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

  • Günter RudolphEmail author
  • Oliver Schütze
  • Heike Trautmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9598)

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.

Keywords

Multi-objective optimization Averaged hausdorff distance Convex front Optimal archives 

Notes

Acknowledgment

Support from CONACYT project no. 207403 and DAAD project no. 57065955 is gratefully acknowledged. Additionally, Heike Trautmann acknowledges support by the European Center of Information Systems (ERCIS).

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Günter Rudolph
    • 1
    Email author
  • Oliver Schütze
    • 2
  • Heike Trautmann
    • 3
  1. 1.Department of Computer ScienceTU Dortmund UniversityDortmundGermany
  2. 2.Department of Computer ScienceCINVESTAVMexico CityMexico
  3. 3.Department of Information SystemsUniversity of MünsterMünsterGermany

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