Stefan Wild Makes Quicker Computation of Mathematical Models Possible at Argonne

Despite the power and speed of today's computing hardware and software, many important science and engineering problems lead to many mathematical optimization models that still take an impractically long time to compute.

While a Ph.D. student in ORIE, Stefan Wild, Ph.D. '09, spent a summer at Argonne National Laboratory working to make these computations more practical. Under the guidance of Jorge Moré, Director of the Laboratory for Advanced Numerical Simulations at Argonne, and Wild's advisor Christine Shoemaker,an ORIE Field Member and Joseph P. Wiley Professor of Engineering, Wild developed techniques to greatly reduce the effort in the central computational step in many engineering and scientific optimization problems. That step typically entails the evaluation of a particular candidate solutions, including the determination of precisely how rapidly the values change in the region around the candidate solutions, i.e. the first and second order partial derivatives of the mathematical functions constituting the model. It must be executed thousands of times during the computational run. 

However in many problems, no representations of the functions and/or of their rates of change are available in the closed algebraic form usually needed by optimization software. Instead they must be estimated by running software programs - often digital simulations - that take an hour or more to compute for a single candidate solution. Wild's optimization technique, which Moré says is "different from most," interpolates from values already known for other candidate solutions to estimate their values for the new candidate.  

As long ago as 2007, Moré noted that Wild's technique "is already beating the competition," and improvements have been made since, according to Wild. His technique has been incorporated into Argonne's Toolkit for Advanced Optimization (TAO), a collection of high-quality, high performance computer software "codes," used by hundreds of research in government, industry and academia. It is also being used by Shoemaker, a world leader in the application of sophisticated computations to solve environmental problems, in her work on ways to stop the spread of pollution and to clean polluted groundwater.

Wild spent his summer at Argonne as component of his Computational Science Graduate Fellowship, a fellowship sponsored by the U.S. Department of Energy (DOE) that requires a "practicuum," or research assignments at a participating DOE laboratory such as Argonne. While many Ph.D. students work on campus during the summer as Research Assistants to their major advisors, Wild greatly valued the opportunity to spend the time at Argonne, in an Illinois suburb of Chicago. The experience "exposed me to the whole national laboratory system," said Wild. He noted that the assignment was particularly timely since the national focus on energy and the environment - two application areas that both Wild and Argonne are interested in - has steadily increased since that summer. Moreover it led to his full time employment at Argonne.

This summer Wild, who regularly spends time in Ithaca where his wife works as an attorney, will welcome another ORIE Ph.D. student to Argonne. Kathleen King was recently awarded a Computational Science Graduate Fellowship and will spend her summer there working on a different class of optimization techniques, one that she is particularly interested in applying to health care and emergency medical response problems. These techniques deal with problems that incorporate a mix of variables, some of which can only meaningfully take on discrete integer values such as the number of ambulances, the presence or absence of a medical facility at a location, or the triage decision for an individual patient. Like Wild, Shoemaker, and other ORIE faculty and graduate students, King takes a "math with a mission" approach, balancing advances in analytical and computational approaches with the solution of crucial problems in the world at large.