The ICNPAA Congress 2018: Mathematical Problems in Engineering, Aerospace and Sciences brought together scientists from a variety of disciplines. MechSE professor Naira Hovakimyan was one of the main conference organizers and a co-chair.
Salapaka presented on “Combinatorial Optimization Problems on Networks: A Maximum-Entropy-Principle Based Framework.”
Abstract: Many physical systems in nature pose combinatorial resource allocation problems that involve a huge number of particles on the order of Avogadro’s number, that is, about particles. Statistical physics provides methods and tools that make it possible to analyze such large systems. There have been many efforts that transfer these tools to large-scale data analysis. This work is one such effort. This talk will present methods and algorithms that mimic free-energy principle from statistical physics to address a class of combinatorial optimization problems. In fact, this principle is viewed as maximum entropy principle (MEP) propounded by E.T. Jaynes. We present a MEP-based framework that gives a common viewpoint to a range of seemingly dissimilar problems that include combinatorial resource allocation problems, data clustering, aggregation and partitioning of large graphical networks, routing and scheduling, and variants of the traveling salesman problem. This framework inherits the key features of Deterministic Annealing (DA) algorithm, which was developed in the data compression/information theory literature for static vector quantization problems, and extends to include control system theoretic problems. Our framework allows for inclusion of several kinds of dynamic, communication, and resource capacity constraints, while also providing quantitative measures of robustness of solutions to the uncertainties in the underlying data. This talk will give an in-depth analysis of this framework.
Salapaka a B.Tech. degree in mechanical engineering from Indian Institute of Technology in 1995, and master’s (1997) and doctoral (2002) degrees in mechanical engineering from the University of California at Santa Barbara. He joined MechSE in 2004, and earned a prestigious NSF CAREER award in 2005. His areas of current research interest include controls for nanotechnology, combinatorial optimization, brownian ratchets, X-ray microscopy, analysis of numerical/dynamic-systems, and control of power systems.