The reduction of the Pareto set of a special structure in bicriteria discrete problems

A. O. Zakharov^a, Yu. V. Kovalenko<sup>b

a</sup> St. Petersburg State University, 7-9 Universitetskaya Embankment, 199034 St. Petersburg, Russia
^b Sobolev Institute of Mathematics, 13 Pevtsov Street, 644099 Omsk, Russia

Abstract: We investigate bicriteria discrete optimization problems in the context of the axiomatic approach of the Pareto set reduction. The degree of the reduction with respect to values of the coefficient of compromise is evaluated for special structures and general case of the Pareto set. The results are applied to the set covering problem and vehicle routing problems. Illustr. 4, bibliogr. 19.

Keywords: discrete optimization, bicriteria problem, the Pareto set reduction, preference relation of the decision maker.

UDC: 519.816+519.854.2

Received: 19.04.2021
Revised: 08.06.2021
Accepted: 10.06.2021

DOI: 10.33048/daio.2021.28.712

 English version: Journal of Applied and Industrial Mathematics, 2021, 15:4, 728–744