基于多目标PSO混合优化的虚拟样本生成

王丹丹; 汤健; 夏恒; 乔俊飞

doi:10.16383/j.aas.c211091

基于多目标PSO混合优化的虚拟样本生成

doi: 10.16383/j.aas.c211091

王丹丹^{1, 2, 3,},
汤健^{1, 2, 3,},
夏恒^{1, 2, 3,},
乔俊飞^{1, 2, 3,}

1.
北京工业大学信息学部北京 100124
2.
北京工业大学智慧环保北京实验室北京 100124
3.
北京工业大学智能感知与自主控制教育部工程研究中心北京 100124

基金项目: 国家自然科学基金(62073006, 62173120, 62021003), 北京市自然科学基金资助项目(4212032, 4192009), 科技创新2030 —— “新一代人工智能”重大项目(2021ZD0112301, 2021ZD0112302)资助

详细信息

作者简介:
王丹丹：北京工业大学信息学部硕士研究生. 主要研究方向为基于虚拟样本生成的小样本数据建模. E-mail: wangdandan@emails.bjut.edu.cn

汤健：北京工业大学信息学部教授. 主要研究方向为小样本数据建模, 城市固废处理过程智能控制. 本文通信作者. E-mail: freeflytang@bjut.edu.cn

夏恒：北京工业大学信息学部博士研究生. 主要研究方向为小样本数据建模和城市固废焚烧过程二噁英排放预测. E-mail: xiaheng@emails.bjut.edu.cn

乔俊飞：北京工业大学信息学部教授. 主要研究方向为污水处理过程智能控制, 神经网络结构设计与优化. E-mail: junfeiq@bjut.edu.cn

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出版历程
- 收稿日期: 2021-11-18
- 录用日期: 2022-05-11
- 网络出版日期: 2022-09-13
- 刊出日期: 2024-04-26

Virtual Sample Generation Method Based on Hybrid Optimization With Multi-objective PSO

WANG Dan-Dan^{1, 2, 3
,},
TANG Jian^{1, 2, 3
,},
XIA Heng^{1, 2, 3
,},
QIAO Jun-Fei^{1, 2, 3
,}

1.
Faculty of Information Technology, Beijing University of Technology, Beijing 100124
2.
Beijing Laboratory of Smart Environmental Protection, Beijing University of Technology, Beijing 100124
3.
Engineering Research Center of Intelligent Perception and Autonomous Control, Ministry of Education, Beijing University of Technology, Beijing 100124

Funds: Supported by National Natural Science Foundation of China (62073006, 62173120, 62021003), Beijing Natural Science Foundation (4212032, 4192009), and National Key Research and Development Program of China (2021ZD0112301, 2021ZD0112302)

More Information

Author Bio:
WANG Dan-Dan　Master student at the Faculty of Information Technology, Beijing University of Technology. Her main research interest is small sample data modeling based on virtual sample generation

TANG Jian　Professor at the Faculty of Information Technology, Beijing University of Technology. His research interest covers small sample data modeling and intelligent control of municipal solid waste treatment process. Corresponding author of this paper

XIA Heng　Ph.D. candidate at the Faculty of Information Technology, Beijing University of Technology. His research interest covers small sample data modeling and dioxin emission prediction of the municipal solid waste incineration process

QIAO Jun-Fei　Professor at the Faculty of Information Technology, Beijing University of Technology. His research interest covers intelligent control of waste water treatment process and structure design and optimization of neural networks

摘要

摘要: 受限于检测技术难度、高时间与经济成本等原因, 难测参数的软测量模型建模样本存在数量少、分布稀疏与不平衡等问题, 严重制约了数据驱动模型的泛化性能. 针对以上问题, 提出一种基于多目标粒子群优化(Multi-objective particle swarm optimization, MOPSO)混合优化的虚拟样本生成(Virtual sample generation, VSG)方法. 首先, 设计综合学习粒子群优化算法的种群表征机制, 使其能够同时编码用于连续变量和离散变量; 然后, 定义具有多阶段多目标特性的综合学习粒子群优化算法适应度函数, 使其能够在确保模型泛化性能的同时最小化虚拟样本数量; 最后, 提出面向虚拟样本生成的多目标混合优化任务以改进综合学习粒子群优化算法, 使其能够适应虚拟样本优选过程的变维特性并提高收敛速度. 同时, 首次借鉴度量学习提出用于评价虚拟样本质量的综合评价指标和分布相似指标. 利用基准数据集和真实工业数据集验证了所提方法的有效性和优越性.
- 小样本建模 /
- 虚拟样本生成 /
- 混合优化 /
- 多目标粒子群优化 /
- 分布相似度
Abstract: Due to the difficulty of detection technology, and high time and economic cost, the modeling samples of soft-sensing model with difficult parameters have some problems, such as small numbers, sparse distribution, and imbalance, which seriously restrict the generalization performance of data-driven models. To solve the above problems, a virtual sample generation (VSG) method based on multi-objective particle swarm optimization (MOPSO) hybrid optimization is proposed. First, the population representation mechanism of the integrated learning particle swarm optimization algorithm is designed, so that it can simultaneously encode the continuous and the discrete variables. Then, the fitness function of the integrated learning particle swarm optimization algorithm with multi-stage and multi-objective characteristics is defined to minimize the number of virtual samples while ensuring the generalization performance of the model. Finally, a multi-objective hybrid optimization task is generated for virtual samples to improve the integrated learning particle swarm optimization algorithm, so that it can adapt to the variable dimension characteristics of the virtual sample optimization process and improve the convergence speed. At the same time, the comprehensive evaluation index and distribution similarity index are proposed for evaluating the quality of virtual samples by referring to metric learning for the first time. In this paper, two benchmark datasets and an actual industrial dataset are used to verify the effectiveness and superiority of the proposed method.
- Small sample modeling /
- virtual sample generation (VSG) /
- hybrid optimization /
- multi-objective particle swarm optimization (MOPSO) /
- distribution similarity

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图 1 虚拟样本与真实样本间的关系

Fig. 1 Relationship between virtual samples and real samples

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图 2 基于MOPSO混合优化的VSG策略

Fig. 2 VSG based on hybrid optimization with MOPSO

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图 3 基于混合优化策略的粒子设计

Fig. 3 Particle design based on hybrid optimization strategy

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图 4 非支配解的Pareto前沿

Fig. 4 Pareto front of non-dominant solutions

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图 5 非支配解的建模性能指标对比

Fig. 5 Comparison of modeling performance indexes of non-dominant solutions

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图 7 非支配解的分布相似度对比

Fig. 7 Comparison of distribution similarity of non-dominant solutions

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图 6 非支配解的综合评价指标对比

Fig. 6 Comparison of comprehensive evaluation indexes of non-dominant solutions

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图 8 基准数据预测输出对比

Fig. 8 Comparison of prediction output for benchmark data

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图 9 MSWI过程工艺流程图

Fig. 9 Flow chart of MSWI process

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图 10 非支配解的Pareto前沿 —— DXN排放浓度

Fig. 10 Pareto front of non-dominated solutions ——DXN emission concentration

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图 11 非支配解的建模性能和综合评价指标对比

Fig. 11 Comparison of modeling performance indexes and comprehensive evaluation indexes of non-dominant solutions

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表 1 本文采用符号的含义

Table 1 The meaning of the symbols used in this article

序号	符号	含义
1	${\rho _i}$	全局最优粒子选择指标
2	${\rho _j}$	虚拟样本综合评价指标
3	$\eta $	数据分布相似度
4	${{\boldsymbol{F}}}\left( {{\boldsymbol{z}}} \right)$	多目标优化问题的目标函数集
5	${ {\boldsymbol{z} } }, {\boldsymbol{z}}_n^p\left( {t + 1} \right)$	优化问题决策变量(粒子的位置矢量), 表示第$t + 1$次迭代时, 粒子$p$的第$n$维位置值
6	${ {\boldsymbol{v} } }, {\boldsymbol{v} }_n^p( {t + 1} )$	粒子的速度矢量, 表示第$t + 1$次迭代时, 粒子$p$的第$n$维速度值
7	${w_{{{\rm{inertia}}}}}$	粒子速度更新的惯性权重
8	${{{\boldsymbol{d}}}^p}\left( {t + 1} \right)$	第$t + 1$次迭代时, 粒子$p$的个体最优
9	$E_n^p$	粒子$p$的第$n$维的学习样例值
10	${N_{{{\rm{refresh}}}}}$	个体最优未更新阈值, 用于控制学习样例的更新
11	$P_c^p$	粒子$p$的学习概率, 用于控制学习样例的更新概率
12	$ran{k^p}$	粒子$p$个体最优的适应度在种群中排名
13	$K$	RF模型中决策树数量
14	${L_F}$	RF模型中切分特征数
15	${\theta _{{{\rm{leaf}}}}}$	RF模型中决策树的叶节点包含样本数量的阈值
16	$F_{_{{{\rm{sel}}}}}^q$	RF模型中决策树的节点$q$最佳切分特征
17	${s^q}$	RF模型中决策树的节点$q$最佳分裂点取值
18	$f_{_{{{\rm{tree}}}}}^k\left( \cdot \right)$	RF模型中第$k$个决策树模型
19	$f_{_{{{\rm{RF}}}}}^{}\left( \cdot \right)$	RF 模型
20	${{\boldsymbol{z}}}_{_{{{\rm{para}}}}}^{}$	指导候选虚拟样本生成的参数决策变量
21	${{\boldsymbol{z}}}_{_{{{\rm{vss}}}}}^{}$	筛选候选虚拟样本选择决策变量
22	$\mathop {{\boldsymbol{R}}}\nolimits_{_{{{\rm{train}}}}} $	原始小样本训练集
23	${ { {\boldsymbol{x} } }_{ { {\rm{vsg\text{-}min} } } }}, { { {\boldsymbol{x} } }_{ { {\rm{vsg\text{-}max} } } }}$	采用改进MTD进行扩展后的输入扩展域的上限和下限
24	${y_{ { {\rm{vsg\text{-}min} } } }}, {y_{ { {\rm{vsg\text{-}max} } } }}$	采用改进MTD进行扩展后的输出扩展域的上限和下限
25	$\mathop { {\boldsymbol{X} } }\nolimits_{_{ { {\rm{vs\text{-}g} } } }}$	混合插值生成的虚拟样本输入
26	$\mathop {{\boldsymbol{X}}}\nolimits_{_{{{\rm{equal}}}}} , \mathop {{\boldsymbol{X}}}\nolimits_{_{{{\rm{rand}}}}} $	等间隔插值、随机插值生成的虚拟样本输入
27	$\mathop { {\boldsymbol{y} } }\nolimits_{_{ { {\rm{vs\text{-}g1} } } } } , \mathop { {\boldsymbol{y} } }\nolimits_{_{ { {\rm{vs\text{-}g2} } } } }$	基于虚拟样本输入, 结合RF、RWNN映射模型生成的虚拟样本输出
28	${ {\boldsymbol{R} } }_{ { {\rm{vs\text{-}g1} } } }^p, { {\boldsymbol{R} } }_{ { {\rm{vs\text{-}g2} } } }^p$	基于虚拟样本输入, 结合RF、RWNN 映射模型生成的虚拟样本
29	$\mathop { {\boldsymbol{R} } }\nolimits_{_{ { {\rm{vs\text{-}g} } } }}$	生成的混合虚拟样本
30	$\mathop { {\boldsymbol{R} } }\nolimits_{_{ { {\rm{vs\text{-}d} } } } }$	对$\mathop { {\boldsymbol{R} } }\nolimits_{_{ { {\rm{vs\text{-}g} } } }}$进行删减后的候选虚拟样本
31	$\mathop { {\boldsymbol{R} } }\nolimits_{_{ { {\rm{vs\text{-}s} } } }}$	对候选虚拟样本进行选择后获得的虚拟样本
32	$\mathop {{\boldsymbol{R}}}\nolimits_{_{{{\rm{valid}}}}} $	原始小样本验证集
33	$\mathop {{\boldsymbol{R}}}\nolimits_{_{{{\rm{vs}}}}} $	最优虚拟样本
34	${f_{{{\rm{num}}}}}({{\boldsymbol{z}}})$	多目标优化问题的目标之一, 筛选后的虚拟样本数量
35	${f_{{{\rm{mod}}}}}({{\boldsymbol{z}}})$	多目标优化问题的目标之一, 筛选后的虚拟样本与原始训练集构建RF模型的性能指标
36	$z_{{\rm{MTD}}}$	粒子的参数决策变量之一, 对应基于MTD方法的扩展率${\gamma _{{{\rm{extend}}}}}$
37	$z_{{{\rm{RF}}}}^{{\rm{1}}}$	粒子的参数决策变量之一, 对应RF映射模型的切分特征数${L_F}$
38	$z_{{{\rm{RF}}}}^{{\rm{2}}}$	粒子的参数决策变量之一, 对应RF映射模型中决策树的中叶节点包含样本数量的阈值${\theta _{{{\rm{leaf}}}}}$
39	${z_{{{\rm{RWNN}}}}}$	粒子的参数决策变量之一, 对应RWNN映射模型的隐含层神经元数量$I$
40	${\gamma _{{{\rm{extend}}}}}$	基于MTD方法的扩展率
41	$I$	RWNN映射模型的隐含层神经元数量
42	$\mathop {{\boldsymbol{X}}}\nolimits_{_{{{\rm{train}}}}} $	原始小样本训练集输入
43	${{{\boldsymbol{y}}}_{{{\rm{train}}}}}$	原始小样本训练集输出
44	${y_{{{\rm{ave}}}}}$	${{{\boldsymbol{y}}}_{{{\rm{train}}}}}$的均值
45	${{{\boldsymbol{y}}}_{{{\rm{high}}}}}, {{{\boldsymbol{y}}}_{{{\rm{low}}}}}$	$\mathop {{\boldsymbol{X}}}\nolimits_{_{{{\rm{train}}}}} $中大于/小于${y_{{{\rm{ave}}}}}$的输出集合
46	${y_{{{\rm{max}}}}}, {y_{{{\rm{min}}}}}$	${{{\boldsymbol{y}}}_{{{\rm{train}}}}}$中最大值、最小值
47	${y_{ { {\rm{H\text{-}ave} } } } }, {y_{ { {\rm{L\text{-}ave} } } } }$	${{{\boldsymbol{y}}}_{{{\rm{high}}}}}, {{{\boldsymbol{y}}}_{{{\rm{low}}}}}$的均值
48	$\mathop N\nolimits_{_{{{\rm{equal}}}}} , \mathop N\nolimits_{_{{{\rm{rand}}}}} $	等间隔插值、随机插值倍数
49	${{\boldsymbol{W}}}, {{\boldsymbol{b}}}$	RWNN模型输入层与隐含层间神经元的连接权重与偏置
50	${{\boldsymbol{H}}}_{}^{_{{{\rm{ori}}}}}$	RWNN模型隐含层输出矩阵
51	${{\boldsymbol{\beta}}}$	RWNN模型隐含层与输出层神经元的连接权重
52	$\mathop N\nolimits_{_{ { {\rm{vs\text{-}g} } } } } \mathop {, N}\nolimits_{{ { {\rm{vs\text{-}d} } } } } , \mathop N\nolimits_{_{ { {\rm{vs\text{-}s} } } } }$	生成、候选、选择后虚拟样本的数量
53	${\theta _{{{\rm{select}}}}}$	虚拟样本的选择阈值
54	${{{\boldsymbol{\tilde z}}}_{{{\rm{vss}}}}}$	对${{{\boldsymbol{z}}}_{{{\rm{vss}}}}}$进行变维度处理后获得
55	$F$	使用虚拟样本集$\mathop { {\boldsymbol{R} } }\nolimits_{_{ { {\rm{vs\text{-}s} } } }}$的建模性能指标
56	$\mathop {{\boldsymbol{R}}}\nolimits_{_{{{\rm{mix}}}}} $	原始训练集$\mathop {{\boldsymbol{R}}}\nolimits_{_{{{\rm{train}}}}} $与$\mathop { {\boldsymbol{R} } }\nolimits_{_{ { {\rm{vs\text{-}s} } } }}$的混合样本集
57	${P_{{{\rm{num}}}}}$	种群中粒子数量
58	${N_{{{\rm{iter}}}}}$	种群迭代次数
59	${{\boldsymbol{A}}}$	种群的外部档案, 保存非支配解

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表 2 基准数据集划分

Table 2 Benchmark data set partitioning

数据集	特征数	训练集		验证集		测试集		数据集编号
数据集	特征数	数量	$\eta $	数量	$\eta $	数量	$\eta $	数据集编号
混凝土抗压强度	8	20	0.3327	20	0.3598	100	0.1255	A1
		40	0.2444	40	0.2628			A2
		60	0.1853	60	0.2070			A3
超导临界温度	81	20	0.3351	20	0.3388	100	0.1538	B1
		40	0.2309	40	0.2423			B2
		60	0.1949	60	0.1966			B3

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表 3 基准数据基于多目标PSO混合优化的VSG参数设定

Table 3 Parameter setting of VSG based on hybrid optimization with multi-objective PSO for benchmark data

数据集	${P_{{{\rm{num}}}}}$	${N_{{{\rm{iter}}}}}$	${N_{{{\rm{refresh}}}}}$	$K$	${z_{{{\rm{MTD}}}}}$	$z_{{{\rm{RF}}}}^{{\rm{1}}}$	$z_{{{\rm{RF}}}}^{{\rm{2}}}$	${z_{{{\rm{RWNN}}}}}$
混凝土抗压强度	30	30	3	30	(0, 1)	(1, 6)	(2, 10)	(3, 20)
超导临界温度	30	30	3	50	(0, 1)	(1, 30)	(2, 10)	(3, 20)

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表 4 基准数据基于多目标PSO混合优化获得的最优虚拟样本

Table 4 Optimal virtual samples obtained based on multi-objective PSO hybrid optimization for benchmark data

数据集	${\mathop {{\boldsymbol{X}}}\nolimits_{_{{{\rm{vs}}}}} }$								${y_{{{\rm{vs}}}}}$
A1	396.50	117.40	0	176.40	11.42	876.70	796.90	60.23	58.83
	200.50	16.35	115.80	161.60	8.27	1071.70	809.90	17.23	29.23
	240.90	0	100.30	183.50	5.87	977.30	852.40	14.00	18.25
	272.40	56.58	0	199.00	0	965.00	786.90	37.38	12.62
	347.40	0	0	190.80	0	1116.40	718.20	15.08	3.42
B1	5.69	95.64	60.78	69.89	36.85	1.48	1.41	182.20	26.79
	4.08	77.39	51.82	60.19	35.09	1.22	1.27	121.40	95.32
	4.00	76.44	50.35	59.37	34.71	1.20	1.29	121.30	80.12
	4.46	82.72	56.99	64.52	36.03	1.30	1.09	131.20	51.89
	3.54	83.97	60.06	66.37	43.11	1.07	0.97	99.90	6.38

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表 5 基准数据原始样本输入/输出范围

Table 5 Input/output range of original samples for benchmark data

数据集		输入								输出
A1	最小值	102.0	0	0	121.8	0	801.0	594.0	1.0	2.3
A1	最大值	540.0	359.4	200.1	247.0	32.2	1145.0	992.6	365.0	82.6
B1	最小值	1.0	6.9	6.4	5.3	2.0	0	0	0	0
B1	最大值	9.0	209.0	209.0	209.0	209.0	2.0	2.0	208.0	185.0

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表 6 基准数据基于多目标PSO混合优化的全局最优解的统计结果

Table 6 Statistical results of global optimal solution based on hybrid optimization with multi-objective PSO for benchmark data

数据集	超参数				虚拟样本数量	验证集		测试集		混合样本$\eta $
数据集	${\gamma _{{{\rm{extend}}}}}$	${L_F}$	${\theta _{{{\rm{leaf}}}}}$	$I$	虚拟样本数量	平均${\rm{RMSE}}$	平均$\rho $	平均${\rm{RMSE}}$	平均$\rho $	混合样本$\eta $
A1	0.6033	3	9	18	82	10.36	0.026	11.59	0.012	0.2354
A2	0.6245	6	5	19	128	10.03	0.012	10.73	0.003	0.2099
A3	0.6528	6	9	20	150	10.40	0.006	10.28	0.002	0.2002
B1	0.3951	5	5	16	20	16.44	0.300	19.07	0.169	0.2407
B2	0.4892	8	6	14	69	20.14	0.019	17.86	0.051	0.2118
B3	0.6775	19	6	15	70	19.57	0	18.05	0.023	0.2076

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表 7 基准数据不同VSG方法的对比统计结果

Table 7 Comparative statistical results of different VSG methods for benchmark data

数据集	方法	虚拟样本数量	混合样本$\eta $	测试${\rm{RMSE} }$			测试$\rho $
数据集	方法	虚拟样本数量	混合样本$\eta $	均值	方差	最优	均值$(\times{10^{ - 3} })$	方差$(\times{10^{ - 4} })$	最优$(\times{10^{ - 3} })$
A1	N-VSG	219	0.2770	16.47	8.785	14.11	4.09	15.44	4.62
	M-VSG	238	0.3018	17.08	8.575	13.65	2.26	19.73	4.55
	PSO-VSG	55	0.4235	16.35	3.822	12.75	3.76	30.20	5.88
	MP-VSG	165	0.2641	14.03	4.525	12.93	6.04	9.93	7.19
	MoHo-VSG	82	0.2354	11.59	0.107	9.67	12.46	1.34	14.72
B1	N-VSG	176	0.2945	24.38	10.541	21.96	13.87	17.96	14.25
	M-VSG	281	0.3100	25.33	12.786	20.12	12.63	56.11	14.12
	PSO-VSG	36	0.3317	26.11	17.710	20.38	1.69	71.20	8.23
	MP-VSG	134	0.2513	20.84	3.452	19.47	17.43	4.37	18.89
	MoHo-VSG	20	0.2076	18.05	0.062	17.84	169.26	1.57	178.69

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表 8 DXN数据基于多目标PSO混合优化的VSG算法参数设定

Table 8 Parameter setting of VSG algorithm based on multi-objective PSO hybrid optimization for DXN data

参数	${P_{{{\rm{num}}}}}$	${N_{{{\rm{iter}}}}}$	${N_{{{\rm{refresh}}}}}$	$K$	${z_{{{\rm{MTD}}}}}$	$z_{{{\rm{RF}}}}^{{\rm{1}}}$	$z_{{{\rm{RF}}}}^{{\rm{2}}}$	${z_{{{\rm{RWNN}}}}}$
数据	30	30	3	50	(0, 1)	(1, 35)	(2, 10)	(3, 20)

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表 9 DXN数据基于多目标PSO混合优化获得的最优虚拟样本

Table 9 Optimal virtual samples obtained based on multi-objective PSO hybrid optimization for DXN data

${\mathop {{\boldsymbol{X}}}\nolimits_{_{{{\rm{vs}}}}} }$							${y_{{{\rm{vs}}}}}$
4.366	1.54	68.78	27.31	241.4	3.96	334.7	0.0289
4.206	0	68.94	28.15	222.5	3.77	306.8	0.0458
4.449	7.69	72.48	30.23	222.8	3.98	315.8	0.0685
4.432	10.00	71.83	30.00	225.9	3.99	319.5	0.0163
4.461	17.69	74.65	30.77	228.5	3.99	321.8	0.0029

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表 10 DXN数据面向VSG的多目标PSO混合优化全局最优解

Table 10 DXN data for VSG-oriented multi-objective PSO hybrid optimization global optimal solution

性能指标	最优解
超参数${\gamma _{{{\rm{extend}}}}}$	0.1206
超参数${L_F}$	2
超参数${\theta _{{{\rm{leaf}}}}}$	5
超参数$I$	15
虚拟样本数量	40
验证集的平均${\rm{RMSE}}$	0.0231
验证集的平均$\rho $	4.41 ×${10^{ - 5}}$
测试集的平均${\rm{RMSE}}$	0.0238
测试集的平均$\rho $	3.18 ×${10^{ - 5}}$
验证集, 小样本建模的${\rm{RMSE}}$	0.0259
测试集, 小样本建模的${\rm{RMSE}}$	0.0251

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表 11 DXN数据的不同VSG方法对比统计结果

Table 11 Comparative statistical results of different VSG methods based on DXN dataset

方法	虚拟样本数量	测试集的${\rm{RMSE} }$			测试集的$\rho $
方法	虚拟样本数量	均值	方差$(\times {10^{ - 4} })$	最优	均值$(\times {10^{ - 5} })$	方差	最优$(\times{10^{ - 5} })$
N-VSG	129	0.0406	0.695	0.0262	0.19	1.94 ×${10^{ - 5}}$	0.36
M-VSG	116	0.0403	1.331	0.0231	0.26	8.83 ×${10^{ - 5}}$	0.53
PSO-VSG	27	0.0328	0.519	0.0245	0.56	8.44 ×${10^{ - 5}}$	1.02
MP-VSG	68	0.0377	1.208	0.0218	1.04	5.16 ×${10^{ - 7}}$	1.78
MoHo-VSG	40	0.0231	0.691	0.0220	3.18	4.47 ×${10^{ - 9}}$	3.45

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