At the core of many societal challenges, particularly in view of sustainability and efficiency, there are hard optimization problems. While these underlying problems can be solved for smaller setups using optimization methods, realistic problem sizes are still prohibitive. Apart from the immediate challenges arising from sheer size, in today's fast-paced and intertwined economies we additionally face the challenge of addressing real-time aspects; otherwise, the obtained solutions might not apply anymore: the problem changed faster than it was solved. This EAGER addresses specific optimization problems arising from societal challenges and will motivate the study of the underlying optimization problems. For this, new methods at the intersection of continuous and discrete optimization as well as machine learning and randomization will be developed.
Intellectual Merit. PIs set out to investigate general solution strategies to address problem size, real-time requirements, as well as uncertainty aspects using recent developments from theoretical computer science and modern optimization theory. At the core of this proposal is the study of real-world challenges related to cargo-vessel routing, palletizing, vehicle and mobile bot routing and related problems. A main difference to classical approaches is that the real-time requirements will not be added on top but will be integral to the whole design process, which is likely to result in better algorithms. Apart from the challenges from the aforementioned problems, PIs intend to develop an online expert system - Ask Minmax. This platform will leverage machine learning techniques to make the theory of optimization methods and tools accessible to industry and other personnel that face challenging optimization problems.
Broader Impact. A key objective of this proposal is outreach. This EAGER will develop a consulting tool that will allow industry and the broader society to learn about most useful methods in algorithms and optimization. In particular, this tool is geared towards helping the user to make a decision regarding which methods are most likely to be applicable to their problem: in an interactive way the tool will collect information from the user about their optimization problem. The system will then determine the most likely model and provide information. Large-scale challenges in palletizing and routing require the combination of various heuristics and algorithms. A second component that will significantly impact industry is the developing of key performance indicators for such algorithms. These metrics will help to gauge efficiency of a particular heuristic and/or algorithms, which will be important when algorithms are combined within a larger solution. Mentoring and collaborating with a graduate student, a shared postdoctoral student across multiple EAGERs, as well as hosting a workshop in relevant frontier topics at the Institute for Mathematics and Applications (IMA) are all parts of the broader impact of this EAGER.
