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The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume

  • Víctor Adrián Sosa HernándezEmail author
  • Oliver Schütze
  • Günter Rudolph
  • Heike Trautmann
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 227)

Abstract

In many applications one is faced with the problem that multiple objectives have to be optimized at the same time. Since typically the solution set of such multi-objective optimization problems forms a manifold which cannot be computed analytically, one is in many cases interested in a suitable finite size approximation of this set. One widely used approach is to find a representative set that maximizes the dominated hypervolume that is defined by the images in objective space of these solutions and a given reference point.

In this paper, we propose a new point-wise iterative search procedure, Hypervolume Directed Search (HVDS), that aims to increase the hypervolume of a given point in an archive for bi-objective unconstrained optimization problems. We present the HVDS both as a standalone algorithm and as a local searcher within a specialized evolutionary algorithm. Numerical results confirm the strength of the novel approach.

Keywords

multi-objective optimization evolutionary computation dominated hypervolume local search directed search 

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Víctor Adrián Sosa Hernández
    • 1
    Email author
  • Oliver Schütze
    • 1
  • Günter Rudolph
    • 2
  • Heike Trautmann
    • 3
  1. 1.Computer Science DepartmentCINVESTAV-IPNMexico CityMexico
  2. 2.Fakultät für InformatikTechnische Universität DortmundDortmundGermany
  3. 3.Statistics and Information SystemsUniversity of MünsterMünsterGermany

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