sparse Jacobians, sparsity, gradients, optimization, wind farm layout, graph coloring


Optimizing wind farm layouts is an important step in designing an efficient wind farm. Optimizing wind farm layouts is also a difficult task due to computation times increasing with the number of turbines present in the farm. The most computationally expensive part of gradient- based optimization is calculating the gradient. In order to reduce the expense of gradient calculation, we performed a study on the use of sparsity in wind farm layout optimization. This paper presents the findings of the sparsity study and provides a method to use sparsity in wind farm layout optimization. We tested this sparsity method by optimizing multiple farms with sparse methods and compared the results to optimizations of the same farms using traditional methods. By using the sparse method to optimize multiple farms, we found that the objective results were comparable between sparse and traditional methods and that sparse methods were 4 times faster than traditional methods on average. We expect more speedups with improved methodology and larger wind farms. By using sparse methods, it is possible to solve the wind farm layout optimization problem more efficiently, thus allowing for a more thorough study of the wind farm layout design space without excessive computational costs. Further work is required to refine the method and prepare for testing on real-world wind farm layout applications.

Original Publication Citation

Varela, B. T. and Ning, A., “Sparsity for Gradient-Based Optimization of Wind Farm Layouts,” AIAA SCITECH Forum, National Harbor, MD, Jan 2023. doi: /10.2514/6.2023-1543

Document Type

Conference Paper

Publication Date







Ira A. Fulton College of Engineering


Mechanical Engineering

University Standing at Time of Publication

Associate Professor