Double adaptive selection strategy for MOEA/D

doi:10.21629/JSEE.2019.01.13

Journal of Systems Engineering and Electronics ›› 2019, Vol. 30 ›› Issue (1): 132-143.doi: 10.21629/JSEE.2019.01.13

收稿日期:2017-07-06 出版日期:2019-02-27 发布日期:2019-02-27

Double adaptive selection strategy for MOEA/D

Jiale GAO*(), Qinghua XING(), Chengli FAN(), Zhibing LIANG()

Air and Missle Defense College, Air Force Engineering University, Xi'an 710000, China

Received:2017-07-06 Online:2019-02-27 Published:2019-02-27
Contact: Jiale GAO E-mail:gaojiale_kgd@163.com;liuxqh@126.com;ff516@163.com;liangzhibing@163.com
About author:GAO Jiale was born in 1990. He received his M.S. degree from Air Force Engineering University (AFEU) in 2015. He is currently pursuing his Ph.D. degree at AFEU. His research interests include the evolutionary multi-objective optimization, and sensor resource scheduling. E-mail:gaojiale_kgd@163.com|XING Qinghua was born in 1966. She is a professor, and received her Ph.D. degree from Air Force Engineering University (AFEU) in 2003. Her research interests include systems modeling and simulation, operation decision analysis in air and missile defense. E-mail:liuxqh@126.com|FAN Chengli was born in 1988. She is a Ph.D. and a lecturer in Air force Engineering University. Her research interests include intelligent optimization algorithm, intelligent information processing, and military battle modeling & simulation. E-mail:ff516@163.com|LIANG Zhibing was born in 1990. He received his M.S. degree from Air Force Engineering University (AFEU) in 2015. He is presently working towards his Ph.D. degree at AFEU. His main research interests include multi-target tracking, and information fusion. E-mail:lzb liangzhibing@163.com
Supported by:
the National Natural Science Foundation of China(71771216);the National Natural Science Foundation of China(71701209);This work was supported by the National Natural Science Foundation of China (71771216; 71701209)

摘要/Abstract

Abstract:

Since most parameter control methods are based on prior knowledge, it is difficult for them to solve various problems. In this paper, an adaptive selection method used for operators and parameters is proposed and named double adaptive selection (DAS) strategy. Firstly, some experiments about the operator search ability are given and the performance of operators with different donate vectors is analyzed. Then, DAS is presented by inducing the upper confidence bound strategy, which chooses suitable combination of operators and donates sets to optimize solutions without prior knowledge. Finally, the DAS is used under the framework of the multi-objective evolutionary algorithm based on decomposition, and the multi-objective evolutionary algorithm based on DAS (MOEA/D-DAS) is compared to state-of-the-art MOEAs. Simulation results validate that the MOEA/D-DAS could select the suitable combination of operators and donate sets to optimize problems and the proposed algorithm has better convergence and distribution.

Key words: multi-objective optimization, adaptive operator selection, adaptive neighbor selection, decomposition

. [J]. Journal of Systems Engineering and Electronics, 2019, 30(1): 132-143.

Jiale GAO, Qinghua XING, Chengli FAN, Zhibing LIANG. Double adaptive selection strategy for MOEA/D[J]. Journal of Systems Engineering and Electronics, 2019, 30(1): 132-143.

图/表 11

参考文献 24

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Name	$n$	$m$	Range	Characteristics
F1	30	2	$x_{i}\in [0, 1]$, $1\le i\le n$	Convex, unimodal
F2	30	2	$x_{1}\in [0, 1]$, $x_{i}\in [0, 1]$, $1<i\le n$	Convex, multimodal
F3	30	2	$x_{1}\in [0, 1]$, $x_{i}\in [0, 1]$, $1<i\le n$	Convex, multimodal
F4	30	2	$x_{1}\in [0, 1]$, $x_{i}\in [0, 1]$, $1<i\le n$	Convex, multimodal
WFG1	12	3	$x_{i}\in [0, 2i]$, $1\le i\le n$	Convex, unimodal, mixed
WFG2	12	3	$x_{i}\in [0, 2i]$, $1\le i\le n$	Convex, multimodal, disconnected
WFG3	12	3	$x_{i}\in [0, 2i]$, $1\le i\le n$	Liner, unimodal, degenerate
WFG4	12	3	$x_{i}\in [0, 2i]$, $1\le i\le n$	Convex, multimodal
DTLZ1	10	3	$x_{i}\in [0, 1]$, $1\le i\le n$	Nonconvex, multimodal
DTLZ2	10	3	$x_{i}\in [0, 1]$, $1\le i\le n$	Nonconvex, unimodal

Problem		DAS3	DAS2	DAS1
F1	Mean	3.268E-02	1.990E-03	1.999E-03
	IQR	3.400E-03	2.420E-05	1.700E-05
	Rank	3	1	2
F2	Mean	3.737E-02	4.276E-03	4.430E-03
	IQR	3.520E-03	1.140E-03	1.280E-03
	Rank	3	1	2
F3	Mean	4.169E-02	3.295E-03	4.354E-03
	IQR	3.540E-03	4.560E-04	2.050E-03
	Rank	3	1	2
F4	Mean	4.672E-02	5.277E-03	3.145E-03
	IQR	9.310E-03	3.550E-03	7.630E-04
	Rank	3	2	1
WFG1	Mean	4.122E-01	3.059E-01	2.884E-01
	IQR	4.050E-02	5.610E-02	4.220E-02
	Rank	3	2$\approx $	1
WFG2	Mean	4.855E-01	4.540E-01	4.316E-01
	IQR	8.220E-03	4.000E-02	5.910E-02
	Rank	3	2$\approx $	1
WFG3	Mean	4.890E-02	4.619E-02	4.627E-02
	IQR	8.210E-04	1.890E-04	8.410E-03
	Rank	3	1	2
WFG4	Mean	2.614E-01	2.320E-01	2.304E-01
	IQR	8.400E-03	4.000E-03	2.210E-03
	Rank	3	2$\approx $	1
DTLZ1	Mean	1.465E-02	1.360E-02	1.370E-02
	IQR	1.010E-04	5.470E-05	3.610E-07
	Rank	3	1	2
DTLZ2	Mean	5.076E-02	4.900E-02	4.886E-02
	IQR	1.430E-04	1.780E-04	2.020E-04
	Rank	3	2$\approx $	1
Rank sum		30	15	15
$+/-/\approx $		0/10/0	5/1/4

Problem		DAS3	DAS2	DAS1
F1	Mean	1.103E-02	3.008E-03	2.934E-03
	IQR	1.850E-02	6.510E-05	2.800E-04
	Rank	3	2$\approx $	1
F2	Mean	4.143E-02	2.119E-02	2.145E-02
	IQR	1.080E-01	4.730E-02	2.290E-02
	Rank	3	1	2
F3	Mean	3.468E-03	3.255E-03	4.910E-03
	IQR	4.090E-03	2.360E-03	3.860E-03
	Rank	2	1	3
F4	Mean	5.601E-03	3.271E-03	2.749E-03
	IQR	4.590E-03	3.180E-03	4.580E-04
	Rank	3	2	1
WFG1	Mean	8.347E-02	1.135E-01	8.561E-02
	IQR	1.600E-02	2.130E-02	1.960E-02
	Rank	1	3	2
WFG2	Mean	7.098E-02	7.427E-02	7.920E-02
	IQR	4.050E-02	2.000E-02	2.930E-03
	Rank	1	2	3
WFG3	Mean	1.910E-01	1.908E-01	1.840E-01
	IQR	3.930E-03	3.430E-03	3.900E-04
	Rank	3	2$\approx $	1
WFG4	Mean	1.870E-01	1.889E-01	1.703E-01
	IQR	9.660E-03	1.020E-02	3.650E-03
	Rank	2	3	1
DTLZ1	Mean	7.696E-02	7.810E-02	7.871E-05
	IQR	1.070E-05	5.660E-05	1.010E-05
	Rank	1	2	3
DTLZ2	Mean	3.699E-02	3.808E-02	3.796E-02
	IQR	1.210E-03	7.870E-04	9.510E-06
	Rank	1	3$\approx $	2
Rank sum		20	21	19
$+/-/\approx $		4/6/0	2/5/3

Problem		NSGAII	MOEAD	MOEAD-DRA	MOEAD-AGR	MOEAD-DAS
F1	Mean	2.014E-03	4.173E-03	1.996E-03	3.425E-03	1.999E-03
	IQR	1.160E-05	8.710E-04	6.790E-06	1.010E-04	1.700E-05
	Rank	3	5	1	4	2
F2	Mean	1.794E-02	1.695E-01	4.848E-03	2.593E-02	4.430E-03
	IQR	3.360E-03	7.210E-02	3.570E-04	6.510E-03	1.280E-03
	Rank	3	5	2	4	1
F3	Mean	6.468E-03	4.851E-02	4.742E-03	1.143E-02	4.354E-03
	IQR	5.480E-04	2.600E-02	2.210E-04	4.030E-03	2.050E-03
	Rank	3	5	2	4	1
F4	Mean	8.164E-03	6.125E-02	6.740E-03	6.945E-03	3.145E-03
	IQR	9.820E-04	3.050E-02	1.180E-03	8.760E-04	7.630E-04
	Rank	4	5	2	3	1
WFG1	Mean	1.659E+00	2.356E-01	1.242E+00	1.800E-01	2.884E-01
	IQR	5.330E-02	5.900E-03	9.650E-02	1.280E-02	4.220E-02
	Rank	5	2	4	1	3
WFG2	Mean	4.400E-01	6.749E-01	4.391E-01	1.307E-01	4.316E-01
	IQR	1.500E-02	1.720E-01	4.080E-02	4.570E-03	5.910E-02
	Rank	4	5	3$\approx $	1	2
WFG3	Mean	5.775E-02	8.325E-02	5.531E-02	5.494E-02	4.627E-02
	IQR	1.450E-03	7.420E-04	3.990E-04	3.260E-04	8.410E-03
	Rank	4	5	3	2	1
WFG4	Mean	2.436E-01	1.784E-01	2.525E-01	1.884E-01	2.304E-01
	IQR	2.870E-03	3.440E-03	5.040E-03	3.090E-03	2.210E-03
	Rank	4	1	5	2	3
DTLZ1	Mean	1.984E-02	1.975E-02	1.979E-02	1.901E-02	1.370E-02
	IQR	2.540E-05	3.130E-05	3.000E-05	5.340E-04	3.610E-07
	Rank	5	3	4	2	1
DTLZ2	Mean	4.894E-02	3.638E-02	4.878E-02	4.772E-02	4.886E-02
	IQR	1.550E-04	3.490E-07	1.350E-04	7.550E-04	2.020E-04
	Rank	5$\approx $	1	3	2	4
Rank sum		40	37	29	25	19
$+/-/\approx $		0/9/1	2/8/0	1/8/1	2/8/0

Problem		NSGAII	MOEAD	ADEMO/D	MOEA/D-AGR	MOEA/D-DAS
F1	Mean	5.138E-03	5.240E-03	5.077E-03	3.712E-03	2.934E-03
	IQR	1.010E-04	6.710E-05	1.300E-04	2.390E-04	2.800E-04
	Rank	4	5	3	2	1
F2	Mean	8.175E-02	9.165E-03	1.411E-02	1.904E-02	2.145E-02
	IQR	7.140E-02	3.190E-03	8.670E-03	2.350E-02	2.290E-02
	Rank	5	1	2	3	4
F3	Mean	6.476E-02	6.509E-03	1.553E-02	6.150E-03	4.910E-03
	IQR	7.130E-02	7.270E-04	2.090E-02	4.340E-03	3.860E-03
	Rank	5	3	4	2	1
F4	Mean	2.158E-02	1.612E-02	1.023E-02	2.110E-02	2.749E-03
	IQR	2.560E-02	1.350E-02	4.770E-03	1.640E-02	4.580E-04
	Rank	5	4	3	2	1
WFG1	Mean	1.258E-01	1.751E-01	1.472E-01	1.110E-01	8.561E-02
	IQR	2.400E-02	1.190E-01	1.350E-01	9.730E-03	1.960E-02
	Rank	3	5	4	2	1
WFG2	Mean	1.301E-01	1.224E-01	1.117E-01	1.518E-01	7.920E-02
	IQR	6.360E-02	2.690E-02	9.160E-03	4.990E-02	2.930E-03
	Rank	4	3	2	5	1
WFG3	Mean	1.494E-01	1.551E-01	1.478E-01	8.373E-02	1.840E-01
	IQR	2.150E-03	3.320E-03	2.970E-03	3.900E-03	3.900E-04
	Rank	3	4	2	1	5
WFG4	Mean	2.444E-01	2.682E-01	2.632E-01	1.507E-01	1.703E-01
	IQR	1.070E-02	1.120E-02	6.560E-03	4.980E-03	3.650E-03
	Rank	3	5	4	1	2
DTLZ1	Mean	2.020E-02	2.027E-02	1.571E-02	1.562E-02	7.871E-05
	IQR	3.900E-04	3.160E-04	3.850E-04	5.360E-04	1.010E-05
	Rank	4	5	3	2	1
DTLZ2	Mean	5.773E-02	5.563E-02	5.674E-02	3.764E-02	3.796E-02
	IQR	4.520E-04	1.820E-03	7.820E-04	2.560E-03	9.510E-06
	Rank	5	3	4	1	2
Rang sum		41	38	31	21	19
$+/-/\approx $		0/10/0	1/9/0	0/10/0	3/7/0

Double adaptive selection strategy for MOEA/D

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Problem	MOEAD	MOEAD-DRA	MOEAD-AGR	MOEAD-DAS
F1	78.9	81.4	88.7	93.7
F2	76.1	78.6	85.9	92.6
F3	75.9	78.3	85.1	96.3
F4	76.2	79.6	88.4	98.2
WFG1	111.5	114.0	124.7	129.4
WFG2	109.2	111.7	118.0	121.7
WFG3	105.9	108.4	119.1	125.5
WFG4	105.6	109.1	116.4	122.6
DTLZ1	70.2	75.6	86.6	93.8
DTLZ2	76.4	79.9	87.0	95.6