Optimization with Decision Diagrams: Theory and Applications

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With both ubiquitous data and use of technology, data-analysis methods have become key in decision-making for businesses and government. These methods apply sophisticated mathematical approaches to help identify the most effective ways to deliver products and services under conditions of scarcity, such as how to route public buses to satisfy demand more efficiently, to optimize an investment portfolio, or to route trucks to deliver products at reduced cost. According to the Institute for Operations Research and Management Science, benefits from such methods provided, conservatively, more than $213 billion in savings between 1974 and 2013. Nevertheless, many current problems in areas such as health care, smart cities and transport involve huge amounts of data and complex operational restrictions that remain incompatible with existing approaches-even as major stakeholders, such as IBM, are identifying advanced analytics as fertile ground for business/economic growth, a sector in which Canada can greatly benefit from. This proposal aims to investigate new mathematical and computational methods to tackle challenging problems in optimization. The research direction is based on innovative uses of decision diagrams (DD), a mathematical data structure originally introduced in logic and computer science. As demonstrated by the applicant's recent research, novel DDs can be particularly useful for solving optimization problems with huge data sets, whereby data is not represented explicitly and comprehensively at the outset, but introduced incrementally during the solution procedure. The applicant will consequently develop new theoretical and computational data-analytics methodologies focusing, over five years, on five challenging applied cases in routing, healthcare, online security, incentive auctions and sports. These methods will advance the field academically short and long term, as well as lay the foundation for robust practical applications for a wide range of other scenarios and persistent challenges, helping establish Canada as one of the leaders in Big Data Analytics. Due to the practical and diverse applicability of the investigated methods, the proposed research fosters collaboration with industrial partners and will be aimed at leveraging substantial grant applications post the five-year program. Under NSERC Discovery, collaborators from Carnegie Mellon University, the University of Connecticut, IBM T. J. Watson Research Center and Google will partner on projects.**