A Benchmark for a Mono and Multi Objective Optimization of the Brushless DC Wheel Motor

Mono-objective optimization

Results of mono-objective optimization are given in table 1. It represents the method, the optimal value of the design variables, the efficiency, the number of evaluations of the objective function and the constraints. Clicking on the name of the method, a description of the method appears with the authors name and associated references.

Table 1– Comparison of the mono-objective optimization results.

  Ds Be δ Bd Bcs η Eval Mtot Imax Dint Dext Ta
Method
mm
T
A/mm²
T
T
%
-
kg
A
mm
mm
°C
SQP
201.2
0.6481
2.0437
1.8
0.8959
95.32
90
15
125
76
238.9
95.35
GA
201.5
0.6480
2.0602
1.799
0.8817
95.31
3380
15
125
76.9
239.2
95.21
GA & SQP
201.2
0.6481
2.0615
1.8
0.8700
95.31
1644
15
125
76
238.9
95.31
ACO
201.2
0.6481
2.0437
1.8
0.8959
95.32
1200
15
125
76
238.9
95.35
PSO
202.1
0.6476
2.0417
1.8
0.9298
95.32
1600
15
125
79.2
239.8
94.98

 


Multi-objective optimization

Results of multi-objective optimization are given in table 2. It represents the method, the average and standard deviations of three performance metrics for 100 runs, the number of evaluations of the objective function. Clicking on the name of the method, a description of the method appears with the authors name and associated references. Clicking on the name of the metric, a description appears. The Pareto front obtained by the variable weighted sum of objectives with SQP is taken as the reference set.

Table 2 – Comparison of the multi-objective optimization results.

Method Contribution Coverage
average
std. dev.
average
std. dev.
average
std. dev.
SQP
/
/
1.86e-1
/
4.0e-1
/
/
0
NSGA-II
8.51e-2
1.7e-2
3.51e-1
1.20e-1
4.22e-1
1.99e-2
0.653
0.4641
SPEA2
8.78e-2
4.22e-2
3.46e-1
1.12e-1
3.34e-1
5.01e-1
0.801
0.75

 

Fig.3– Pareto front found with the all SQP, NSGA-II, and SPEA2.

 

 



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