variation stayed below 1% (max CV = 0.962%). DEM achieved 8.2% mean absolute percentage error for mass flow rate across 42 CCD operating conditions. The MOGA-optimised 100 mm pitch (4.86°, 138.86 rpm) delivered 0.416 kg/s at 6.95 N·m, a specific energy consumption of 0.0675 kWh/tonne and a 63.0% reduction against the 75 mm baseline.