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Fig. 4. Final non-dominated fronts for the two-stage planetary gear transmission system opti-
mization using MOEA/D-CDP-ID compared to MOEA/D-CDP
We conducted experiments for 30 runs to verify the results. In the study, a refer-
ence point of [5, 5] is used, which is taken by estimating the maximum value of each
objective across the runs. As shown in Table 4, MOEA/D-CDP-ID achieves higher
values of hypervolume [9] and smaller values of Inverted Generational Distance(IGD)
[13] and Averaged Hausdorff Distance( P) [14] as compared to MOEA/D-CDP.
Because the smaller value of IGD and Hausdorff Distance the better the performance
of the algorithm, we can conclude that MOEA/D-CDP-ID outperforms MOEA/D-
CDP.
Table 4. Mean and standard devation of metric values obtained by MOEA/D-CDP-ID
compared to MOEA/D-CDP on the two-stage planetary gear transmission system optimization
Hypervolume
(ref[5,5])
Instance
(Runs=30)
IGD
P(P=2)
mean
std
mean
std
mean
std
MOEA/D-CDP-ID
2.09e+1
3.59e-2
1.67e-2
5.63e+1
2.87e-2
1.07e-2
MOEA/D-CDP
4.43e+1
1.66e+1
3.90e-2
8.83e-2
2.78e-2
6.94e-2
5
Conclusions
In this paper, two mechanisms, namely infeasibility driven and constrained-domination
principle are embedded within the framework of multi-objective evolutionary algorithm
based on decomposition (MOEA/D) [1] to deal with constrained multiobjective
 
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