Due to the complexity in the design of hybrid PVT-SAH system with fins and a lack of guideline for optimal design of the system. This work is undertaken to develop a multi-objective design optimisation strategy to simultaneously maximise the conflicting outputs of the useful thermal energy generation and net electricity gains. The Taguchi method with analysis of variance (ANOVA) is first used to design the simulation exercises and identify the non-significant system parameters to reduce the optimisation size. The multi-objective design optimisation problem is then formulated to determine optimal values of the key design parameters identified. A decision-making method using TOPSIS is further used to determine the final optimal deign from the set of Pareto fronts generated. The sensitivity analysis reduced the number of parameters from twelve to seven and revealed that the material parameter and the thickness of construction components are non-sensitive to the performance of the PVT-SAH. The final determined optimal design can increase both useful thermal energy and net electricity gains under the conditions of this study by 21.9% and 20% respectively over a chosen baseline design and by 24.7% and 126% respectively in comparison to a second chosen baseline design. To make the optimisation results more generic and useful, an uncertainty study was also conducted and the results showed that the optimal design of the PVT-SAH system c an offer the robust performance over a wide range of climate conditions and roof scenarios. Within the boundaries of the uncertainty analysis, the useful thermal efficiency ranged from 48.8% to 56.9% while the change of net electrical efficiency was less than 1.0%.