TY - GEN
T1 - Generating data sets with known hypervolume & estimating the dominated hypervolume of random datasets
AU - Yukish, Michael A.
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85088758158&partnerID=8YFLogxK
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U2 - 10.2514/6.2012-5488
DO - 10.2514/6.2012-5488
M3 - Conference contribution
AN - SCOPUS:85088758158
SN - 9781600869303
T3 - 12th AIAA Aviation Technology, Integration and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
BT - 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
PB - American Institute of Aeronautics and Astronautics Inc.
T2 - 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
Y2 - 17 September 2012 through 19 September 2012
ER -