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