My research is concerned with using mathematical optimization to provide guaranteed optimal or near-optimal solutions for important classes of large-scale discrete nonlinear optimization problems arising in engineering applications. Conic optimization is a highly successful tool to obtain high-quality solutions to hard engineering optimization problems. My research in this area is primarily concerned with improving models and algorithms for the application of conic optimization to solving facility layout problems and computing optimal power flows in electricity grids.
In particular, mathematical optimization can help to improve the overall performance of the electric power system, which is of critical importance to our society. I am working to support the development of smart grids. A smart grid combines a traditional electrical power production, transmission, and distribution system with a two-way flow of information and energy between suppliers and consumers.
- how to use the existing network more efficiently?
- how to incorporate renewable energy such as wind and solar?
- when to store energy until it is needed?
- how to include customers as active participants in the system operation?
As a service to the community, I host three benchmark datasets: QAPLIB (still challenging), FLPLIB, and the Jones Benchmark.