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Computationally efficient approach for solving lexicographic multicriteria optimization problems

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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.

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Notes

  1. From a general point of view, the MCOlex problem can be considered as a special case of the MMCOlex problem for \(t=1\).

  2. Data ordering is reflected by using a subscript.

  3. If \(M=m+1\), then \(z_M^*\) is the minimum value of the function \(\varphi (x)\).

  4. This method is also known as the index method—see [29].

  5. The values \(r_{\nu } > 1\), \(1 \le \nu \le m+1\), are the AGCS reliability parameters used for computing the interval characteristics in (25).

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Acknowledgements

The work was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No 075-15-2020-808.

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  1. Mathematical Center, Lobachevsky State University of Nizhni Novgorod, Gagarin ave., 23, Nizhni, Novgorod, Russia

    Victor Gergel, Evgeniy Kozinov & Konstantin Barkalov

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  1. Victor Gergel
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  2. Evgeniy Kozinov
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  3. Konstantin Barkalov
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Gergel, V., Kozinov, E. & Barkalov, K. Computationally efficient approach for solving lexicographic multicriteria optimization problems. Optim Lett 15, 2469–2495 (2021). https://doi.org/10.1007/s11590-020-01668-y

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