A multi-objective optimization framework for wave farm design: Balancing coastal protection and energy output

• Multi-objective optimisation of wave farms for coastal protection and energy. • Optimisation framework integrates Delft3D, surrogate modelling, NSGA-II, and SHAP analysis. • Surrogates trained on 36 runs predicted energy and wave attenuation. • NSGA-II identified Pareto-optimal designs balancing energy and protection. • SHAP showed spacing influences attenuation, rows and distance influence energy. Wave farms are increasingly being proposed as dual-purpose infrastructure that provides both renewable energy and coastal protection. However, the optimal design for one objective often conflicts with the other, and existing studies lack a systematic framework to quantify and balance these trade-offs. This study develops and demonstrates a novel multi-objective optimization framework that integrates process-based numerical modelling, machine learning surrogates, and evolutionary optimization. A coupled depth-averaged (2DH) hydrodynamic and spectral wave model (Delft3D) was used to simulate 36 wave farm configurations defined by inter-device spacing, number of rows, and distance from the shore. From these simulations, surrogate models were trained to predict wave attenuation and energy production. The surrogates reproduced the simulations with high accuracy and were embedded in the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to identify Pareto-optimal designs. Model interpretability was achieved using SHapley Additive exPlanations (SHAP), which quantified the influence of each design parameter on system performance. Results showed a clear divergence between designs that maximize attenuation (dense, nearshore arrays) and those that maximize energy yield (offshore, wider-spaced arrays). The optimization identified two distinct non-dominated solutions within the discrete design grid, while SHAP analysis explained the physical drivers behind this trade-off. This study represents the first integration of Delft3D simulations, machine learning surrogates, NSGA-II optimization, and SHAP analysis for dual-purpose wave farm design. The framework is computationally efficient, transparent, and transferable, providing a pathway for future site-specific applications and for extending assessments to include morphodynamic and multi-directional wave forcing.