A Comparative Study of Structure-Preserving Representations for Variable-Turbine-Number Wind Farm Layout Optimization

Wind farm layout optimization is commonly studied under a fixed number of turbines, although turbine quantity is closely coupled with wake effects and power generation efficiency. This study formulates the problem as a variable-turbine-number optimization task and systematically compares three representative variable-length approaches: dimension activation/deactivation, representation mapping, and variable-length evolutionary representation. The study also investigates structure-preserving search strategies based on binary occupancy representations. The findings suggest that, for variable-turbine-number wind farm layout optimization, the effective preservation and exploitation of spatial layout structures are more critical than merely handling dimensional changes. From a fitness-landscape perspective, structure-preserving representations appear to create more coherent neighborhoods and more accessible search topologies. These properties facilitate transitions across heterogeneous turbine-number subspaces and improve search performance.