On the Closest Averaged Hausdorff Archive for a Circularly Convex Pareto Front

Rudolph G, Schütze O, Trautmann H


Abstract
The averaged Hausdorff distance has been proposed as an indicator for assessing the quality of finitely sized approximations of the Pareto front of a multiobjective problem. Since many set-based, iterative optimization algorithms store their currently best approximation in an internal archive these approximations are also termed archives. In case of two objectives and continuous variables it is known that the best approximations in terms of averaged Hausdorff distance are subsets of the Pareto front if it is concave. If it is linear or circularly concave the points of the best approximation are equally spaced. Here, it is proven that the optimal averaged Hausdorff approximation and the Pareto front have an empty intersection if the Pareto front is circularly convex. But the points of the best approximation are equally spaced and they rapidly approach the Pareto front for increasing size of the approximation.



Publication type
Chapter in Book

Peer reviewed
Yes

Publication status
Published

Year
2016

Book title
Applications of Evolutionary Computation: 19th European Conference, EvoApplications 2016, Porto, Portugal, March 30 -- April 1, 2016, Proceedings, Part II

Editor
Squillero G, Burelli P

Pages range
42-55

Publisher
Springer International Publishing

Place
Cham

Language
English

ISBN
978-3-319-31153-1

DOI

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