Chennai Mathematical Institute


3.30 p.m., Seminar Hall
Graphical models for analysis and control of infrastructure networks

Dvijotham Krishnamurthy
Center for Mathematics of Information, Caltech, USA.


Graphical models have proved to be a powerful tool for representing and reasoning with structured probability distributions - this power has been successfully leveraged in diverse applications ranging from computer vision and computational biology to error-correcting codes. In this talk, we show that several problems arising in the design, analysis and control of infrastructure networks (like the electric power grid, the natural gas pipeline network, water distribution networks or the transportation network) can be naturally posed in the language of graphical models. However, computing solutions to infrastructure network problems poses two challenges that have previously received little attention in the graphical models literature: 1) Mixed discrete/continuous variables and 2) Handling stringent constraints (maintaining voltages in the power grid or pressures in the gas pipeline at acceptable levels, for example). In the concrete setting of optimization problems in radial electricity distribution networks, we show that these challenges can be dealt with efficiently using ideas from Constraint Programming (CP). The result is a polynomial type approximation algorithm for nonlinear mixed integer programs (MINLPs) arising in electricity distribution networks. Numerical tests show that the algorithm is practical and greatly outperforms off-the-shelf global MINLP solvers. Finally, we outline directions for future work and extending our approach to other infrastructure networks and broader analysis problems like probabilistic security analysis and market design for the electric power grid.

Joint work with Pascal Van Hentenryck (University of Michigan), Michael Chertkov (Los Alamos National Lab), Marc Vuffray (Los Alamos National Lab), Sidhant Misra (Los Alamos National Lab), Adam Wierman (California Institute of Technology), Navid Azizan Ruhi (California Institute of Technology) and Niangjun Chen (California Institute of Technology).

Based on the papers: (appeared at GREENMETRICS, under review at IEEE Transactions on Smart Grid) (to appear at CP 2016 and the journal Constraints)