Multidisciplinary design optimization of BLISS-2000 based on OpenMDAO:research on process, strategy and parameters

设计变量	初始点	上限	下限	最小上限	最大上限
z₁	1.0	−10.0	10.0	−10.0	10.0
z₂	2.0	0	10.0	0	10.0
x	5.0	0	10.0	0	10.0
y₁	10.0	0	100.0	0	100.0
y₂	4.0	−100.0	100.0	−100.0	100.0
w_y1	1.0	−2.0	2.0	−∞	+∞
w_y2	1.0	−2.0	2.0	−∞	+∞

Table 2. Optimization results of BLISS-2000 method for Sellar
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Table 2. Optimization results of BLISS-2000 method for Sellar
变量最优解 BLISS-2000优化解绝对误差
z₁ 1.978 0 1.964 4 −0.013 6
z₂ 0 0 0
x 0 0.042 9 0.042 9
y₁ 3.160 0 3.153 6 −0.006 4
y₂ 3.756 0 3.740 2 −0.015 8
f 3.183 4 3.179 2 −0.004 2

Table 3. Errors between the optimization results and the optimal solutions for different sampling levels

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Table 3. Errors between the optimization results and the optimal solutions for different sampling levels

变量	最优解	采样水平
变量	最优解	n = 6	n = 8	n = 10	n = 12
z₁	1.978 0	−0.013 6	−0.007 7	−0.013 2	−0.016 3
z₂	0	0	0	0	0.002 3
x	0	0.042 9	0.023 6	0.042 8	0.052 5
y₁	3.160 0	−0.006 4	−0.003 9	−0.004 8	−0.005 0
y₂	3.756 0	−0.015 8	−0.009 2	−0.014 8	−0.015 8
f	3.183 4	−0.004 2	−0.003 1	−0.002 6	0.000 4
δ_f /%		0.13	0.10	0.08	0.01

Table 4. BLISS-2000 optimization efficiency for different sampling levels
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Table 4. BLISS-2000 optimization efficiency for different sampling levels
采样水平
n=6 n=8 n=10 n=12
迭代次数 127 64 49 29
目标函数调用次数 55 576 16 438 3 761 342

Table 5. The errors between the optimization results and the optimal solution at different constraint relaxation factors

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Table 5. The errors between the optimization results and the optimal solution at different constraint relaxation factors

变量	最优解	ε = 0.01	ε = 0.001	ε = 0.0001
z₁	1.978 0	−3.611 4	−0.007 9	−0.008 1
z₂	0	0.525 5	0	0
x	0	0.088 6	0.023 9	0.024 1
y₁	3.160 0	0.002 1	−0.003 3	−0.004 7
y₂	3.756 0	−3.096 3	−0.008 2	−0.009 7
f	3.183 4	1.013 8	−0.003 6	−0.004 0
δ_f /%		31.85	0.11	0.13

Table 6. BLISS-2000 optimization efficiency at different constraint relaxation factors
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Table 6. BLISS-2000 optimization efficiency at different constraint relaxation factors
松弛因子
ε=0 ε=0.01 ε=0.001 ε=0.000 1
迭代次数 64 53 71 90
目标函数调用次数 16 438 3 088 3 227 3821

Table 7. Errors between the optimization results and the optimal solutions for different boundary update factors

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Table 7. Errors between the optimization results and the optimal solutions for different boundary update factors

变量	最优解	f_s = 0.9	f_s = 0.8	f_s = 0.7	f_s = 0.6
z₁	1.978 0	−0.008 1	−0.007 9	−3.577 3	未收敛
z₂	0	0	0	0.666 6
x	0	0.024 7	0.023 9	0
y₁	3.160 0	−0.003 2	−0.003 3	−0.018 1
y₂	3.756 0	−0.008 3	−0.008 2	−2.917 2
f	3.183 4	−0.003 4	−0.003 6	1.062 9
δ_f/%		0.11	0.11	33.39

Table 8. BLISS-2000 optimization efficiency for different boundary update factors
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Table 8. BLISS-2000 optimization efficiency for different boundary update factors
边界更新因子f_s
0.9 0.8 0.7
迭代次数 130 71 54
目标函数调用次数 8 120 3 227 4 797

Table 9. Optimization results of BLISS-2000 method for supersonic business jet

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Table 9. Optimization results of BLISS-2000 method for supersonic business jet

变量	BLISS-98优化解	BLISS-2000优化解	相对误差/%
t/c	0.06	0.06	0
h	60 000	60 000	0
M	1.40	1.40	0
AR	2.50	2.50	0
Λ	70.00	70.00	0
S_REF	1 500.00	1 500.00	0
λ	0.387 57	0.400 00	3.21
x	0.75	0.75	0
C_f	0.75	0.75	0
T	0.156 24	0.156 20	0.03
R	3 963.980 0	3 973.685 3	0.24

Table 10. BLISS-2000 optimization efficiency for supersonic business jet
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Table 10. BLISS-2000 optimization efficiency for supersonic business jet
参数数值
迭代次数 11
目标函数调用次数 158

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Yuhao GAO, Tengwu HE, Min ZHAO. Multidisciplinary design optimization of BLISS-2000 based on OpenMDAO:research on process, strategy and parameters[J]. Chinese Journal of Ship Research, 2024, 19(6): 135

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Paper Information

Category: Theory and Method of Intelligent Design for Ship and Ocean Engineering

Received: Jul. 15, 2024

Accepted: Sep. 6, 2024

Published Online: Mar. 14, 2025

The Author Email:

DOI:10.19693/j.issn.1673-3185.04064

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Start points and start boundaries of design variable for the Sellar problem

Table 1. Start points and start boundaries of design variable for the Sellar problem

Table 2. Optimization results of BLISS-2000 method for Sellar

Table 2. Optimization results of BLISS-2000 method for Sellar

Table 3. Errors between the optimization results and the optimal solutions for different sampling levels

Table 3. Errors between the optimization results and the optimal solutions for different sampling levels

Table 4. BLISS-2000 optimization efficiency for different sampling levels

Table 4. BLISS-2000 optimization efficiency for different sampling levels

Table 5. The errors between the optimization results and the optimal solution at different constraint relaxation factors

Table 5. The errors between the optimization results and the optimal solution at different constraint relaxation factors

Table 6. BLISS-2000 optimization efficiency at different constraint relaxation factors

Table 6. BLISS-2000 optimization efficiency at different constraint relaxation factors

Table 7. Errors between the optimization results and the optimal solutions for different boundary update factors

Table 7. Errors between the optimization results and the optimal solutions for different boundary update factors

Table 8. BLISS-2000 optimization efficiency for different boundary update factors

Table 8. BLISS-2000 optimization efficiency for different boundary update factors

Table 9. Optimization results of BLISS-2000 method for supersonic business jet

Table 9. Optimization results of BLISS-2000 method for supersonic business jet

Table 10. BLISS-2000 optimization efficiency for supersonic business jet

Table 10. BLISS-2000 optimization efficiency for supersonic business jet