Research

Our research group’s interest mainly lies in sequential decision-making and optimization under uncertainty, with applications in transportation and supply chain management. Our research addresses the existing challenges by bridging theories in stochastic programming, distributionally robust optimization, integer programming, and dynamic programming, as well as proposing efficient algorithms for solving large-scale real-world problems under uncertainty.

Current Projects:

Research Areas:

1. Multistage Decision-Making with Decision-Dependent Uncertainty or Risk Management

Data uncertainty appears ubiquitously in decision-making processes in practice, where system design and operational decisions are made sequentially and dynamically over a finite time horizon, to be adaptive to varying parameters. In practice, customer demand in various types of service industries is random and hard to predict due to the lack of prior data. Its probability distribution can be greatly dependent on the locations of service centers or facilities. This type of uncertainty is called endogenous uncertainty, or decision-dependent uncertainty. In [1], we investigate multistage distributionally robust mixed-integer programs with endogenous uncertainty, where the probability distribution of stage-wise uncertainty depends on decisions made in previous stages. To handle multi-period uncertainty, a multistage stochastic dynamic program has more flexibility than the two-stage counterpart. It remains an open question to bound the gap between these two models using risk-averse objective functions. In [2], we provide tight lower bounds for the gaps between optimal objective values of risk-averse multistage stochastic facility location models and their two-stage counterparts using expected conditional risk measures.

Selected Publications:

  1. Xian Yu, Siqian Shen, “Multistage Distributionally Robust Mixed-Integer Programming with Decision-Dependent Moment-Based Ambiguity Sets,” Mathematical Programming, volume 196, 1025-1064, 2022. [link]

  2. Xian Yu, Siqian Shen, “On the Value of Multistage Risk-Averse Stochastic Facility Location with or without Prioritization,” under review, 2022. [arXiv (PDF)]

2. Risk-Sensitive Distributional Reinforcement Learning

In traditional risk-neutral RL, the agent seeks a policy that maximizes the expected total reward. However, maximizing the expected reward does not necessarily avoid the rare occurrences of catastrophic events. In high-stakes settings where it is important to maintain reliable performance, we aim to evaluate and control the risk. Here, risk refers to intrinsic uncertainty over possible outcomes, and a risk-sensitive policy relies on criteria more than the mean. Both risk-neutral and risk-sensitive RL are value-based methods as they maintain a value function based on the specific objective function. Recently, [Bellemare et al., 2017] proposed a distributional RL (DRL) method to estimate the distribution of the random reward instead of only modeling a single value. Having full information on reward distribution provides a unified framework for handling a variety of risk measures. However, the fundamental properties of this risk-sensitive DRL framework have yet to be fully understood. For example, what safety and risk guarantees can DRL provide, beyond the traditional RL? How can we guarantee global convergence under DRL and what is the fundamental iteration/sample complexity (i.e., the minimum number of iterations/samples required for learning the optimal policy)?

Selected Publications:

  1. Xian Yu, Lei Ying, “On the Global Convergence of Risk-Averse Policy Gradient Methods with Expected Conditional Risk Measures,” accepted in the 40th International Conference on Machine Learning (ICML 2023), Honolulu, Hawaii, 2023. [link][arXiv (PDF)]

3. Smart Transportation and Mobility-as-a-Service (MaaS)

Mitigating traffic congestion and enhancing transportation accessibility are crucial for addressing environmental concerns and improving urban mobility. In [2], we study on-demand ride pooling to dynamically match available drivers with randomly arriving passengers and also decide pick-up and drop-off routes. A spatial-and-temporal decomposition scheme is combined with Approximate Dynamic Programming to speed up computation. This type of services can be also extended to cover non-emergency medical transportation requests ([1]) and attended home service requests ([3]), where we collaborate with Ford Motor Company and propose two-stage stochastic integer programs to optimize vehicle routes and estimated arrival time or time windows with a goal of reducing customers’ waiting, vehicle idleness, and overtime. To further mitigate traffic congestion by better coordinating the control of traffic signals, working with Center for Connected and Automated Transportation (CCAT) at University of Michigan Transportation Research Institute (UMTRI), we also develop distributed algorithms for solving a two-stage stochastic cell transmission model that considers the uncertainty of traffic demand and vehicle turning ratios on corridors and grid networks in [4].

Selected Publications:

  1. Xian Yu, Siqian Shen, Huizhu Wang, “Integrated Vehicle Routing and Service Scheduling under Time and Cancellation Uncertainties with Application in Non-Emergency Medical Transportation,” Service Science, 13(3), 172-191, 2021. [link]

  2. Xian Yu, Siqian Shen, “An integrated decomposition and Approximate Dynamic Programming approach for on-demand ride pooling,” IEEE Transactions on Intelligent Transportation Systems, 21(9), 3811-3820, 2020. [link]

  3. Xian Yu, Siqian Shen, Babak Badri-Koohi, Haitham Seada, ”Time Window Optimization for Attended Home Service Routing and Scheduling under Uncertainty,” Computers and Operations Research, volume 150, 2023. [link]

  4. Xinyu Fei, Xingmin Wang, Xian Yu, Yiheng Feng, Henry Liu, Siqian Shen, Yafeng Yin, “Optimization and Decentralized Algorithms for Traffic Signal Control under Uncertain Travel Demand and Vehicle Turning Ratio,” to appear in European Journal of Operational Research, 2023. [link]