Dr. Li’s research focuses on new search method to solve the traveling salesman problem (TSP). More specially, this new method uses multi-start local search to construct the solution attractor, search all solutions in the attractor, and then identify the globally optimal solution. He has used this method to tackle classic TSP, multi-objective TSP, dynamic TSP, and probabilistic TSP.
My interests are in personalized medicine with a focus on optimization of screening and treatment decisions for chronic diseases. This work has been funded by the National Science Foundation, the Agency for Healthcare Research and Quality, and other funding sources. This work involves the use of very large data sets comprising longitudinal data from electronic medical records and healthcare claims data. Screening and treatment optimization models are computationally challenging, owing to large state spaces caused, in part, by the dependence on the patient medical history, the large number of risk factors for chronic diseases, and the growing number of genetic screening tests and medications for treatment. I study several variants of stochastic optimal control problems for screening and treatment of diseases. For instance, in the context of diabetes I study optimal treatment policies for cholesterol, blood pressure, and blood sugar control medications. In the context of prostate cancer I have studied properties of the optimal policy for screening using biomarkers based on partially observable Markov decision processes. My research seeks to establish useful structural properties of optimal policies that can be exploited to achieve computational advantages, and insights that motivate understanding of the clinical decision rules. The computationally challenges that arise has motivated my work on exact and approximation methods for solving multi-stage stochastic programs and stochastic dynamic programs. Most recently I have been investigating robust optimization approaches that account for uncertainty or ambiguity in model parameters and model assumptions. Several chronic diseases have been test-beds for my research including: bladder cancer, diabetes, heart disease, and prostate cancer. I have selected these because they are among the diseases having the greatest impact on the U.S. population and they bring together characteristics of many chronic diseases creating the opportunity for broader impact through the development of generalizable solution methods.