Computationally efficient approach for solving lexicographic multicriteria optimization problems
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Computationally efficient approach for solving lexicographic multicriteria optimization problems Victor Gergel1 · Evgeniy Kozinov1
· Konstantin Barkalov1
Received: 29 January 2020 / Accepted: 8 November 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, we propose a computationally efficient approach for solving complex multicriteria lexicographic optimization problems, which can be complicated by the multiextremal nature of the efficiency criteria and extensive volume of computations required to calculate the criteria values. The formulation of problems is assumed to be the subject to change as well, which, in turn, may require solving dynamically defined sets of multicriteria optimization problems. The proposed approach is based on reducing multidimensional problems to one-dimensional global optimization problems, utilizing efficient global search algorithms, and reusing the search information obtained in the process of calculations. The results of numerical experiments confirm that the proposed approach demonstrates high computational efficiency of solving multicriteria global optimization problems. Keywords Multicriteria optimization · Lexicographic ordering · Global optimization · Dimensional reduction · Search information · Computational complexity
1 Introduction Multicriteria optimization (MCO) problems are among the most general statements used to address decision-making problems. These statements are commonly used in various applications. Multicriteria optimization is a dynamic area of scientific research.
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Evgeniy Kozinov [email protected] Victor Gergel [email protected] Konstantin Barkalov [email protected]
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Mathematical Center, Lobachevsky State University of Nizhni Novgorod, Gagarin ave., 23, Nizhni, Novgorod, Russia
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V. Gergel et al.
So far, researchers proposed a large number of efficient methods of multicriteria optimization and found solutions to many practical problems (see, e.g., monographs [1–5] and reviews [6–9]). A key aspect of MCO problems is the absence, in most cases, of a single decision, which would best satisfy all the efficiency criteria, since these criteria can be contradictory. As a result, solving MCO problems usually requires finding several compromise decisions (efficient and non-dominated) that cannot be improved without worsening the effectiveness of other efficiency criteria in the MCO problem. Finding the whole set of efficient decisions may require a lot of computations and is often deemed redundant for the decision-maker. As a result, approaches that allow obtaining only particular limited sets of efficient decisions are used in practice more often. Among these approaches is the scalarization approach, which is based on methods involving the convolution of criteria to a single scalar criterion (see, e.g. [2,10]). Another approach relies on the iterative methods [6,11]—the decision-maker is actively involved in the process of selecting decisions. Another popular approach is to develop and apply evolut
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