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On Solution Methods for Robust Combinatorial Optimization Problems

Student: Vasiliy Malinin

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: 2021

The optimization problem is widely known in mathematics, computer science, and operations research; it is to the maximization or minimization problems that most of the decision-making problems encountered in real life are reduced. Every day a lot of optimization problems are solved: what product and what ratio is better to produce, how to build a better transportation route, what resources are more profitable to use for the production of the product and much more. In practice, however, there is often a need to insure against an unpleasant set of circumstances, which can occur in the case of the slightest discrepancy between the parameters used to build a mathematical model and what is happening in reality. In order to level out errors, the model must have the property of robustness. This paper considers the construction of robust mathematical models based on linear programming problems. One of the fundamental optimization problems - the search for the shortest path in a weighted, oriented graph - will be considered in this vein. Methods for solving bi-level optimization problems obtained in the course of constructing robust models will also be discussed. Particular attention will be paid to the consideration of the iterative algorithm, which allows both an exact solution and a solution with a given level of error. This method will be opposed to the classical method of solving through reduction to a one-level problem. Both algorithms will be implemented and evaluated in terms of running time and correctness of the solution obtained.

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