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About Distributionally Robust Optimization Problems on the Example of the Shortest Path Problem

Student: Evgeniy Burashnikov

Supervisor: Sergey Ketkov

Faculty: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Year of Graduation: 2019

In this research paper, distributionally robust optimization problems on the example of the shortest path problem are considered and investigated. Distributionally robust optimization is a paradigm for decision-making under uncertainty, where the uncertain problem data is governed by a probability distribution that is itself subject to uncertainty. The purpose of the current work is to learn the approaches for solving robust optimization problems with distributional information. We consider the shortest path problem and assume that the edge costs are unknown in advance and there is an interval containing the nominal cost of the edge. An approach will be regarded that there is some additional prior information about the distribution, including, for example, linear constraints on confidence intervals. A robust optimization problem is constructed, which then reduces to an integer programming problem using dualization of a lower level problem. The resulting problem has a specific structure and can be solved using modern state-of-the-art solvers. By controlling the problem parameters, one can also adjust the degree of conservatism of the solution obtained.

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