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Fig. 15 The non-dominated
solutions of the hybrid
method for the ZDT1 test
function
Pareto optimal front
Hybrid algorithm
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
f 1 (x)
Fig. 16 The non-dominated
solutions of the hybrid
method for the ZDT2 test
function
1.2
Pareto optimal front
Hybrid algorithm
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
f 1 (x)
solutions and Pareto optimal front. If all members in the set of non-dominated
solutions are in Pareto optimal front then
! ¼
0
:
(2) The metric of diversity
(Deb et al. 2002 ) measures the extension of spread
achieved among non-dominated solutions, which is given as
ðDÞ
d l þ P n 1
i¼1 d i d
d f þ
D ¼
ð
14
Þ
Þ d
d f þ
d l þð
n
1
In this formula, df f and d l denote the Euclidean distance between the boundary
solutions and the extreme solutions of the non-dominated set, n stands for the
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