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ETH Zürich - D-ITET - TIK - SOP - Downloads & Materials - Supplementary Materials - Testproblems
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Untitled Document

Density and approximations of µ-distribution for different testproblems

Results

For the following testproblems, different information is provided: (i) the formulation, (ii) the Pareto front, (iii) relevant publications, (iv) the density, and (v) approximated optimal distributions for different number of points with corresponding hypervolume values.

ZDT

  • ZDT 1
  • ZDT 2
  • ZDT 3
  • ZDT 4
  • ZDT 5 has a discrete Pareto front
  • ZDT 6
  • DTLZ

  • DTLZ 1
  • DTLZ 2
  • DTLZ 3
  • DTLZ 4
  • The Pareto front of DTLZ 5 consists of one point only.
  • The Pareto front of DTLZ 6 consists of one point only.
  • DTLZ 7
  • Maple Worksheets and HTML ouput

    The following Maple worksheets and HTML output thereof contain the derivation of the density and a lower bound for the reference point.
  • ZDT1 as html output, as maple worksheet
  • ZDT2 as html output, as maple worksheet
  • ZDT3 as html output, as maple worksheet
  • ZDT6 as html output, as maple worksheet
  • DTLZ1 as html output, as maple worksheet
  • DTLZ2 as html output, as maple worksheet
  • DTLZ7 as html output, as maple worksheet
  • WFG1 as html output, as maple worksheet
  • WFG2 as html output, as maple worksheet
  • WRG3 as html output, as maple worksheet
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