A neighborhood search integer programming approach for wind farm layout optimization

Abstract. Two models and a heuristic algorithm to address the wind farm layout optimization problem are presented. The models are linear integer programming formulations where candidate locations of wind turbines are described by binary variables. One formulation considers an approximation of the power curve by means of a stepwise constant function. The other model is based on a power-curve-free model where minimization of a measure closely related to total wind speed deficit is optimized. A special-purpose neighborhood search heuristic wraps these formulations with increasing tractability and effectiveness compared to the full model that is not contained in the heuristic. The heuristic iteratively searches for neighborhoods around the incumbent using a branch-and-cut algorithm. The number of candidate locations and neighborhood sizes are adjusted adaptively. Numerical results on a set of publicly available benchmark problems indicate that a proxy for total wind speed deficit as an objective is a functional approach, since high-quality solutions of the metric of annual energy production are obtained when using the latter function as an substitute objective. Furthermore, the proposed heuristic is able to provide good results compared to a large set of distinctive approaches that consider the turbine positions as continuous variables.