Research Projects

Methodologies

• • Distributionally robust optimization

  • Stochastic programming

  • Approximation algorithms

  • Discrete optimization

Applications

• • Machine learning 

  • Optimal experimental design

  • Logistics and network design problems under uncertainty

  • Stochastic/robust power system design

Ongoing Research Topics

• • Data-driven distributionally robust optimization

  • Approximation algorithms for statistical learning, data analytics, and machine learning

  • Multi-product revenue management

  • Chance-constrained stochastic programming

  • Integer programming

  • Submodular optimization

  • Decomposition algorithms for stochastic programming

  • Supply chain network design under service disruption

  • Infrastructure maintenance

Summary of Completed Research Projects

1. On approximation algorithms of D-optimal design:

• • Proposed constant-factor approximation algorithms for D-optimal design with or without repetitions

  • Improved the approximation ratio in the asymptotic domain

  • Provided deterministic implementations of the randomized algorithms

  • Analyzed the well-known local search algorithm and proved its approximation guarantees

  • Extended the analysis to A-optima design

2. On distributionally robust joint chance constrained optimization problems (DRCCP)

• • Deterministic Reformulation

    • Proposed a deterministic reformulation of DRCCP

    • Explored sufficient conditions that a DRCCP can be reformulated as a convex program

    • Showed that a binary DRCCP can be equivalent to a deterministic mixed integer convex program

  • Bi-criteria Approximation

    • Studied covering chance constrained program (CCP) and DRCCP and proved its inapproximability

    • Proposed relaxation schemes and showed their tractability

    • Provided constant bicriteria approximation for both CCP and DRCCP

3. Relaxations and Approximations of Chance Constrained Programs (CCP):

• • On the quantile closure of the chance constrained problems:

    • Proposed a closure of quantile cuts, and show that iterative application of the closure recovers the convex hull of a chance constrained problem

    • Showed that this procedure only takes a finite number of iterations for a chance constrained problem with integer variables

    • Studied an approximated closure by deriving quantile cuts only from the constraints of the original problem

  • On the nonanticipativity duality of the chance constrained problems:

    • Derived two different Lagrangian duality bounds by relaxing the nonanticipativity constraints of the chance constrained problems

    • Proposed two extended formulations of the chance constrained problem and demonstrated that the continuous relaxation values of these two formulations yield the same as the dual bounds

    • Implemented scenario decomposition algorithm for the binary decision variables and branch and cut algorithm for the continuous decision variables

4. Reliable Network Design under Probabilistic Disruptions

• Developed modeling framework for jointly optimizing location and vehicle routing under service disruptions

• Incorporated facility disruption, en-route congestion and in-facility queuing into reliable emergency service facility location decisions

• Investigated efficient approximation algorithms and conducted empirical study using real-world railroad data

Acknowledgment

We thank the following agencies/organizations for supporting our research and education activities.