Weight space decomposition algorithms provide an intuitive and objective method for making sense of a nondominated frontier, especially for triobjective integer programs. Previous work established the weight space decomposition for supported points in the nondominated frontier (by using the weighted sum scalarization), but this leaves out many points and gives a distorted view of their value in the weight space. This motivated my work with using weighted Tchebychev scalarization for a new weight space decomposition. This results in a much more complex geometry, where convexity is lost but we found many convexity-like properties. Using this approach, we provide a dual perspective to many existing findings in the primal perspective of solving for the nondominated frontier of a triobjective integer programs. 

This work has been submitted to Journal of Global Optimization.
Guinea worm is a parasite that infects humans and many mammals via transmission through water sources. Thanks to The Carter Center's Guinea Worm Eradication Program, the countries with active infections have been reduced to just a few countries in Africa. Chad, specifically, was challenged by infections entering the dog population, where infection monitoring and control is much more difficult. We developed an agent-based simulation model to represent the life cycle of Guinea Worm and trained the multi-water source model to accurately fit regional infection data. More recent work asks which interventions should be prioritized in different regions, where equity is measured.

​This work has been published in The American Journal of Tropical Medicine and Hygiene. 
Biobjective mixed integer programming began receiving great attention beginning in 2015. Like all multiobjective optimization approaches, the goal is to find the nondominated frontier, a.k.a., the Pareto optimal frontier. Unlike purely discrete problems, however, mixed integer problems have a nondominated frontier with continuous portions. I introduced the Boxed Line Method, which remains a major competitor in this class of algorithms. Furthermore, the recursive variant of the Boxed Line Method has a linear bound on the number of IPs solved with respect to the number of line segments in the nondominated frontier. This was  the first complexity result of its kind for this class of algorithms. 

This work was published in the INFORMS Journal on Computing, and received the INFORMS Computing Society Student Paper Award.
The COVID-19 pandemic has been challenging for experts and the general public, alike. One challenge has been the deluge of infection data made available, which complicates the daily task of making sense of this data and making sound conclusions from it. To this end, I developed an interactive COVID-19 dashboard specifically for the counties of Georgia. This tool includes basic data from the Georgia Department of Public Health, but also goes further by using published ranking and prediction methods. The dashboard makes all levels of the data clear to explore, as well as the ranked risk for each of the 159 counties, and some future projections, as well. 

What else inspires me?

I write about social good applications of mathematical optimization on my medium blog.
Posts are written at an introductory level, designed for the non-expert. 
The narratives lay the groundwork for ways in which mathematical modeling and linear programming
​can be used to solve real-world problems. 


​Research
​Statement
I see the field of operations research on the cusp of a revolution in replacing single objective methods with multiobjective techniques. With these powerful tools, operations researchers can empower decision makers of all fields with making more socially responsible decisions by including social good outcomes in their optimization strategy.

My doctoral research has focused on algorithmic development for multiobjective optimization as well as applied epidemiological modeling for infectious diseases. 

My algorithmic approach to multiobjective problems is dimension-reduction in one of many ways.
  • Criterion space search methods, where each dimension represents an individual objective function, use commercial solvers as black boxes, for which constraints on one or more objectives is straightforward and efficient.
  • Weight space methods display the dual perspective of the nondominated frontier, and can be helpful in evaluating the relative value of each solution.
  • Lastly, dynamic programming uses incremental additions and reductions to the state space to search the set of all feasible solutions in an efficient manner. 

I have applied epidemiological tools to both Guinea Worm disease, which still affects portions of subsaharan Africa, as well as SARS-CoV-2, a.k.a., COVID-19. 
  • Simulation provides an experimental laboratory to answer questions about a disease that cannot be answered in the field. By using an agent-based simulation tool, I modeled the transmission of the Guinea Worm parasite through water sources in Chad and provided evidence for the environmental effects that influence the seasonality of transmission in dogs.
  • Data analysis and visualization, especially at the local level, have been critical during the current COVID-19 pandemic. I built an interactive dashboard that presented raw data as well as more advanced analysis for counties in my home state of Georgia.