Research

AREAS OF INTEREST

Data-driven and Robust Optimization 

Dealing with uncertain data in mathematical models. Optimization and decision-making under uncertainty. 
 

Large-Scale Optimization and Decomposition Algorithms

Developing problem-specific decomposition-based algorithms to solve computationally intensive mathematical programming models. Designing heuristics for solving extremely large-scale applications.
 

Inverse Optimization

Inferring implicit decision-making criteria based on observed decisions. Data classification and constraint and objective inferences in structured models. Finding the optimization parameters for a given optimal solution. Robust inverse optimization with uncertain observations.
 
 
 

EXAMPLES OF RESEARCH TOPICS

Radiation Therapy Treatment Planning

Radiation therapy is one of the main treatment methods for cancer. The process of RT starts with a medical image (e.g., CT, MRI) of the patient's anatomy and computerized 3D-contours that delineate cancerous and healthy regions. The goal is to irradiate cancerous cells with high-energy radiation beams while minimizing the radiation to the healthy tissue. We use robust optimization to mitigate uncertainties in the patient's anatomical features throughout the treatment and find high-quality treatment plans that meet clinically-prescribed criteria while minimizing possible side effects. Radiation therapy optimization problems are extremely large-scale and solving them is computationally intensive. We develop specialized solution algorithms that can be employed to solve these problems efficiently. 

 

Patient Scheduling

Patients often have to wait a long time before receiving medical services of different types. This long waiting time may be of critical importance to some patients, depending on the urgency of care they need. The scheduling of patient appointments with different priority levels is therefore challenging, especially since the future arrival rates of patients and their priority levels are uncertain. We employ robust optimization to provide efficient multi-period multi-priority patient scheduling policies that aim to meet certain waiting time thresholds for patients in each priority level and minimize their excess waiting times.