My research interests
Data-driven decision-making under uncertainty, modeled by two-stage stochastic optimization, is my main academic interest both in theory and practice. For this, I take on relevant societal and environmental problems and formulate them as data-driven mathematical optimization models. Specifically, I am interested in chance-constrained optimization: such models cater to the design of resilient systems under extremely high risk of damage. I am interested in designing algorithms to solve such stochastic programs. My particular motivation is critical risk management during disasters, especially in energy systems and governmental response to pandemics. A unique element is modeling subjective human behavior within the decision-making process.
Several European countries are investing on renewable energy sources.
Climate change goals
As countries head towards Net-Zero Strategies or the Energiewende, joint chance constraints are especially suitable to ensure highly reliable operations of critical energy systems where there is an uncertain availability of renewables. Examples include, photovoltaic (PV) systems systems and coupled wind-diesel systems. Mathematical optimization models that formulate such systems are typically challenging to solve (both due to their structure and size) requiring novel algorithmic approaches. In my works, we have designed iterative algorithms towards their solution or employed Lagrangian-based heuristics: see here and here. (click for more)
At Sandia National Labs, US (2016-19), I worked on solving large-scale energy system models motivated by critical risks faced by the US electrical grid. Several of my works are available on the US Department of Energy's Office of Scientific and Technical Information's website here. At FAU, Germany (2019-22), I led the chair's efforts in the multi-institute ``METIS'' research collaboration with the Jülich Research Center. This project seeks to develop open-source tools for optimizing large scale energy system models under the German Energiewende (transition towards clean-fuel yet reliable energy suppliers). See more about the project, here, and technical details, here.
Waste management
Recently, perhaps inspired by public policy in Germany, I have become interested in waste-management. I supervised two talented students on this subject for their theses (resulting in an article published in IJOC, a follow-up in Networks, and another in-review). Recycling centers (Wertstoffhöfe) - places where populations must travel to dispose certain recyclable waste - are important for meeting sustainability goals, however they also cause pollution and public nuisance. Consequently, governments are closing these down. How should we make such decisions fairly? Currently, I am working with a postdoctorate researcher on quantifying the subjective opinions populations have towards recycling campaigns. In our ongoing works, supported by the Bavarian State Ministry for Science and Arts and the University of Southampton, we design discrete optimization models that achieve this: see here. (click for more)
Theoretically, we define new axioms of fairness. Mathematically, this leads to new classes of facility location problems that have interesting mathematical properties related to their KKT optimality conditions. Computationally, they are intractable to solve naively and we design specialized algorithms for their solution. They provide a wide impact to society enabling ethically fair closures of such facilities without hindering public accessibility. See here, here, and here.
The Bavarian government is shutting down recycling centers in the past two decades.
The system of staged lockdowns used by Austin, Texas during the COVID-19 pandemic designed by our collaborative work.
Pandemic risk management
I began collaborating with the Texas Department of State Health Services, US as a MSc student in 2012, preparing them for future pandemics way-before the COVID-19 pandemic. During my PhD, motivated by Texas' response to the 2009 H1N1 pandemic, we designed a series of web-based optimization-backed decision-support tools for the government: https://flu.tacc.utexas.edu. These help the state in fair and efficient allocations of critical resources such as antivirals and vaccines. (click for more)
During the COVID-19 pandemic, we reinitiated this collaboration. We measured the reach of COVID-19 testing throughout the US, and most notably also designed the staged-dashboard lockdown system that was employed by the City of Austin, see left (this system too employs a chance constraint). I am currently a recipient of a 3-year grant by the Deutsche Forschungsgemeinschaft (German Research Foundation) on this subject. Jointly, I published several works on pandemics and optimization, see, e.g., here, here, and here.
Union bounds and chance-constrained optimization
This is a purely theoretical interest. I am interested in viewing joint-chance constraints as union of sets, and bounding these using classical probability theory, see right. Bounding the probability of the union of n events by joint probabilities of k < n events has been studied extensively since the time of Boole and Bonferroni. (click for more)
Interestingly, when these bounds are used in an optimization model constrained by the chance constraint, we obtain corresponding upper and lower bounds on the optimal objective function value. My interest here started during my PhD, but my independent direction began with my first major grant as a PI during my time at Sandia National Labs, US (2018). See, two of my published works on this particular topic: here and a follow-up here. Currently, we are extending this with my PhD student.
Satisfying a joint chance constraint is an intersection of "successes".
