Medal Research Group studies networked systems vulnerability, seeking to understand how networks respond to disruptions and using this knowledge to design and protect them so as to mitigate the effects of these disruptions.
We focus on modeling systems as networks and then using mathematical programming to formulate an optimization problem that estimates the vulnerability of the network.
We typically model these problems as bi-level and/or stochastic programs and design decomposition methods that take advantage of problem structure. We use this methodology for a range of applications, as detailed below.
The increasing demand for innovative designs often outpaces the rate at which new designs are developed, in part, due to the time needed to search within a vast set of alternatives, especially when evaluating alternatives requires a time-consuming experiment. Helping to accelerate the search for designs, modern sequential experimental design (SED) methods iteratively use machine learning to predict the best points to sample. This project seeks to develop new machine learning methods for optimizing configurationally complex materials, accounting for the complexity associated with conducting physical experiments.
Understanding the movement of ions through a material is crucial to understanding important properties such as radiation, stress cracking, and ion conductivity. Fundamentally, these dynamics are determined by the relevant energy barriers to ion motion. As such, in order to advance our understanding of the mechanisms of materials processes for complex systems, there is a need to determine the energy landscapes for such ionic motion. However, determining complete maps of high-dimensional landscapes is currently not computationally feasible for systems with a large number of atoms or defects, mainly because of the challenge of finding all of the energy transition states (TSs). Without all of the TSs for a system, the simulator may not be able to uncover important mechanisms that govern the dynamics of material processes.
In my dissertation, I developed models for locating and protecting facilities that are subject to disruptions caused by attacks from an adversary (i.e., interdictions) or random events (e.g., natural disasters). In my dissertation, I developed models for locating and protecting facilities that are subject to disruptions caused by attacks from an adversary (i.e., interdictions) or random events (e.g., natural disasters). Complementing my dissertation, I have done other work on designing and protecting networks. One of my Ph.D. students and I have completed a study on using fault trees to model disruptions in a supply chain. We are currently working on developing algorithms for optimizing the allocation of resources to minimize the probability that a fault occurs.
I have also used network interdiction modeling to study the vulnerability of wireless networks. Although the field of network interdiction has produced a mature set of modeling and algorithmic tools, these models and algorithms are tailored for “wired” networks, such as supply chains and road networks, and not for wireless ones. Thus, there is a need to extend the concept of interdiction modeling to the wireless domain.
Networks can also be a useful way of modeling the spread of a wildfire. A landscape can be divided into cells and the midpoints of the cells form the nodes of the network. Arcs connect nodes to their neighbors and the weight on an arc represents the time a fire takes to travel between nodes, based on landscape and weather characteristics. Thus, we have applied network interdiction to the problem of allocating resources to a landscape prior to a fire in order to prevent fire outbreak.
My first foray into cyber security was a study of how to control virus outbreaks within a network. There has been a considerable amount of work done on how contagion spreads through a network; however, there is been much less work on how to design control strategies based on a network’s topology.
One of my former students, Aaron Hoskins, and I have done some work on using optimization to improve the ability of satellites to monitor an event (e.g, a wildfire). We developed several different stochastic programming models for locating ground stations that download data from satellites (Hoskins and Medal, 2019) and optimizing the orbital parameters of a constellation of satellites (Hoskins and Medal, 2017). Extending the work of Hoskins and Medal (2017), which only considered data collection during the ascending pass of a satellite’s orbit, we also developed a model for collecting data during both the ascending and descending passes (Hoskins and Medal, 2020).
I have done a bit of work on optimizing the design of transportation networks, mostly under the theme of usability. In a project funded by the U.S. Department of Transportation, we examined how to optimally retrofit a transportation network to make it more pedestrian-friendly (Rashidi et al., 2016). To accomplish this, we formulated an optimization model for optimally allocating limited resources to different traffic calming actions such as adding sidewalks and crosswalks. In another paper, we developed a model for designing a transportation network to make it more accessible to pedestrians (Li, Medal, and Qu, 2019).