Exploiting Hardware and Software Advances for Quadratic Models of Wind Farm Layout Optimization

A key aspect of the design of a wind farm is the wind farm layout optimization (WFLO) problem: given a wind farm site and information about the wind patterns, the problem is to decide the location of individual wind turbines to maximize energy production subject to proximity restrictions and wake-based interference between turbines. Given the pairwise wake interactions, it is natural to model the energy objective as a quadratic function as, indeed, has been done in some existing optimization approaches. However, state-of-the-art solutions often trade-off between speed in producing designs and quality in terms of finding and proving optimal solutions. In this work, we aim to find a balanced approach to obtain WFLO solutions quickly for interactive design and solve the problem to optimality when quality is more important. To this end, we exploit recent advances in optimization hardware and software that target quadratic constraints: commercial mixed integer linear solvers have been extended to address some quadratic problems and nascent specialized hardware, including quantum computing systems, have focused on solving quadratic unconstrained binary optimization (QUBO) problems. We introduce two novel quadratic programming models for WFLO: a quadratic constrained optimization problem (QCOP) with binary decision variables and a QUBO. A thorough numerical evaluation using a commercial solver and specialized QUBO hardware show that our quadratic framework achieves fast, high-quality solutions that improve the state of the art and strike a balance between speed and quality. In particular, the QUBO model delivers high quality solutions in a few seconds while the QCOP model can be used to find better solutions and provide quality guarantees over a longer run-time.