Some comments on GD and IGD and relations to the Hausdorff distance

Oliver Schuetze; Xavier Esquivel; Adriana Lara; Carlos A.Coello Coello

doi:10.1145/1830761.1830837

Some comments on GD and IGD and relations to the Hausdorff distance

Oliver Schuetze, Xavier Esquivel, Adriana Lara, Carlos A.Coello Coello

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

12 Scopus citations

Abstract

When measuring distances between different objects such as different sets the use of metrics has been well established in literature. We investigate here two widely used indicators for the evaluation of Multi-objective Evolutionary Algorithms, the Generational Distance (GD) and the Inverted Generational Distance (IGD), with respect to the properties of a metric. Since the outcome is quite poor, we propose further on a new indicator which is made up of GD and IGD. The novel indicator can be viewed as an 'averaged version' of the Hausdorff distance and forms a pseudo-metric under certain assumptions.

Original language	English
Title of host publication	Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 - Companion Publication
Pages	1971-1974
Number of pages	4
DOIs	https://doi.org/10.1145/1830761.1830837
State	Published - 2010
Externally published	Yes
Event	12th Annual Genetic and Evolutionary Computation Conference, GECCO-2010 - Portland, OR, United States Duration: 7 Jul 2010 → 11 Jul 2010

Publication series

Name	Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 - Companion Publication

Conference

Conference	12th Annual Genetic and Evolutionary Computation Conference, GECCO-2010
Country/Territory	United States
City	Portland, OR
Period	7/07/10 → 11/07/10

Keywords

Distance measurement
Metric
Multi-objective optimization

Access to Document

10.1145/1830761.1830837

Cite this

Schuetze, O., Esquivel, X., Lara, A., & Coello, C. A. C. (2010). Some comments on GD and IGD and relations to the Hausdorff distance. In Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 - Companion Publication (pp. 1971-1974). (Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 - Companion Publication). https://doi.org/10.1145/1830761.1830837

Schuetze, Oliver ; Esquivel, Xavier ; Lara, Adriana et al. / Some comments on GD and IGD and relations to the Hausdorff distance. Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 - Companion Publication. 2010. pp. 1971-1974 (Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 - Companion Publication).

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title = "Some comments on GD and IGD and relations to the Hausdorff distance",

abstract = "When measuring distances between different objects such as different sets the use of metrics has been well established in literature. We investigate here two widely used indicators for the evaluation of Multi-objective Evolutionary Algorithms, the Generational Distance (GD) and the Inverted Generational Distance (IGD), with respect to the properties of a metric. Since the outcome is quite poor, we propose further on a new indicator which is made up of GD and IGD. The novel indicator can be viewed as an 'averaged version' of the Hausdorff distance and forms a pseudo-metric under certain assumptions.",

keywords = "Distance measurement, Metric, Multi-objective optimization",

author = "Oliver Schuetze and Xavier Esquivel and Adriana Lara and Coello, {Carlos A.Coello}",

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booktitle = "Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 - Companion Publication",

note = "12th Annual Genetic and Evolutionary Computation Conference, GECCO-2010 ; Conference date: 07-07-2010 Through 11-07-2010",

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Schuetze, O, Esquivel, X, Lara, A & Coello, CAC 2010, Some comments on GD and IGD and relations to the Hausdorff distance. in Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 - Companion Publication. Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 - Companion Publication, pp. 1971-1974, 12th Annual Genetic and Evolutionary Computation Conference, GECCO-2010, Portland, OR, United States, 7/07/10. https://doi.org/10.1145/1830761.1830837

Some comments on GD and IGD and relations to the Hausdorff distance. / Schuetze, Oliver; Esquivel, Xavier; Lara, Adriana et al.
Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 - Companion Publication. 2010. p. 1971-1974 (Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 - Companion Publication).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - When measuring distances between different objects such as different sets the use of metrics has been well established in literature. We investigate here two widely used indicators for the evaluation of Multi-objective Evolutionary Algorithms, the Generational Distance (GD) and the Inverted Generational Distance (IGD), with respect to the properties of a metric. Since the outcome is quite poor, we propose further on a new indicator which is made up of GD and IGD. The novel indicator can be viewed as an 'averaged version' of the Hausdorff distance and forms a pseudo-metric under certain assumptions.

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Schuetze O, Esquivel X, Lara A, Coello CAC. Some comments on GD and IGD and relations to the Hausdorff distance. In Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 - Companion Publication. 2010. p. 1971-1974. (Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10 - Companion Publication). doi: 10.1145/1830761.1830837

Some comments on GD and IGD and relations to the Hausdorff distance

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