Technological advances in computing, communication, and in multi-purpose sensing capabilities at any scales have the potential to radically transform key existing activities and processes and, in some cases, allow the emergence of new ones. It also leads to interesting mathematical and algorithmic challenges. In particular we are interested in data-driven optimization problems with (i) incomplete and uncertain input streams, (ii) time-sensitive objectives, and (iii) short time requirements and capacity constraints for some decisions. After providing some contexts and application in searching, routing/transportation, autonomous spatial exploration, and dynamic resource allocation, we will discuss in more details some results we have obtained on basic canonical problems (online traveling salesman problems, online graph searching, online bipartite matching). We will then discuss the challenges associated with combining online, real-time, and stochastic features for these problems into a single rigorous framework. We will present one possible framework, with some illustrations of corresponding possible results.
Research funded in part by ONR, NSF, Singapore, AFOSR
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