Title: Exploiting Decomposable Structure to Design Better Algorithms for Solving Integer Programs

Abstract
Optimization problems in which some or all of the variables are constrained to take integer values are of broad applicability in a wide range of fields, from medicine and healthcare to banking and finance to environmental management and conservation. Over recent decades, exact algorithms for their solution have become faster and more efficient, culminating in a variety of commercial software platforms and public domain codes that provide exceptional capability for solving practical problems to optimality. However, this seems to have only increased the appetite of practitioners to solve ever-larger problems, which challenge the state-of-the-art. In this talk, we bring together two apparently disparate observations: (i) many practical problems have decomposable structure and (ii) despite the enormous strides in solution algorithms, one key element common to all of them, namely, the branching rule, has remained largely untouched since it was first presented in the 1960's. Yet the branching rule defines how the search space is divided in the "divide-and-conquer" paradigm that forms the basis of all exact algorithms; it is central to the algorithm. Here, we will describe a new idea for exploiting decomposable structure in problems to derive alternative, powerful, new branching rules. These rules are demonstrated to speed up commercial solvers by orders of magnitude, on two classes of problems having different characteristics. The potential to generalize these ideas will also be discussed.

Bio
Martin Savelsbergh is a logistics and optimization specialist with over 25 years of experience in mathematical modeling, operations research, optimization methods, algorithm design, performance analysis, transport, supply chain management, and production planning. He has published over 160 research papers in many of the top operations research and optimization journals and has supervised more than 30 Ph.D. students. Martin has a track record of creating innovative techniques for solving large-scale optimization problems in a variety of areas, ranging from service network design, to last-mile and crowdsourced delivery, to ridesharing. He has demonstrated an ability to design and implement highly sophisticated and effective optimization algorithms as well as an ability to analyze practical decision problems and translate the insights obtained into optimal business solutions. Martin holds the James C. Edenfield Chair in the H. Milton Stewart School of Industrial and Systems Engineering (ISyE) at Georgia Institute of Technology. He is co-director of The Supply Chain and Logistics Institute (SCL). SCL coordinates all supply chain and logistics activities on the Georgia Tech campus. Martin Savelsbergh is Editor-in-Chief of Transportation Science, one of the most prestigious academic journals in the area of transportation science and logistics. Martin Savelsbergh was a founding partner of Axioma, Inc., a privately held company delivering state-of-the-art software solutions and consulting services (www.axioma.com). As Chief Technology Officer, he was responsible for managing large-scale software development projects. Currently, Axioma focuses entirely on financial optimization applications.