Puneet Sharma - Research

Research Focus


My current research involves developing scalable combinatorial optimization algorithms for solving static and dynamic resource allocation (clustering) problems. Most of these problems are intimately related to a class of combinatorial resource allocation problems that have been studied extensively in various formulations such as the minimum distortion problem in data compression, facility location assignments, optimal quadrature rules and discretization of partial differential equations, pattern recognition, drug discovery, neural networks, and clustering analysis. In contrast, these problems are relatively recent in the control literature, having arisen in coarse quantization, coverage control, mobile sensing networks, and motion coordination algorithms.

We have addressed the static clustering problem in a Maximum Entropy Principle framework and developed algorithms that are scalable and amenable to distributed implementation. The MEP framework was augmented with additional constraints for addressing the issues of scalability and computational efficiency. The proposed algorithm outperforms the non-scalable algorithm in terms of computation time and handles much larger datasets. We have successfully implemented these scalable algorithms for solving the library selection problems in combinatorial drug-discovery, by simultaneously addressing the key issues of diversity, representativeness, inclusion/exclusion and scalability. Similar framework is also used for solving the state-space discretization problem in quantized control.

Presently, we are working on clustering and coverage problems associated with moving objects. We have developed a Maximum Entropy based algorithm for solving this dynamic locational optimization problem. Our emphasis is on hierarchical clustering algorithms that are designed to avoid local minima and insensitive to initial placement of clusters. The algorithm has been addressed in a control-theoretic framework to ensure that the coverage metric (clustering cost function) is continuously improved. Bifurcation conditions for the underlying optimization problem lead to its hierarchical structure.

Publications

  • Sharma, P., Salapaka, S., and Beck, C., Coverage Problems with Mobile Sites and Resources, IEEE Transactions on Automatic Control (in preparation).

  • Sharma, P., Salapaka, S., and Beck, C., A Scalable Approach to Combinatorial Library Design for Drug Discovery
    J. Chem. Inf. Model., 48, 1, 27 - 41, 2008.

  • Sharma, P., Salapaka, S., and Beck, C., Entropy Based Algorithm for Combinatorial Optimization Problems with Mobile Sites and Resources
    Proc. of American Control Conference, 2008.

  • Sharma, P., Salapaka, S., and Beck, C., A Maximum Entropy Based Scalable Algorithm for Resource Allocation Problems
    Proc. of American Control Conference, 516-521, 2007.

  • Sharma, P., Salapaka, S., and Beck, C., A Scalable Deterministic Annealing Algorithm for Resource Allocation Problems
    Proc. of American Control Conference, 3092-3097, 2006.

  • Sharma, P., Salapaka, S., and Beck, C., A Deterministic Annealing Approach to Combinatorial Library Design for Drug Discovery
    Proc. of American Control Conference, 979- 984 vol. 2, 2005.

  • Sharma, P., and Beck, C., Modelling and distributed control of mobile offshore bases
    Proc. of American Control Conference, 5238- 5243 vol.6, 2004.

    • Ph.D. Prelim Report
  • Entropy Based Algorithms for Static and Dynamic Combinatorial Resource Allocation Problems [pdf]

    • Ph.D. Qualifying Exam Presentation
  • Stochastic Approximation [ppt]

    • M.S. Thesis
  • Modelling and Distributed Control of Spatial Array Systems - Advisor: Prof. Carolyn Beck.

Talks, Presentations & Reports
  • PhD. Preliminary Exam presentation, Urbana, 2007. [pdf]
  • American Control Conference, Seattle, WA, 2008. [pdf]
    (awarded best paper in session)
  • American Control Conference, New York, NY, 2007. [pdf]
  • American Control Conference, Minneapolis, MN, 2006. [pdf]
  • American Control Conference, Portland, OR, 2005. [pdf]
  • American Control Conference, Boston, MA, 2004.[ppt]
    (awarded best paper in session)
  • Spectral Graph Partitioning Algorithms for Resource Allocation Problems [pdf]
  • Office of Naval Resaerch, Autonomous Intelligent Networks and Systems, UCLA, 2003. Poster presentation [ppt]
  • Application of Duality Theory in Multi-objective Control Problems[pdf]
  • Optimal Control - A Game Theoretic Approach[pdf]
    Report [pdf]
  • Optimal Control applied to Cancer Chemotherapy[pdf]
  • H2 and H-infinity control of a Pendubot (movie) (Report) [pdf]
  • Averaging and Vibrational Control of Mechanical Systems [pdf]
  • Data Based Modelling and Identification Methods
    Project 1[pdf] Project2 [pdf] Paper Review [pdf]

Graduate Coursework
  • ME 598 - Convex Optimization
  • ECE 580/MATH 587 - Optimization by Vector Space Methods
  • ECE 534 - Random Processes
  • ECE 543 - Optimal Control
  • ME 598 - Robust Control and Convex Methods
  • GE 598RS - Game Theory
  • FIN 514 - Financial Engineering II (Option Pricing)
  • ME 598 - Computational Methods in Dynamical Systems
  • GE 598CB - Data Based Modeling and Identification
  • ECE 528 - Analysis of Nonlinear Systems
  • ECE 515 - Control Systems- Theory and Design
  • GE 591 - Simulation of Dynamical Systems
  • GE 589 - Robot Control Theory
  • GE 598SC - Technology Innovation and Market Strategy
  • GE 598JM - Finance for Engineering Managers
  • GE 598HC - Design for Six-Sigma
  • MA 447 - Introduction to Analysis (Real Variables)
  • MA 448 - Introduction to Analysis (Complex Variables)