Integrated Layout and Cable Routing in Wind Farm Optimal Design

We address a very important problem in offshore wind farm design, namely, the combined optimization of the turbine location and of the connection cables required to bring the electrical power produced by the turbines to a given substation, and eventually to shore. We first describe a mixed-integer linear programming model that combines previous proposals from the literature. Then we improve it by a number of additional inequalities intended to strengthen its linear programming relaxation. In particular, we propose new classes of Benders-like cuts derived from an induced-clique substructure of the problem. The validity of these cuts is established in a purely combinatorial way, without resorting to Benders's standard duality theory, and efficient separation procedures are proposed. The practical effectiveness of the proposed cuts is established through computational tests, showing that they do improve very significantly the dual bound provided by the standard model. We also present an exact branch-and-cut solver for the problem, which separates the new cuts at run time. Computational results confirm that the new cuts are instrumental for the success of our exact solver.