基于混合加点准则的LOLA-DIST序贯设计方法

doi:10.12305/j.issn.1001-506X.2025.11.16

Abstract

Abstract:

An efficient simulation experimental design method is the basis for establishing high-fidelity response surface models, but the existing sequential experimental design is difficult to cope with the dilemma of dimensional explosion and relies on a single model characteristic, which is less general. Therefore, a sequential design method based on the local nonlinear approximations-intersite and projected distance （LOLA-DIST） criterion is proposed, which adaptively samples in the region with high nonlinearity and low distribution density, and better balances the global exploration and local development strategies, and is not dependent on the characteristics of the response model with good generality. Finally, the effectiveness of the proposed method is verified based on 7 types of functions. Experiment results show that the sequential design based on LOLA-DIST criterion has the highest computational efficiency compared with LOLA-Voronoi, Latin hypercube sampling design and stochastic design, which effectively reduces the sample size and the number of trials on the basis of ensuring the model prediction accuracy with better global optimization performance.

Key words: sequential experimental design, hybrid sampling criterion, local nonlinear approximations （LOLA）, intersite and projected distance （INPD）

CLC Number:

O 212.6

Jian ZHONG, Zhijun CHENG, Zhengqiang PAN, Jun FAN, Tianyu LIU. LOLA-DIST sequential design method based on hybrid sampling criterion[J]. Systems Engineering and Electronics, 2025, 47(11): 3672-3684.

Figures/Tables 12

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References 34

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函数序号	函数名	取值范围	维度
F1	MATYAS	[−10, 10]	2
F2	PEAKS	[−5, 5]	2
F3	SIX-HUMP CAMEL	[−2, 2]	2
F4	ACKLEYS	[−32, 32]	2，10
F5	ROSENBROCK	[−5, 10]	4
F6	BRATLEY ET AL	[0, 1]	4~6
F7	DETTE&PEPELYSHEV	[0, 1]	8

函数序号	函数名	维度	样本数	LOLA-DIST	LOLA-Vorinoi	随机设计	LHS
F1	MATYAS	2	22	0.0001	0.0001	0.1736	0.0569
F2	PEAKS	2	214	0.0181	0.0435	1.1085	0.4825
F3	SIX-HUMP CAMEL	2	86	0.0027	0.0473	0.0267	0.0678
F4	ACKLEYS	2	40	0.0458	0.0760	0.0856	0.0962
F4	ACKLEYS	10	406	0.0485	0.0534	0.1309	0.0715
F5	ROSENBROCK	4	102	0.0382	0.0437	0.0916	0.0653
F6	BRATLEY ET AL.	4	46	0.0410	0.0267	0.2210	0.0855
		5	65	0.0482	0.0469	0.0662	0.0732
		6	178	0.0425	0.0497	0.0649	0.0571
F7	DETTE&PEPELYSHEV	8	190	0.0499	0.0543	0.0699	0.0593

函数序号	维度	加点准则	收敛点	MAPE	函数序号	维度	加点准则	收敛点	MAPE
F1	2	LOLA-DIST	12	0.0170	F5	4	LOLA-DIST	88	0.0628
		LOLA-Voronoi	15	0.0220			LOLA-Voronoi	89	0.0986
		随机设计	28	0.0788			随机设计	89	0.0944
		LHS	16	0.0826			LHS	91	0.0979
F2	2	LOLA-DIST	166	0.0867	F6	4	LOLA-DIST	24	0.0978
		LOLA-Voronoi	178	0.0860			LOLA-Voronoi	21	0.0778
		随机设计	238	0.6562			随机设计	82	0.0853
		LHS	358	0.0945			LHS	46	0.0855
F3	2	LOLA-DIST	43	0.0816		5	LOLA-DIST	45	0.0836
		LOLA-Voronoi	85	0.0728			LOLA-Voronoi	61	0.0566
		随机设计	64	0.0922			随机设计	36	0.0978
		LHS	82	0.0843			LHS	46	0.0971
F4	2	LOLA-DIST	25	0.0902		6	LOLA-DIST	106	0.0749
		LOLA-Voronoi	30	0.0918			LOLA-Voronoi	70	0.0944
		随机设计	40	0.0962			随机设计	70	0.0885
		LHS	35	0.0910			LHS	82	0.0917
	10	LOLA-DIST	226	0.0836	F7	8	LOLA-DIST	58	0.0889
		LOLA-Voronoi	190	0.0818			LOLA-Voronoi	94	0.0954
		随机设计	598	0.1000			随机设计	70	0.0873
		LHS	238	0.0889			LHS	58	0.0962

函数序号	维度	加点准则	收敛点	MAPE	函数序号	维度	加点准则	收敛点	MAPE
F1	2	LOLA-DIST	12	0.0170	F5	4	LOLA-DIST	93	0.0451
		LOLA-Voronoi	15	0.0220			LOLA-Voronoi	102	0.0437
		随机设计	39	0.0365			随机设计	106	0.0360
		LHS	19	0.0345			LHS	126	0.0443
F2	2	LOLA-DIST	178	0.0214	F6	4	LOLA-DIST	34	0.0454
		LOLA-Voronoi	214	0.0435			LOLA-Voronoi	46	0.0267
		随机设计	394	0.0385			随机设计	166	0.0423
		LHS	370	0.0459			LHS	70	0.0416
F3	2	LOLA-DIST	44	0.0289		5	LOLA-DIST	56	0.0487
		LOLA-Voronoi	86	0.0473			LOLA-Voronoi	65	0.0469
		随机设计	69	0.0496			随机设计	79	0.0489
		LHS	90	0.0395			LHS	71	0.0484
F4	2	LOLA-DIST	40	0.0458		6	LOLA-DIST	166	0.0491
		LOLA-Voronoi	56	0.0472			LOLA-Voronoi	178	0.0497
		随机设计	106	0.0468			随机设计	286	0.0481
		LHS	120	0.0498			LHS	298	0.0499
	10	LOLA-DIST	406	0.0485	F7	8	LOLA-DIST	238	0.0499
		LOLA-Voronoi	442	0.0490			LOLA-Voronoi	298	0.0496
		随机设计	>1210	—			随机设计	490	0.0500
		LHS	670	0.0467			LHS	502	0.0498

函数序号	维度	加点准则	收敛点	MAPE	函数序号	维度	加点准则	收敛点	MAPE
F1	2	LOLA-DIST	13	0.0045	F5	4	LOLA-DIST	173	0.0094
		LOLA-Voronoi	22	0.0001			LOLA-Voronoi	197	0.0093
		随机设计	54	0.0095			随机设计	193	0.0099
		LHS	39	0.0092			LHS	210	0.0095
F2	2	LOLA-DIST	238	0.0068	F6	4	LOLA-DIST	58	0.0077
		LOLA-Voronoi	346	0.0092			LOLA-Voronoi	82	0.0064
		随机设计	466	0.0075			随机设计	466	0.0097
		LHS	538	0.0067			LHS	178	0.0079
F3	2	LOLA-DIST	50	0.0098		5	LOLA-DIST	156	0.0098
		LOLA-Voronoi	125	0.0067			LOLA-Voronoi	167	0.0097
		随机设计	125	0.0074			随机设计	207	0.0097
		LHS	131	0.0080			LHS	201	0.0093
F4	2	LOLA-DIST	322	0.0091		6	LOLA-DIST	586	0.0099
		LOLA-Voronoi	430	0.0099			LOLA-Voronoi	610	0.0100
		随机设计	490	0.0096			随机设计	694	0.0096
		LHS	466	0.0095			LHS	658	0.0098
F4	10	LOLA-DIST	>1210	—	F7	8	LOLA-DIST	682	0.0096
		LOLA-Voronoi	>1210	—			LOLA-Voronoi	718	0.0093
		随机设计	>1210	—			随机设计	742	0.0099
		LHS	>1210	—			LHS	802	0.0094

LOLA-DIST sequential design method based on hybrid sampling criterion

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