My research is on the design of efficient (approximation) algorithms for combinatorial optimization problems. I work on deterministic optimization models, as well as richer models that handle uncertainty in data: stochastic, robust and online optimization. I am also interested in algorithms for scheduling and energy-efficiency in data centers.
The research of Shen’s group covers the following aspects that are closely related to data science and decision making.
- We develop modeling techniques and computational paradigms for complex service systems that incorporate a variety of information and decisions. We design risk optimization approaches that are capable of handling integrated system design and service operations with multiple resources, multiple stages of service, and multiple stakeholders with diverse decision preferences under data uncertainty.
- We develop new decomposition paradigms for stochastic integer programming models. We focus on two-stage stochastic integer programs, and advance decomposition paradigms based on special structures of specific risk-averse programs, and also based on special integer-programming structures. We have implemented the related approaches in a series of research projects that optimize stochastic problems of (i) project management, (ii) resource allocation, (iii) appointment scheduling, and (iv) network interdiction. Moreover, the new decomposition paradigms can be widely applied to large-scale complex system design and operations management, including optimizing critical interdependent infrastructures such as power grids, transportation systems, and cyber-clouds.
- We study network interdiction models and design algorithms for specially structured networks (e.g., trees, small-world networks) in defense-related problems. Dynamic programming and heuristic approaches are used for deriving solutions in polynomial time, and generating valid bounds to the corresponding stochastic optimization models.
- With increasing penetrations of fluctuating renewable energy sources, such as wind power plants and solar photovoltaics, and active participation of electric loads in power system operation, uncertainty will increase. Specifically, we develop data-driven and distribution-free optimization methods that are suited to dispatching power systems with both fluctuating renewable energy sources and flexible loads contributing to balancing reserves via load control. The flexibility of an aggregation of loads is difficult to compute and uncertain. Investigating, characterizing, and managing this uncertainty is the focus of this research. Moreover, we quantify the tradeoff between the uncertainty and profitability of load control, and the effect of uncertainty and methods for managing it on power system dispatch, which affects pollutant emissions.
To develop new data fusion methodologies for improving system operation and quality with the emphasis on fusion of data and engineering knowledge collected from disparate sources by integrating multidisciplinary methods. Her research has been widely applied in both manufacturing and service industry by providing techniques for knowledge discovery and risk-informed decision making. Key research issues are being pursued:
- Advanced quality control methodologies for system monitoring, diagnosis and control with temporally and spatially dense operational/sensing data.
- Multi-scale data transform and high order tensor data analysis for modeling, analysis, classification, and making inferences of multistream sensing signals.
- Optimal sensor distribution and hierarchical variable selection methods for system abnormal detection and sensor fusion decisions, which integrates the causal probability network model, statistical change detection, set-covering algorithm, and hierarchical lasso regression.
- A unified approach for variation reduction in multistage manufacturing processes (MMPs) using a state space model, which blend the control theory with advanced statistics for MMPs sensing, monitoring, diagnosis and control, integrative design of process tolerance and maintenance policy considering the interaction between product quality and tool reliability.
Data science applications: (a) Smart manufacturing with sensor fusion, process monitoring, diagnosis and control (e.g., metal forming including stamping, forging, casting and rolling), assembly, ultrasonic welding, photovoltaic thin film deposition. (b) Travel time estimation and traffic prediction for intelligent transportation systems. (c) Multi-stream data analysis of human motion/vehicle crash testing data for improving vehicle design and safety. (d) Risk informed decision support for healthcare and clinical decisions. (e) Customer behavior modeling for fraud detection in healthcare and telecommunication. (f) Human decision-making behavior modeling in a dynamic/emergency environment.
Jon’s research focus is on nonlinear discrete optimization (NDO). Many practical engineering problems have physical aspects which are naturally modeled through smooth nonlinear functions, as well as design aspects which are often modeled with discrete variables. Research in NDO seeks to marry diverse techniques from classical areas of optimization, for example methods for smooth nonlinear optimization and methods for integer linear programming, with the idea of successfully attacking natural NDO models for practical engineering problems.
Amy Cohn, PhD, is an Associate Professor and Thurnau Professor in the Department of Industrial and Operations Engineering at the University of Michigan College of Engineering and Director of the Center for Healthcare Engineering and Patient Safety. Her primary research interest is in robust and integrated planning for large-scale systems, predominantly in healthcare and aviation applications. She also collaborates on projects in satellite communications, vehicle routing problems for hybrid fleets, and robust network design for power systems and related applications. Her primary teaching interest is in optimization techniques, at both the graduate and undergraduate level.