Title: Location Science meets Machine Learning: Mathematical (discrete) Optimization approaches for Data Science
Abstract: Location Science (LS) is one of the hot topics in Operations Research and its goal is to find the ‘optimal’ position of a set of ‘services’ to meet the demand of a set of ‘users’. There is a large body of literature in this field with tons of different versions of problems within this framework. Furthermore, they are usually combined with other types of logistics problems, such as routing, distribution, or inventory management, being then these problems attractive not only for their mathematical insights but also for their real-world applications. However, less attention has been paid to the synergies between LS and Machine Learning (ML), even though it is easy to see that most mathematical optimization-based ML tools are equivalent to a location problem with the adequate identification of the ‘ users’ and the ‘services’ to locate. This identification allows one to use known tools and features in LS to develop new ML tools by means of mathematical optimization models.
In this talk, we will provide an overview of some classic facility location problems and show some of our recent works on the development and analysis of new mathematical optimization-based ML approaches. We will present a unified framework for fitting hyperplanes to sets of points by using generalized residuals and aggregation measures, some theoretical and empirical results on the mathematical insights of SVM-based classifiers with l_p norm margins, and mathematical optimization models to build classifiers for multiclass instances using arrangements of hyperplanes, optimal classification trees, or robust classifiers under noisy labels.