Generating data sets with known hypervolume & estimating the dominated hypervolume of random datasets

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper presents two methods for generating data sets with known dominated hypervolumes. The first method, based on creating a block pyramid of dimension 2 or greater generates highly structured data with limited flexibility in number of Pareto points and results in a Pareto front with all points residing on a hyperplane. The second method generates Pareto sets with an arbitrary number of points and some control over the shape of the front (convex or concave). Both methods provide an exact dominated hypervolume, and so can be used to provide test data for testing algorithms that calculate hypervolume approximations. Additionally, the paper presents a method to estimate the expected hypervolume of a set of Pareto points that are distributed on the face of a simplex, and demonstrates the sensitivity of the ratio of the hypervolume to the dimensionality of the problem.

Original languageEnglish (US)
Title of host publication12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
StatePublished - Dec 1 2012
Event12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference - Indianapolis, IN, United States
Duration: Sep 17 2012Sep 19 2012

Publication series

Name12th AIAA Aviation Technology, Integration and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

Other

Other12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
CountryUnited States
CityIndianapolis, IN
Period9/17/129/19/12

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All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Mechanical Engineering

Cite this

Yukish, M. A. (2012). Generating data sets with known hypervolume & estimating the dominated hypervolume of random datasets. In 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (12th AIAA Aviation Technology, Integration and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference).
Yukish, Michael Andrew. / Generating data sets with known hypervolume & estimating the dominated hypervolume of random datasets. 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. 2012. (12th AIAA Aviation Technology, Integration and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference).
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Yukish, MA 2012, Generating data sets with known hypervolume & estimating the dominated hypervolume of random datasets. in 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. 12th AIAA Aviation Technology, Integration and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Indianapolis, IN, United States, 9/17/12.

Generating data sets with known hypervolume & estimating the dominated hypervolume of random datasets. / Yukish, Michael Andrew.

12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. 2012. (12th AIAA Aviation Technology, Integration and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Yukish MA. Generating data sets with known hypervolume & estimating the dominated hypervolume of random datasets. In 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. 2012. (12th AIAA Aviation Technology, Integration and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference).