Computationally efficient approach for solving lexicographic multicriteria optimization problems

• Published in: Optimization letters Vol. 15; no. 7; pp. 2469 - 2495
• Main Authors: Gergel, Victor, Kozinov, Evgeniy, Barkalov, Konstantin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2021
• Subjects: Computational Intelligence; Mathematics; Mathematics and Statistics; Numerical and Computational Physics; Operations Research/Decision Theory; Optimization; Original Paper; Simulation; Multicriteria optimization; Global optimization; Search information; Dimensional reduction; Computational complexity; Lexicographic ordering
• ISSN: 1862-4472; 1862-4480
• DOI: 10.1007/s11590-020-01668-y

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.