组合加点准则的代理辅助多目标粒子群优化

doi:10.16180/j.cnki.issn1007-7820.2022.12.004

摘要/Abstract

摘要：

针对小样本数据构建代理模型初期优化效率低、模型精度差的问题,文中提出组合加点准则的代理辅助多目标粒子群优化算法。该算法通过加权平均法将Kriging模型和径向基函数网络模型组合成异构集成模型,使用改善期望准则和最小化代理模型预测准则相结合的组合加点准则对代理模型进行管理,加快了模型收敛速度。此外,该算法采用实际目标函数对每次迭代中增加的样本点进行评估,并对代理模型进行更新以增加模型准确性。实验结果表明,在适应度函数评估次数上,所提算法与非代理模型算法相比减少了10倍,证明该算法可提高代理模型的优化效率及准确性,并在勘探与开发之间取得了更好的平衡。

关键词: 代理模型, Kriging模型, 径向基函数网络模型, 异构集成, 组合加点准则, 适应度函数评估, 模型管理, 多目标粒子群优化算法

Abstract:

In view of the problem of low initial optimization efficiency and poor model accuracy when constructing surrogate models with small sample data, a surrogate-assisted multi-objective particle swarm optimization algorithm based on the combined infill sampling criterion is proposed in this study. The algorithm combines the Kriging model and the radial basis function network model into a heterogeneous ensemble model through the weighted average method, and uses the combined infill sampling criterion of the improved expectation criterion and the minimum surrogate model prediction criterion to manage the surrogate model to speed up the convergence of the model. In addition, the proposed algorithm adopts the actual objective function to evaluate the sample points added in each iteration, and updates the surrogate model to increase the model accuracy. The experimental results show that compared with the non-surrogate model algorithm, the proposed algorithm reduces the evaluation times of the fitness function by 10 times, which proves that the proposed algorithm can improve the optimization efficiency and accuracy of the surrogate model, and achieve a better balance between exploration and development.

Key words: surrogate model, Kriging model, radial basis function network model, heterogeneous ensemble, combined infill sampling criterion, fitness function evaluation, model management, multi-objective particle swarm optimization algorithm

中图分类号:

TP18

陈万芬,王宇嘉,林炜星. 组合加点准则的代理辅助多目标粒子群优化[J]. 电子科技, 2022, 35(12): 26-34.

CHEN Wanfen,WANG Yujia,LIN Weixing. Surrogate Assisted Multi-Objective Particle Swarm Optimization Based on Combined Infill Sampling Criterion[J]. Electronic Science and Technology, 2022, 35(12): 26-34.

图/表 11

参考文献 33

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算法名称	代理模型方法	模型管理策略
OMOPSO^[29]	无	无
NSGAIII^[30]	无	无
HE-OMOPSO	异构集成模型	无
HE-OMOPSO-EI	异构集成模型	单一加点准则
HE-OMOPSO-CIP	异构集成模型	组合加点准则

测试函数	变量范围	函数特性
DTLZ1	D=7, 0≤x_i≤1	多模态,包含多个局部极值,难以收敛全局Pareto前沿
DTLZ2	D=12, 0≤x_i≤1	具有测试问题多样性维护的能力
DTLZ3	D=12, 0≤x_i≤1	多模态,包含多个局部极值,难以收敛全局Pareto前沿
DTLZ4	D=12, 0≤x_i≤1	DTLZ2具有偏差区域的变体,参数α=100
DTLZ7	D=12, 0≤x_i≤1	具有多个不连续的Pareto前沿

测试函数	种群规模	决策变量	真实函数评估次数	近似函数评估次数
DTLZ1	100	7	10 000	1 000
DTLZ2	100	12	10 000	1 000
DTLZ3	100	12	10 000	1 000
DTLZ4	100	12	10 000	1 000
DTLZ7	100	12	10 000	1 000

测试函数	M	D	指标	NSGAIII	OMOPSO	HE-OMOPSO	HE-OMOPSO-EI	HE-OMOPSO-CIP
DTLZ1	3	7	GD	0.781 783	1.637 838	0.015 461	0.013 791	0.016 580
DTLZ1	3	7	SP	1.057 316	0.719 976	1.012 225	0.979 615	1.165 889
DTLZ2	3	12	GD	0.004 032	0.003 235	0.007 579	0.010 306	0.020 607
DTLZ2	3	12	SP	0.077 598	0.064 806	0.092 176	0.083 077	0.098 543
DTLZ3	3	12	GD	4.753 833	1.074 708	0.061 030	0.061 110	0.047 881
DTLZ3	3	12	SP	2.132 415	2.581 264	3.035 824	3.051 903	2.937 612
DTLZ4	3	12	GD	0.033 529	0.047 561	9.313 025	3.448 13	1.682 354
DTLZ4	3	12	SP	0.090 833	0.090 203	0.127 381	0.429 518	0.421 106
DTLZ7	3	12	GD	0.364 110	0.450 572	0.476 337	0.750 161	1.530 544
DTLZ7	3	12	SP	0.124 177	0.081 720	0.139 025	0.263 528	0.229 165

测试函数	M	D	指标	NSGAIII	OMOPSO	HE-OMOPSO	HE-OMOPSO-EI	HE-OMOPSO-CIP
DTLZ1	3	7	GD	0.843 610	1.491 720	0.001 272	0.001 554	0.001 721
DTLZ1	3	7	SP	0.311 322	0.179 325	0.121 373	0.117 135	0.083 827
DTLZ2	3	12	GD	0.000 174	0.000 115	0.000 605	0.000 792	0.001 627
DTLZ2	3	12	SP	0.003 854	0.005 398	0.006 559	0.006 725	0.005 243
DTLZ3	3	12	GD	2.392 910	6.811 090	0.006 446	0.004 494	0.003 796
DTLZ3	3	12	SP	0.397 680	0.698 996	0.172 701	0.230 019	0.230 019
DTLZ4	3	12	GD	0.013 921	0.011 886	3.353 000	5.088 000	1.342 000
DTLZ4	3	12	SP	0.026 589	0.020 837	0.077 574	0.193 824	0.159 270
DTLZ7	3	12	GD	0.007 771	0.021 923	0.207 848	0.226 970	0.364 183
DTLZ7	3	12	SP	0.022 571	0.007 540	0.114 841	0.131 889	0.058 693

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参考文献 33

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组合加点准则的代理辅助多目标粒子群优化

Surrogate Assisted Multi-Objective Particle Swarm Optimization Based on Combined Infill Sampling Criterion

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测试函数	M	D	NSGAIII	OMOPSO	HE-OMOPSO	HE-OMOPSO-EI	HE-OMOPSO-CIP
DTLZ1	3	7	0.958 385	0.937 484	0.912 172	0.811 930	0.907 399
DTLZ2	3	12	0.977 874	0.960 337	0.381 782	0.513 731	0.850 874
DTLZ3	3	12	0.961 162	0.970 020	0.994 284	0.992 462	0.985 235
DTLZ4	3	12	0.911 239	0.957 262	0.958 300	1.000 000	1.000 000
DTLZ7	3	12	0.955 206	0.949 845	1.000 000	1.000 000	0.980 100

测试函数	M	D	NSGAIII	OMOPSO	HE-OMOPSO	HE-OMOPSO-EI	HE-OMOPSO-CIP
DTLZ1	3	7	0.037 100 00	0.014 773 0	0.006 699	0.018 626 000	0.009 946
DTLZ2	3	12	0.000 083 83	0.000 305 0	0.016 939	0.009 872 000	0.008 428
DTLZ3	3	12	0.060 860 00	0.005 867 0	0.001 181	0.001 548 000	0.002 919
DTLZ4	3	12	0.032 718 00	0.001 587 0	0.044 901	0.000 001 654	0.000 000
DTLZ7	3	12	0.013 348 00	0.002 035 1	0.004 829	0.012 341 000	0.036 405