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Journal of Applied and Industrial Mathematics
Published in: Journal of Applied and Industrial Mathematics 4/2021

01-11-2021

Reduction of the Pareto Set of a Special Structure in Bicriteria Discrete Problems

Authors: A. O. Zakharov, Yu. V. Kovalenko

Published in: Journal of Applied and Industrial Mathematics | Issue 4/2021

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Abstract

We investigate the bicriteria discrete optimization problems in the context of the axiomatic approach reducing the Pareto set. The degree of the reduction with respect to values of the coefficient of compromise is evaluated for the special structures and general case of the Pareto set. We apply the results to the set covering problems and the vehicle routing problems.
previous article Optimization of the Location of Interconnected Facilities on Parallel Lines with Forbidden Zones

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Literature
1.
O. I. Larichev, Decision-Making Theory and Methods as Well as a Chronicle of Events in Magical Lands (Logos, Moscow, 2006) [in Russian].
2.
A. V. Lotov and I. I. Pospelova, Multicriteria Decision Making Problems (MAKS Press, Moscow, 2008) [in Russian].
3.
A. V. Petrovsky, Decision Making Theory (Akademija, Moscow, 2009) [in Russian].
4.
A. Ishizaka and P. Nemery, Multi-Criteria Decision Analysis: Methods and Software (Wiley, Hoboken, NJ, 2013).CrossRef
5.
M. Ehrgott, J. L. Figueira, and S. Greco, Trends in Multiple Criteria Decision Analysis (Springer, New York, 2010).CrossRef
6.
S. Greco, M. Ehrgott, and J. L. Figueira, Multiple Criteria Decision Analysis: State of the Art Surveys (Springer, New York, 2016).CrossRef
7.
O. I. Larichev, Verbal Analysis of Solutions, Ed. by A. B. Petrovsky (Nauka, Moscow, 2006) [in Russian].
8.
V. D. Nogin, Pareto Set Reduction: An Axiomatic Approach (Fizmatlit, Moscow, 2016) [in Russian].
9.
A. O. Zakharov and Yu. V. Kovalenko, “Reduction of the Pareto Set in Bicriteria Asymmetric Traveling Salesman Problem,” in Optimization Problems and Their Applications. Revised Selected Papers. 7th International Conference (Omsk, Russia, July 8–14, 2018), Ed. by A. Eremeev, M. Khachay, Yu. Kochetov, and P. Pardalos (Cham: Springer, 2018), pp. 93–105.
10.
A. O. Zakharov and Yu. V. Kovalenko, “Construction and Reduction of the Pareto Set in Asymmetric Travelling Salesman Problem with Two Criteria,” Vestnik St.-Petersburg Univ. Ser. Prikl. Mat., Informat., Proc. Upravl. 14 (4), 378–392 (2018).MathSciNet
11.
A. O. Zakharov and Yu. V. Kovalenko, “Structures of the Pareto Set and Their Reduction in Bicriteria Discrete Problems,” J. Phys. Conf. Ser. 1260 (8), 082007:1–082007:8 (2019).CrossRef
12.
N. Christofides, Graph Theory: An Algorithmic Approach (Acad. Press, London, 1975).MATH
13.
A. V. Eremeev, L. A. Zaozerskaya, and A. A. Kolokolov, “A Set Covering Problem: Complexity, Algoritms, Experimental Research,” Diskret. Anal. Issled. Oper. Ser. 2, 7 (2), 22–46 (2000).MATH
14.
M. I. Nechepurenko, V. K. Popkov, S. M. Majnagashev, S. B. Kaul’, V. A. Proskuryakov, V. A. Kohov, and A. V. Gryzunov, Algorithms and Programs for Solving Problems on Graphs and Networks (Nauka, Novosibirsk, 1990) [in Russian].MATH
15.
A. A. Kolokolov and L. A. Zaozerskaya, “Solving a Bicriteria Problem of Optimal Service Centers Location,” J. Math. Model. Algorithms 12, 105–116 (2013).MathSciNetCrossRef
16.
J. Saksena, “Mathematical Model for Scheduling Clients through Welfare Agencies,” J. Can. Oper. Res. Soc. 8, 185–200 (1970).MathSciNetMATH
17.
A. Henry-Labordere, “The Record Balancing Problem: A Dynamic Programming Solution of a Generalized Traveling Salesman Problem,” Rev. Franç. Inform. Rech. Opér. 3 (B-2), 43–49 (1969).MATH
18.
M. Yu. Khachai and E. D. Neznakhina, “Approximate Schemes for the Generalized Traveling Salesman Problem,” Trudy Inst. Mat. Mekh. Ural. Otdel. Ross. Akad. Nauk 22 (3), 283–292 (2016).
19.
A. G. Chentsov, M. Yu. Khachai, and D. M. Khachai, “An Exact Algorithm with Linear Complexity for a Problem of Visiting Megalopolises,” Trudy Inst. Mat. Mekh. Ural. Otdel. Ross. Akad. Nauk 21 (3), 309–317 (2015).MATH
Metadata
Title
Reduction of the Pareto Set of a Special Structure in Bicriteria Discrete Problems
Authors
A. O. Zakharov
Yu. V. Kovalenko
Publication date
01-11-2021
Publisher
Pleiades Publishing
Published in
Journal of Applied and Industrial Mathematics / Issue 4/2021
Print ISSN: 1990-4789
Electronic ISSN: 1990-4797
DOI
https://doi.org/10.1134/S1990478921040153

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