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 step-wise 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 aimed. A special-purpose neighborhood search heuristic wraps the formulations in order to increase tractability and effectiveness compared to the full model. The heuristic iteratively searches 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 velocity deficit as objective is a functional approach, since high-quality solutions of an annual energy production metric are found. Furthermore, the proposed heuristic is able to match and in some cases improve the results obtained when considering the turbine positions as continuous variables.