NSF Award
2319157
Navigation on a network with obstacles is a natural way to model optimal travel between two locations (e.g., two cities or two inventory storage locations). This subject is highly interdisciplinary, drawing on operations research, statistics, probability, optimization, computer science, and graph theory, and has applications across defense logistics, decentralized control of robot swarms, autonomous path planning in obstacle rich environments, target tracking and neutralization, and naval logistics. Despite network (traversal) optimization having seen some success, there are several basic and applied research challenges that need to be addressed to enable its widespread use in practice. Progress in network optimization affects areas such as manufacturing and logistics analysis, supply chain management, communication networks and traffic management and many aspects of our daily life. Thus, the development of faster and better optimization algorithms in network traversal/blocking will have a direct impact on science and society. This research will also result in increased collaboration and partnership between academia and industry. Results of this project will be disseminated through research articles, conference proceedings, and seminar series. Relevant code will be made publicly available as open-source software packages. The project will integrate research and education by teaching special topics courses and organizing seminars for graduate students and postdocs, with efforts made to support underrepresented minority, female, and young researchers working on this topic.<br/><br/>The goal of this project is finding optimal or near-optimal solutions to the stochastic obstacle scene (SOS) problem using spatial network optimization. The investigator will study two variants of the SOS problem. First is the original SOS problem, also called the Optimal Traversal Path (OTP) problem), in which a single navigating agent (NAVA) chooses a cost-minimal path in a space containing “forbidden regions.” In the second SOS problem (optimal obstacle placement (OOP), recently introduced by the investigator), an obstacle placing agent (OPA) inserts obstacles in the traversal window so as to maximize NAVA’s traversal length. The main goals of this research are to improve heuristic algorithms for both variants, to introduce new variants, and to study theoretical underpinnings. The SOS problem setting is quite general and applies to adversarial agents in a medium where traversal cost is heterogeneous with possibly untraversable regions. The research objectives of this project are to (a) extend the SOS problem in various directions, e.g., high dimensional version and develop potential strategies to improve OTP and OOP algorithms, (b) introduce and develop the weight constraint versions of both SOS variants, study the solution strategies and develop a more comprehensive approach to network traversal optimization/obstruction all from the probabilistic / statistical and computational points of view, and (c) study the theoretical properties (including complexity) of the network traversal and obstruction algorithms together with the characterization of the cost functions for the OTP problem.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
