IEEE Computational Intelligence Magazine - May 2020 - 46
The PaletteViz plot allows a DM to look at only about
20 critical points (marked in red color) from a set of 1,292
non-dominated points. If the DM prefers boundary points
(for which at least one of the objectives has an extreme
value) a few red-circled points can be further looked into,
however if the DM prefers a point which lies at the core of
the data-set (with a good compromise of all four objectives)
then three red-circled points in Layer 3 (from top) can be
further looked into.
D. Disjointed Pareto-Optimal Front
As we have discussed before, in the presence of a Pareto set having multiple disjointed clusters in the original high-dimensional
objective space, a DM may be interested in the boundary points
of each cluster.To illustrate this scenario, we have used the palette
0.8
visualization on three- and five-objective C2DTLZ2 problem
[26]. The Pareto set consists of multiple clusters that are generated by applying (m + 1) constraints on DTLZ2 [30] problem. A
three-dimensional scatter plot of C2DTLZ2 is presented in Figure 13. Three extreme points have a large trade-off, due to the
concavity of the Pareto-optimal surface. Figure 14 shows the
PaletteViz plot for a five-objective C2DTLZ2 problem. Six
clusters and their relative locations are noticeable from the PaletteViz plot. The pink points are closer to a constraint boundary
and cyan colored points are well inside the feasible region. It is
interesting to note that the top-most layer has mixed pink and
cyan-colored, providing vital information to a DM. Not all
boundary points are on constraint surfaces. If a boundary point
near the constraint surface is desired, the DM can only analyze
the pink points further. Otherwise, if a core point near the constraint surface is desired, a pink point from one of the bottom
layers can be chosen.
In order to compare PaletteViz plot with another existing
visualization method, we plot the same data-set for the fiveobjective C2DTLZ2 problem in a heatmap [9] visualization in
Figure 15. For this particular application, heatmap does not
provide much information about six clusters that the data possess and nearness of any point to a constraint boundary.
f3
VI. PaletteViz for Engineering Design Problems
0.4
0
0
0.4 f
1
0
0.8
0.4
So far, we have seen the proposed palette visualization technique can address different scenarios that a DM may come
across during a decision-making process. Next, we apply PaletteViz on two engineering design problems.
0.8
f2
A. Vehicle Crash-Worthiness Problem
FIGURE 13 Pareto set for the three-objective C2DTLZ2 problem.
There are four isolated regions on the data-set. The data-set contains
2,373 points.
We apply our method to the vehicle crash-worthiness problem
from [18].This is a three-objective optimization problem, however the Pareto set in this problem is observed to have two separate
1
f3
f4
f2
0.8
0.6
0.4
0.2
f5
f1
FIGURE 14 PaletteViz plot of the five-objective C2DTLZ2 problem
indicating five extreme and one central cluster in the original data-set
containing 5,170 points.
46
IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2020
f1
f2
f3
f4
f5
0
FIGURE 15 The heatmap [9] visualization of five objective C2DTLZ2
problem. This visualization does not convey any interesting information about the Pareto set. All the points are sorted in descending
order with respect to f1. The cluster closer to extreme f1 value has a
large difference in f1 values from other clusters.
IEEE Computational Intelligence Magazine - May 2020
Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - May 2020
IEEE Computational Intelligence Magazine - May 2020 - Cover1
IEEE Computational Intelligence Magazine - May 2020 - Cover2
IEEE Computational Intelligence Magazine - May 2020 - 1
IEEE Computational Intelligence Magazine - May 2020 - 2
IEEE Computational Intelligence Magazine - May 2020 - 3
IEEE Computational Intelligence Magazine - May 2020 - 4
IEEE Computational Intelligence Magazine - May 2020 - 5
IEEE Computational Intelligence Magazine - May 2020 - 6
IEEE Computational Intelligence Magazine - May 2020 - 7
IEEE Computational Intelligence Magazine - May 2020 - 8
IEEE Computational Intelligence Magazine - May 2020 - 9
IEEE Computational Intelligence Magazine - May 2020 - 10
IEEE Computational Intelligence Magazine - May 2020 - 11
IEEE Computational Intelligence Magazine - May 2020 - 12
IEEE Computational Intelligence Magazine - May 2020 - 13
IEEE Computational Intelligence Magazine - May 2020 - 14
IEEE Computational Intelligence Magazine - May 2020 - 15
IEEE Computational Intelligence Magazine - May 2020 - 16
IEEE Computational Intelligence Magazine - May 2020 - 17
IEEE Computational Intelligence Magazine - May 2020 - 18
IEEE Computational Intelligence Magazine - May 2020 - 19
IEEE Computational Intelligence Magazine - May 2020 - 20
IEEE Computational Intelligence Magazine - May 2020 - 21
IEEE Computational Intelligence Magazine - May 2020 - 22
IEEE Computational Intelligence Magazine - May 2020 - 23
IEEE Computational Intelligence Magazine - May 2020 - 24
IEEE Computational Intelligence Magazine - May 2020 - 25
IEEE Computational Intelligence Magazine - May 2020 - 26
IEEE Computational Intelligence Magazine - May 2020 - 27
IEEE Computational Intelligence Magazine - May 2020 - 28
IEEE Computational Intelligence Magazine - May 2020 - 29
IEEE Computational Intelligence Magazine - May 2020 - 30
IEEE Computational Intelligence Magazine - May 2020 - 31
IEEE Computational Intelligence Magazine - May 2020 - 32
IEEE Computational Intelligence Magazine - May 2020 - 33
IEEE Computational Intelligence Magazine - May 2020 - 34
IEEE Computational Intelligence Magazine - May 2020 - 35
IEEE Computational Intelligence Magazine - May 2020 - 36
IEEE Computational Intelligence Magazine - May 2020 - 37
IEEE Computational Intelligence Magazine - May 2020 - 38
IEEE Computational Intelligence Magazine - May 2020 - 39
IEEE Computational Intelligence Magazine - May 2020 - 40
IEEE Computational Intelligence Magazine - May 2020 - 41
IEEE Computational Intelligence Magazine - May 2020 - 42
IEEE Computational Intelligence Magazine - May 2020 - 43
IEEE Computational Intelligence Magazine - May 2020 - 44
IEEE Computational Intelligence Magazine - May 2020 - 45
IEEE Computational Intelligence Magazine - May 2020 - 46
IEEE Computational Intelligence Magazine - May 2020 - 47
IEEE Computational Intelligence Magazine - May 2020 - 48
IEEE Computational Intelligence Magazine - May 2020 - 49
IEEE Computational Intelligence Magazine - May 2020 - 50
IEEE Computational Intelligence Magazine - May 2020 - 51
IEEE Computational Intelligence Magazine - May 2020 - 52
IEEE Computational Intelligence Magazine - May 2020 - 53
IEEE Computational Intelligence Magazine - May 2020 - 54
IEEE Computational Intelligence Magazine - May 2020 - 55
IEEE Computational Intelligence Magazine - May 2020 - 56
IEEE Computational Intelligence Magazine - May 2020 - 57
IEEE Computational Intelligence Magazine - May 2020 - 58
IEEE Computational Intelligence Magazine - May 2020 - 59
IEEE Computational Intelligence Magazine - May 2020 - 60
IEEE Computational Intelligence Magazine - May 2020 - 61
IEEE Computational Intelligence Magazine - May 2020 - 62
IEEE Computational Intelligence Magazine - May 2020 - 63
IEEE Computational Intelligence Magazine - May 2020 - 64
IEEE Computational Intelligence Magazine - May 2020 - 65
IEEE Computational Intelligence Magazine - May 2020 - 66
IEEE Computational Intelligence Magazine - May 2020 - 67
IEEE Computational Intelligence Magazine - May 2020 - 68
IEEE Computational Intelligence Magazine - May 2020 - 69
IEEE Computational Intelligence Magazine - May 2020 - 70
IEEE Computational Intelligence Magazine - May 2020 - 71
IEEE Computational Intelligence Magazine - May 2020 - 72
IEEE Computational Intelligence Magazine - May 2020 - 73
IEEE Computational Intelligence Magazine - May 2020 - 74
IEEE Computational Intelligence Magazine - May 2020 - 75
IEEE Computational Intelligence Magazine - May 2020 - 76
IEEE Computational Intelligence Magazine - May 2020 - 77
IEEE Computational Intelligence Magazine - May 2020 - 78
IEEE Computational Intelligence Magazine - May 2020 - 79
IEEE Computational Intelligence Magazine - May 2020 - 80
IEEE Computational Intelligence Magazine - May 2020 - 81
IEEE Computational Intelligence Magazine - May 2020 - 82
IEEE Computational Intelligence Magazine - May 2020 - 83
IEEE Computational Intelligence Magazine - May 2020 - 84
IEEE Computational Intelligence Magazine - May 2020 - 85
IEEE Computational Intelligence Magazine - May 2020 - 86
IEEE Computational Intelligence Magazine - May 2020 - 87
IEEE Computational Intelligence Magazine - May 2020 - 88
IEEE Computational Intelligence Magazine - May 2020 - 89
IEEE Computational Intelligence Magazine - May 2020 - 90
IEEE Computational Intelligence Magazine - May 2020 - 91
IEEE Computational Intelligence Magazine - May 2020 - 92
IEEE Computational Intelligence Magazine - May 2020 - Cover3
IEEE Computational Intelligence Magazine - May 2020 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202311
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202308
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202305
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202302
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202211
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202208
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202205
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202202
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202111
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202108
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202105
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202102
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202011
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202008
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202005
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202002
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201911
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201908
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201905
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201902
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201811
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201808
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201805
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201802
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter12
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall12
https://www.nxtbookmedia.com