On a practical notion of Geoffrion proper optimality in multicriteria optimizationCitation formats

Standard

On a practical notion of Geoffrion proper optimality in multicriteria optimization. / Shukla, Pradyumn; Dutta, Joydeep; Deb, Kalyanmoy; Kesarwani, Poonam.

In: Optimization: a journal of mathematical programming and operations research, Vol. 69, No. 7-8, 16.05.2019, p. 1513.

Research output: Contribution to journalArticlepeer-review

Harvard

Shukla, P, Dutta, J, Deb, K & Kesarwani, P 2019, 'On a practical notion of Geoffrion proper optimality in multicriteria optimization', Optimization: a journal of mathematical programming and operations research, vol. 69, no. 7-8, pp. 1513. https://doi.org/10.1080/02331934.2019.1613403

APA

Shukla, P., Dutta, J., Deb, K., & Kesarwani, P. (2019). On a practical notion of Geoffrion proper optimality in multicriteria optimization. Optimization: a journal of mathematical programming and operations research, 69(7-8), 1513. https://doi.org/10.1080/02331934.2019.1613403

Vancouver

Shukla P, Dutta J, Deb K, Kesarwani P. On a practical notion of Geoffrion proper optimality in multicriteria optimization. Optimization: a journal of mathematical programming and operations research. 2019 May 16;69(7-8):1513. https://doi.org/10.1080/02331934.2019.1613403

Author

Shukla, Pradyumn ; Dutta, Joydeep ; Deb, Kalyanmoy ; Kesarwani, Poonam. / On a practical notion of Geoffrion proper optimality in multicriteria optimization. In: Optimization: a journal of mathematical programming and operations research. 2019 ; Vol. 69, No. 7-8. pp. 1513.

Bibtex

@article{7c27223b865b4599bff4c7b2a652920b,
title = "On a practical notion of Geoffrion proper optimality in multicriteria optimization",
abstract = "Geoffrion proper optimality is a widely used optimality notion in multicriteria optimization that prevents exact solutions having unbounded trade-offs. As algorithms for multicriteria optimization usually give only approximate solutions, we analyze the notion of approximate Geoffrion proper optimality. We show that in the limit, approximate Geoffrion proper optimality may converge to solutions having unbounded trade-offs. Therefore, we introduce a restricted notion of approximate Geoffrion proper optimality and prove that this restricted notion alleviates the problem of solutions having unbounded trade-offs. Furthermore, using a characterization based on the infeasibility of a system of inequalities, we investigate the convergence properties of different approximate optimality notions in multicriteria optimization. These convergence properties are important for algorithmic reasons. The restricted notion of approximate Geoffrion proper optimality seems to be the only approximate optimality notion that shows favourable convergence properties. This notion bounds the trade-offs globally and can be used in multicriteria decision-making algorithms as well. Due to these, it seems to be a practical optimality notion.",
author = "Pradyumn Shukla and Joydeep Dutta and Kalyanmoy Deb and Poonam Kesarwani",
year = "2019",
month = may,
day = "16",
doi = "https://doi.org/10.1080/02331934.2019.1613403",
language = "English",
volume = "69",
pages = "1513",
journal = "Optimization",
issn = "0233-1934",
publisher = "Taylor & Francis",
number = "7-8",

}

RIS

TY - JOUR

T1 - On a practical notion of Geoffrion proper optimality in multicriteria optimization

AU - Shukla, Pradyumn

AU - Dutta, Joydeep

AU - Deb, Kalyanmoy

AU - Kesarwani, Poonam

PY - 2019/5/16

Y1 - 2019/5/16

N2 - Geoffrion proper optimality is a widely used optimality notion in multicriteria optimization that prevents exact solutions having unbounded trade-offs. As algorithms for multicriteria optimization usually give only approximate solutions, we analyze the notion of approximate Geoffrion proper optimality. We show that in the limit, approximate Geoffrion proper optimality may converge to solutions having unbounded trade-offs. Therefore, we introduce a restricted notion of approximate Geoffrion proper optimality and prove that this restricted notion alleviates the problem of solutions having unbounded trade-offs. Furthermore, using a characterization based on the infeasibility of a system of inequalities, we investigate the convergence properties of different approximate optimality notions in multicriteria optimization. These convergence properties are important for algorithmic reasons. The restricted notion of approximate Geoffrion proper optimality seems to be the only approximate optimality notion that shows favourable convergence properties. This notion bounds the trade-offs globally and can be used in multicriteria decision-making algorithms as well. Due to these, it seems to be a practical optimality notion.

AB - Geoffrion proper optimality is a widely used optimality notion in multicriteria optimization that prevents exact solutions having unbounded trade-offs. As algorithms for multicriteria optimization usually give only approximate solutions, we analyze the notion of approximate Geoffrion proper optimality. We show that in the limit, approximate Geoffrion proper optimality may converge to solutions having unbounded trade-offs. Therefore, we introduce a restricted notion of approximate Geoffrion proper optimality and prove that this restricted notion alleviates the problem of solutions having unbounded trade-offs. Furthermore, using a characterization based on the infeasibility of a system of inequalities, we investigate the convergence properties of different approximate optimality notions in multicriteria optimization. These convergence properties are important for algorithmic reasons. The restricted notion of approximate Geoffrion proper optimality seems to be the only approximate optimality notion that shows favourable convergence properties. This notion bounds the trade-offs globally and can be used in multicriteria decision-making algorithms as well. Due to these, it seems to be a practical optimality notion.

U2 - https://doi.org/10.1080/02331934.2019.1613403

DO - https://doi.org/10.1080/02331934.2019.1613403

M3 - Article

VL - 69

SP - 1513

JO - Optimization

JF - Optimization

SN - 0233-1934

IS - 7-8

ER -