Computational stochastic optimization addresses the intractable challenge of making decisions over time in the presence of different sources of uncertainty. These problems arise in an astonishing array of real world problems.
*** September, 2012 ***
We have prepared a step by step linkage between the classical statement of Bellman's optimality equation and the two standard algorithmic strategies used in stochastic programming. A brief summary is presented in the Informs Computing Society newsletter. A longer paper that unifies stochastic search, stochastic programming, policy search and dynamic programming using examples from transportation and logistics is available here. This is part of a broader effort to build bridges between the communities of computational stochastic optimization.
Our research can be divided between fundamental research into new methods, and the application of these methods to a range of applications. Our methodological research all falls under the broad umbrella of computational stochastic optimization, with a special focus on the modeling and algorithmic framework of approximate dynamic programming. For a broader perspective, see our new website on computational stochastic optimization. Recently, we became involved in a closely related area that we are calling optimal learning, which addresses the problem of efficiently collecting information. Our applied and computational research is supported by a strong program of theoretical research.
Our application areas are varied. We have a long history of working in transportation and logistics, which introduced us to the challenge of modeling complex operations, and solving resource allocation problems under uncertainty. These problems often involve either modeling the operations of large control centers, or providing tools to help people within control centers, such as the control center at Netjets to the right. Over the years, our work has enjoyed a significant impact on industry. The application of approximate dynamic programming to a large-scale fleet management problem at Schneider National was recently featured in Forbes magazine.
We are also heavily involved in research in energy, with problems spanning energy policy models, optimization of energy R&D, planning the placement of wind farms, dynamic pricing and demand response, power grid modeling, and optimizing the design and control of storage portfolios. We have recently started PENSA, the Princeton laboratory for Energy Systems Analysis, to represent the growing activities at Princeton in energy systems. PENSA builds on our expertise in stochastic optimization to solve a wide range of problems involving the design and control of energy systems.
I hope you find the material interesting, and perhaps useful. If you have any questions, please contact me.
(c) Warren B. Powell, 1997-2013.