Finding preferred solutions under weighted Tchebycheff preference functions for multi-objective integer programs
•Considers weighted Tchebycheff preference functions.•Develops an interactive algorithm that finds the most preferred solution.•Exploits the characteristics of Tchebycheff functions in the search process.•Quickly converges to the most preferred solution. Many interactive approaches in multi-objectiv...
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| Vydáno v: | European journal of operational research Ročník 308; číslo 1; s. 215 - 228 |
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| Jazyk: | angličtina |
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Elsevier B.V
01.07.2023
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| ISSN: | 0377-2217, 1872-6860 |
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| Abstract | •Considers weighted Tchebycheff preference functions.•Develops an interactive algorithm that finds the most preferred solution.•Exploits the characteristics of Tchebycheff functions in the search process.•Quickly converges to the most preferred solution.
Many interactive approaches in multi-objective optimization assume the existence of an underlying preference function that represents the preferences of a decision maker (DM). In this paper, we develop the theory and an exact algorithm that guarantees finding the most preferred solution of a DM whose preferences are consistent with a Tchebycheff function for multi-objective integer programs. The algorithm occasionally presents pairs of solutions to the DM and asks which one is preferred. It utilizes the preference information together with the properties of the Tchebycheff function to generate solutions that are candidates to be the most preferred solution. We test the performance of the algorithm on a set of three and four-objective combinatorial optimization problems. |
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| AbstractList | •Considers weighted Tchebycheff preference functions.•Develops an interactive algorithm that finds the most preferred solution.•Exploits the characteristics of Tchebycheff functions in the search process.•Quickly converges to the most preferred solution.
Many interactive approaches in multi-objective optimization assume the existence of an underlying preference function that represents the preferences of a decision maker (DM). In this paper, we develop the theory and an exact algorithm that guarantees finding the most preferred solution of a DM whose preferences are consistent with a Tchebycheff function for multi-objective integer programs. The algorithm occasionally presents pairs of solutions to the DM and asks which one is preferred. It utilizes the preference information together with the properties of the Tchebycheff function to generate solutions that are candidates to be the most preferred solution. We test the performance of the algorithm on a set of three and four-objective combinatorial optimization problems. |
| Author | Karakaya, G. Köksalan, M. |
| Author_xml | – sequence: 1 givenname: G. surname: Karakaya fullname: Karakaya, G. email: kgulsah@metu.edu.tr organization: Department of Business Administration, Middle East Technical University, Ankara 06800, Turkey – sequence: 2 givenname: M. surname: Köksalan fullname: Köksalan, M. organization: Ross School of Business, University of Michigan, Ann Arbor, MI 48109, USA |
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| Cites_doi | 10.1287/mnsc.30.11.1336 10.1002/1520-6750(199004)37:2<263::AID-NAV3220370206>3.0.CO;2-6 10.1016/0377-2217(81)90275-7 10.1007/BF01584098 10.1057/palgrave.jors.2602019 10.1016/j.ejor.2017.07.028 10.1016/S0377-2217(98)00218-5 10.1080/0740817X.2014.882532 10.1007/s10479-014-1545-2 10.1016/j.ejor.2013.03.006 10.1016/j.swevo.2019.100602 10.1287/mnsc.41.7.1158 10.1080/02331939508844109 10.1016/j.ejor.2016.05.029 10.1287/mnsc.22.6.652 10.1142/S0219622012400056 10.1016/0270-0255(82)90038-0 10.1016/j.dss.2010.11.023 10.1016/j.cor.2018.02.015 10.1016/0377-2217(86)90050-0 10.1007/BF02591870 10.1109/TSMC.1984.6313266 10.1016/j.cor.2019.04.008 10.1002/mcda.1499 |
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| Keywords | Tchebycheff function Interactive approach Multiple objective programming Preferred solution |
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approximation publication-title: Journal of Multi-Criteria Decision Analysis doi: 10.1002/mcda.1499 |
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| Title | Finding preferred solutions under weighted Tchebycheff preference functions for multi-objective integer programs |
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