Research

Quantum control aims to manipulate quantum systems towards specific quantum states or generate desired operations. Designing highly accurate control steps is an important task in quantum computing. we study a quantum pulse optimization problem with binary controls and restricted feasible regions derived by linear constraints. We focus on the mechanistic aspects of how to apply classical optimization techniques to the problem of designing and finding solutions to a variety of control problems. We demonstrate the performance of our algorithmic framework on instances of multiple specific quantum control examples with diverse objective functions and controllers.

The COVID-19 pandemic has spread worldwide and has led to significant, unprecedented disruptions of global economy and businesses. To control the virus spread, countries impose lockdown and travel restrictions, but mainly implement them locally instead of cooperating at the global level by examining business relations across multiple regions. We study the problem of how to balance between economy and outbreak control, using a two-stage stochastic mixed-integer programming model for reopening/lockdown decision making during the COVID-19 pandemic. Our model takes into account economic activities in different regions, their profits, relations, as well as the uncertainty of future virus spread, infections and available medical resources in these regions.

The outbreak of coronavirus disease 2019 (COVID-19) has led to significant challenges for schools, workplaces and communities to return to operations during the pandemic, while policymakers need to balance between individuals’ safety and operational efficiency. We present a mixed-integer programming model for redesigning routes and bus schedules for the University of Michigan (UM)’s campus bus system, to prepare for students’ return in the 2020 Fall semester. We propose a hub-and-spoke design and utilize real data of student activities to identify hub locations and reduce the number of bus stops used in the new routes. The new bus routes, although using only 50% or even fewer seats in each bus, can still satisfy peak-hour demand in regular semesters at UM. Our approach can be generalized to redesign public transit systems with social distancing requirement during the pandemic, to reduce passengers’ infection risk.

Traffic congestion is characterised by slower vehicle speed, longer trip duration, and increased vehicular queueing on urban road networks and has grown substantially in cities of all sizes. Network-based traffic signal control plays an important role in modern transportation and can effectively mitigate congestion. We optimize traffic signal control using cell transmission model (CTM), with coordination between intersections, to maximize vehicle throughput on corridors and road networks. We study distributed algorithmic frameworks for solving the large-scale optimization model via spatial-temporal decomposition. We also consider a two-stage stochastic CTM taking into account uncertain stochastic traffic demand and turning ratio of vehicles. Numerical studies are conducted on instances generated using synthetic and real-world road networks and traffic data.