A balance-aware geometric multi-objective evolutionary algorithm for offshore wind farm layout optimization with capacity dependent cable cost evaluation

Offshore wind farm layout optimization involves a fundamental trade-off between energy production and investment cost, as turbine locations affect both wake losses and the cable requirements of the electrical collection system. The resulting aero-electrical coupling gives rise to a complex and heterogeneous optimization landscape. However, in many existing studies, the cost of the electrical collection system is often assessed only after the layout has been determined, thereby limiting its influence on the layout optimization process. This paper proposes a balance-aware geometric multi-objective evolutionary algorithm (BaGMOEA) for offshore wind farm layout optimization with the objectives to maximize annual energy production (AEP) and minimize capital expenditure (CAPEX), where the CAPEX includes capacity dependent cable cost evaluation. The proposed approach integrates balance-aware environmental selection and geometry-guided variation operators within a unified aero-electrical evaluation framework, enabling the preservation of spatial layout structures while maintaining balanced diversity during evolutionary search. Experiments on eight offshore wind farms demonstrate that BaGMOEA consistently improves Pareto-front coverage and convergence behavior. Ablation studies further indicate that the integration of these two operators improves search behavior and solution quality in large-scale offshore wind farm optimization.