基于差分进化邻域自适应的大规模多目标算法

doi:10.12305/j.issn.1001-506X.2022.07.06

Abstract

Abstract:

Since there are large scale decision variables in large-scale multi-objective optimization problems (LSMOPs), the algorithm is difficult to converge and the distribution of the solution set is uneven. It is an effective way to classify the decision variables and optimize them respectively by analyzing the characteristics of the variables. However, there are some shortcomings, such as inaccurate variable classification and insufficient pertinence of variable processing. Therefore, a large-scale multi-objective optimization based on differential evolution with neighborhood adaptive strategy (NAS-MOEA) is proposed to solve LSMOPs. Firstly, by analyzing the dominant relationship of the disturbance solution, the mixed variables are divided into diversity variables and convergence variables to make the variable classification more accurate. Secondly, the principal component analysis of convergence variables is used to reduce noise and computational cost. The alternative evolution strategy of population and the neighborhood adaptive update operation of differential evolution are designed to improve the convergence in the process of population evolution. Experimental results show that the proposed algorithm has good performance in convergence speed and uniformity distribution of the solution set.

Key words: large-scale multi-objective optimization, cooperative coevolution, decision variable analysis, principal component analysis, neighborhood adaptive update

CLC Number:

TP301.6

Shiying YAN, Kefei YAN, Wei FANG, Hengyang LU. Large-scale multi-objective algorithm based on neighborhood adaptive of differential evolution[J]. Systems Engineering and Electronics, 2022, 44(7): 2112-2124.

Figures/Tables 25

Fig.1

Fig.2

Fig.3

Fig.4

Table 1

IGD and runtime results of three algorithms on UF and LSMOP"

问题	目标数	决策变量数	LMEA		MOEA/DVA		NAS-MOEA
问题	目标数	决策变量数	IGD	平均运行时间	IGD	平均运行时间	IGD	平均运行时间
LSMOP1	3	300	1.042 1e-1-	5.460 4e+2+	4.528 3e-2-	6.593 4e+2+	4.124 2e-2	8.356 9e+2
LSMOP1	3	1 000	1.423 3e-1-	1.262 3e+4-	4.496 7e-2-	7.736 1e+3+	3.829 3e-2	8.359 8e+3
LSMOP2	3	300	9.436 3e-2-	5.460 9e+2+	8.274 1e-2-	7.382 8e+2+	7.744 6e-2	8.665 9e+2
LSMOP2	3	1 000	6.793 1e-2-	1.277 0e+4-	4.986 9e-2-	8.263 3e+3+	4.267 9e-2	9.642 7e+3
LSMOP3	3	300	1.086 2e+0-	5.680 9e+2+	5.633 9e-1-	8.115 1e+2+	4.007 0e-1	9.332 5e+2
LSMOP3	3	1 000	1.298 8e+0-	1.085 8e+4-	2.885 4e-1-	8.081 5e+3+	2.229 6e-1	8.625 5e+3
LSMOP4	3	300	9.786 4e-2≈	5.573 5e+2+	7.952 0e-2-	7.763 8e+2 ≈	6.646 9e-2	7.730 9e+2
LSMOP4	3	1 000	7.173 2e-2-	1.139 6e+4-	5.032 9e-2-	8.486 7e+3+	4.868 6e-2	9.077 2e+3
LSMOP5	3	300	3.319 0e+0-	5.348 6e+2+	5.898 7e-2≈	6.746 0e+2+	5.813 0e-2	7.709 7e+2
LSMOP5	3	1 000	4.950 3e+0-	1.242 3e+4-	5.855 4e-2-	8.072 9e+3+	5.304 3e-2	8.576 1e+3
LSMOP6	3	300	1.003 3e+2-	4.885 4e+2+	4.563 3e+0-	7.621 1e+2+	8.726 5e-1	8.594 2e+2
LSMOP6	3	1 000	7.143 0e+2-	1.186 6e+4-	2.844 7e+0-	8.148 6e+3+	1.112 0e+0	1.045 8e+4
LSMOP7	3	300	1.309 1e+0-	4.882 6e+2+	8.553 8e-1-	7.090 3e+2+	8.019 4e-1	7.633 4e+2
LSMOP7	3	1 000	5.470 4e-1≈	1.180 4e+4-	5.905 1e-1-	8.160 0e+3≈	5.493 8e-1	8.109 9e+3
LSMOP8	3	300	1.089 9e-1-	5.261 4e+2+	7.451 4e-2-	7.409 9e+2+	6.093 8e-2	8.354 8e+2
LSMOP8	3	1 000	5.938 2e-2-	1.147 6e+4-	6.009 0e-2-	8.293 7e+3+	4.939 6e-2	8.597 1e+3
LSMOP9	3	300	1.128 4e+0-	5.079 8e+2+	1.599 3e-1-	6.436 7e+2+	1.220 3e-1	7.216 6e+2
LSMOP9	3	1 000	8.685 7e-1-	9.727 1e+3-	1.033 4e-1-	7.428 5e+3+	5.754 0e-2	7.693 2e+3
UF1	2	100	5.840 6e-3-	5.931 0e+1+	2.504 7e-3+	1.106 6e+2+	3.185 0e-3	1.364 5e+2
		300	7.055 3e-3-	5.262 2e+2+	2.516 9e-3+	5.357 2e+2+	2.660 5e-3	5.779 0e+2
		1 000	5.905 1e-3-	9.009 6e+3-	2.483 0e-3+	6.301 2e+3+	2.649 0e-3	6.854 6e+3
UF2	2	100	9.195 3e-3-	7.101 9e+1+	2.483 3e-3+	1.441 1e+2+	3.060 0e-3	1.820 6e+2
		300	9.679 0e-3-	5.695 8e+2+	2.484 5e-3+	6.510 0e+2+	2.659 0e-3	6.856 7e+2
		1 000	6.870 9e-3-	9.611 2e+3-	2.481 4e-3+	7.511 3e+3+	2.906 0e-3	8.046 2e+3
UF3	2	100	4.817 7e-2-	7.412 0e+1+	1.607 1e-2-	1.317 5e+2+	1.281 1e-2	1.559 9e+2
		300	3.312 9e-2-	6.252 0e+2+	3.850 5e-3+	6.558 5e+2+	4.061 7e-3	6.948 4e+2
		1 000	2.074 5e-2-	1.071 4e+4-	2.493 5e-3+	8.642 1e+3+	2.716 7e-3	9.245 6e+3
UF4	2	100	3.306 5e-2-	5.529 2e+1+	3.059 2e-2-	1.134 0e+2+	2.825 3e-2	1.378 9e+2
		300	3.470 6e-2-	5.057 6e+2+	2.953 0e-2-	5.608 5e+2+	2.818 0e-2	6.034 9e+2
		1 000	2.332 4e-2-	1.025 6e+4-	1.985 3e-2-	6.683 3e+3+	1.591 2e-2	7.187 8e+3
UF5	2	100	1.270 3e-1-	6.711 7e+1+	7.789 7e-2-	1.170 9e+2+	5.164 9e-2	1.419 9e+2
		300	1.429 6e-1-	5.631 3e+2+	8.975 9e-2-	5.389 8e+2+	7.147 1e-2	5.808 0e+2
		1 000	9.519 2e-2-	9.002 6e+3-	2.671 6e-2-	6.482 3e+3+	2.123 4e-2	7.179 7e+3
UF6	2	100	6.051 6e-2-	6.212 5e+1+	2.864 6e-2-	1.191 2e+2+	1.165 5e-2	1.448 2e+2
		300	4.108 8e-2-	5.503 4e+2+	1.530 9e-2-	5.618 1e+2+	7.000 4e-3	6.073 4e+2
		1 000	1.228 4e-2-	9.495 6e+3-	2.962 1e-3-	7.063 7e+3+	2.129 4e-3	8.279 6e+3
UF7	2	100	5.630 0e-2≈	5.773 5e+1+	5.078 2e-2-	1.137 2e+2+	3.426 5e-2	1.424 9e+2
		300	5.367 4e-2≈	5.162 9e+2+	5.079 2e-2-	5.329 8e+2+	4.451 0e-2	5.648 9e+2
		1 000	4.926 9e-2≈	9.497 4e+3-	5.076 2e-2-	7.442 3e+3+	3.448 8e-2	8.678 6e+3
UF8	3	100	1.011 7e-1-	5.981 1e+1+	6.754 6e-2+	1.207 6e+2+	7.986 8e-2	1.468 9e+2
		300	1.081 1e-1≈	5.332 3e+2+	2.527 8e-1-	5.483 2e+2+	1.649 3e-1	6.378 2e+2
		1 000	9.196 3e-2+	1.073 4e+4-	4.152 7e-1-	8.006 2e+3+	2.776 5e-1	8.388 8e+3
UF9	3	100	7.522 9e-2+	6.652 3e+1+	6.571 1e-2+	1.245 1e+2+	8.263 5e-2	1.381 5e+2
		300	7.773 8e-2+	5.210 4e+2+	1.349 1e-1-	5.495 5e+2+	9.185 1e-2	6.358 8e+2
		1 000	6.269 5e-2-	1.109 3e+4-	4.318 1e-2+	8.021 5e+3+	4.360 6e-2	8.693 9e+3
UF10	3	100	4.888 3e-1-	6.222 2e+1+	1.426 4e-1-	1.195 7e+2+	1.026 3e-1	1.376 4e+2
		300	4.849 9e-1-	5.541 9e+2+	1.769 2e-1-	5.789 4e+2+	1.571 6e-1	6.587 0e+2
		1 000	4.861 8e-1-	1.157 3e+4-	1.878 2e-1-	8.573 4e+3+	1.653 6e-1	9.094 8e+3
+/-/≈	-	-	3/39/6	29/19/0	11/36/1	46/0/2	-	-

Table 1

Table 2

HV results of three algorithms on UF and LSMOP"

问题	目标数	决策变量数	LMEA	MOEA/DVA	NAS-MOEA
LSMOP1	3	300	7.447 3e-1-	8.201 4e-1-	8.323 7e-1
LSMOP1	3	1 000	6.812 0e-1-	8.225 4e-1-	8.399 1e-1
LSMOP2	3	300	7.770 0e-1≈	7.655 6e-1-	7.891 8e-1
LSMOP2	3	1 000	8.115 3e-1-	8.075 7e-1-	8.299 7e-1
LSMOP3	3	300	2.119 3e-1-	1.499 9e-1-	3.585 5e-1
LSMOP3	3	1 000	3.508 5e-1-	4.820 7e-1-	5.821 6e-1
LSMOP4	3	300	7.573 4e-1-	7.656 1e-1-	8.016 8e-1
LSMOP4	3	1 000	8.054 4e-1-	8.075 2e-1-	8.237 4e-1
LSMOP5	3	300	1.305 0e-1-	5.247 5e-1-	5.458 0e-1
LSMOP5	3	1 000	1.039 3e-1-	5.341 9e-1-	5.551 6e-1
LSMOP6	3	300	1.162 1e-3-	0.000 0e+0-	3.152 4e-3
LSMOP6	3	1 000	0.000 0e+0≈	0.000 0e+0≈	5.707 8e-5
LSMOP7	3	300	1.667 3e-3-	0.000 0e+0-	4.776 6e-2
LSMOP7	3	1 000	2.257 8e-2-	6.270 3e-2-	1.052 2e-1
LSMOP8	3	300	4.336 7e-1-	4.875 1e-1-	5.281 1e-1
LSMOP8	3	1 000	5.233 1e-1-	5.270 5e-1-	5.604 9e-1
LSMOP9	3	300	8.774 2e-2-	2.144 8e-1-	2.343 4e-1
LSMOP9	3	1 000	7.160 1e-2-	2.497 7e-1-	2.709 2e-1
UF1	2	100	7.158 2e-1-	7.213 7e-1+	7.209 2e-1
		300	7.135 7e-1-	7.212 9e-1-	7.213 4e-1
		1 000	7.170 2e-1-	7.215 9e-1+	7.215 0e-1
UF2	2	100	7.114 0e-1-	7.216 0e-1+	7.210 9e-1
		300	7.104 1e-1-	7.215 9e-1+	7.214 9e-1
		1 000	7.146 4e-1-	7.216 4e-1+	7.212 9e-1
UF3	2	100	6.466 0e-1-	6.974 6e-1-	7.032 4e-1
		300	6.693 1e-1-	7.188 0e-1≈	7.187 0e-1
		1 000	6.918 0e-1-	7.215 5e-1+	7.214 0e-1
UF4	2	100	3.994 6e-1-	4.042 7e-1-	4.081 1e-1
		300	3.975 4e-1-	4.063 8e-1-	4.085 7e-1
		1 000	4.141 7e-1-	4.197 8e-1-	4.255 1e-1
UF5	2	100	3.988 9e-1-	4.670 5e-1-	5.049 8e-1
		300	3.746 8e-1-	4.522 5e-1-	4.773 0e-1
		1 000	4.471 9e-1-	5.357 6e-1-	5.426 4e-1
UF6	2	100	4.349 0e-1-	4.923 3e-1-	5.168 0e-1
		300	4.689 9e-1-	5.131 7e-1-	5.235 4e-1
		1 000	5.112 9e-1-	5.299 2e-1-	5.318 5e-1
UF7	2	100	5.241 8e-1-	5.271 9e-1-	5.460 2e-1
		300	5.248 2e-1≈	5.271 1e-1-	5.341 3e-1
		1 000	5.276 3e-1-	5.273 8e-1-	5.464 0e-1
UF8	3	100	4.774 5e-1-	5.329 8e-1+	5.265 9e-1
		300	4.696 1e-1≈	4.234 4e-1-	4.763 3e-1
		1 000	4.964 3e-1+	3.957 4e-1-	4.278 1e-1
UF9	3	100	7.069 0e-1-	7.680 6e-1+	7.360 1e-1
		300	6.995 8e-1-	7.057 2e-1-	7.335 8e-1
		1 000	7.265 6e-1-	7.950 7e-1+	7.902 9e-1
UF10	3	100	3.091 8e-1-	3.499 5e-1-	4.188 1e-1
		300	2.564 6e-1-	2.945 0e-1-	3.657 1e-1
		1 000	3.339 7e-1-	4.436 0e-1-	4.771 3e-1
+/-/≈	-	-	1/43/4	9/37/2	-

Table 2

Table 3

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

Fig.15

Fig.16

Fig.17

Fig.18

Fig.19

Fig.20

Table 4

IGD results of operator validity verification of five algorithms on UF and LSMOP"

问题	M	D	NAS-DVA	NAS-PCA	NAS-EVO	NAS-NAS	NAS-MOEA
LSMOP1	3	300	4.381 0e-2≈	4.456 1e-2≈	4.806 4e-2-	4.486 8e-2≈	4.378 0e-2
LSMOP1	3	1 000	4.002 3e-2≈	4.026 3e-2≈	4.696 4e-2-	3.992 1e-2≈	3.981 4e-2
LSMOP2	3	300	7.862 5e-2≈	7.724 5e-2≈	7.375 0e-2+	7.710 0e-2≈	7.806 4e-2
LSMOP2	3	1 000	4.299 5e-2≈	4.302 4e-2≈	5.150 6e-2-	4.304 7e-2≈	4.306 8e-2
LSMOP3	3	300	3.750 8e-1≈	3.920 0e-1≈	4.186 0e-1-	3.989 5e-1≈	3.872 2e-1
LSMOP3	3	1 000	2.322 3e-1-	2.281 3e-1≈	2.461 1e-1-	2.349 7e-1-	2.283 9e-1
LSMOP4	3	300	6.856 6e-2≈	6.622 0e-2≈	8.082 4e-2-	7.065 3e-2≈	6.889 0e-2
LSMOP4	3	1 000	4.871 4e-2≈	4.847 1e-2≈	5.294 7e-2-	5.001 7e-2≈	4.958 0e-2
LSMOP5	3	300	5.764 6e-2≈	5.792 0e-2≈	6.163 7e-2-	5.677 7e-2≈	5.871 2e-2
LSMOP5	3	1 000	5.594 8e-2≈	5.510 1e-2≈	6.157 1e-2-	5.557 9e-2≈	5.524 4e-2
LSMOP6	3	300	8.242 5e-1≈	9.655 4e-1-	1.489 9e+0-	8.882 7e-1-	8.179 9e-1
LSMOP6	3	1 000	1.037 2e+0≈	1.129 9e+0≈	1.553 0e+0-	1.063 4e+0≈	1.067 3e+0
LSMOP7	3	300	7.544 5e-1≈	7.855 5e-1-	8.029 3e-1≈	8.073 5e-1-	7.675 0e-1
LSMOP7	3	1 000	5.252 7e-1≈	6.005 3e-1-	5.660 2e-1-	5.644 2e-1≈	5.453 7e-1
LSMOP8	3	300	6.117 8e-2≈	6.504 4e-2-	6.845 2e-2-	6.058 7e-2≈	6.183 3e-2
LSMOP8	3	1 000	5.140 6e-2≈	5.254 8e-2≈	6.411 8e-2-	5.132 4e-2≈	5.147 9e-2
LSMOP9	3	300	1.345 5e-1≈	1.346 3e-1≈	1.701 4e-1-	1.356 7e-1≈	1.329 8e-1
LSMOP9	3	1 000	6.234 4e-2≈	6.126 1e-2≈	1.065 6e-1-	6.305 0e-2≈	6.123 3e-2
UF1	2	100	2.977 1e-3≈	2.806 9e-3+	2.484 0e-3+	2.948 0e-3≈	2.930 0e-3
		300	2.517 6e-3≈	2.523 5e-3≈	2.485 7e-3+	2.521 3e-3≈	2.530 0e-3
		1 000	2.574 6e-3≈	2.568 1e-3≈	2.481 4e-3+	2.546 1e-3≈	2.568 1e-3
UF2	2	100	2.962 7e-3≈	2.647 1e-3+	2.484 1e-3+	2.953 3e-3≈	2.960 3e-3
		300	2.607 9e-3≈	2.584 2e-3≈	2.481 8e-3+	2.592 4e-3≈	2.583 2e-3
		1 000	2.763 0e-3≈	2.739 7e-3≈	2.481 3e-3+	2.758 8e-3≈	2.745 7e-3
UF3	2	100	1.546 0e-1-	6.722 4e-2-	5.688 6e-2-	5.052 2e-2-	4.444 2e-2
		300	1.199 4e-1-	3.173 3e-2-	3.635 7e-3+	3.888 3e-3≈	3.784 7e-3
		1 000	2.131 5e-1-	7.879 3e-3-	2.492 2e-3+	2.596 4e-3≈	2.605 2e-3
UF4	2	100	2.577 9e-2+	2.532 1e-2+	2.588 2e-2≈	2.597 5e-2≈	2.615 3e-2
		300	2.715 1e-2≈	2.671 9e-2+	2.715 8e-2≈	2.728 2e-2-	2.718 9e-2
		1 000	1.559 5e-2≈	1.571 3e-2-	1.560 0e-2≈	1.562 6e-2≈	1.559 5e-2
UF5	2	100	4.310 5e-2≈	4.542 5e-2≈	4.230 7e-2≈	4.303 6e-2≈	4.407 3e-2
		300	5.608 6e-2≈	5.632 5e-2≈	5.819 5e-2-	5.483 2e-2≈	5.616 8e-2
		1 000	2.224 4e-2≈	2.224 0e-2≈	2.270 9e-2-	2.200 5e-2≈	2.211 4e-2
UF6	2	100	4.408 8e-2-	3.735 4e-2≈	5.183 3e-2-	4.519 3e-2-	3.529 0e-2
		300	6.158 0e-3≈	6.208 1e-3≈	7.307 4e-3-	7.342 1e-3-	6.142 7e-3
		1 000	2.162 5e-3≈	2.151 5e-3≈	2.472 4e-3-	2.239 5e-3-	2.142 2e-3
UF7	2	100	4.078 8e-2≈	4.544 0e-2≈	5.076 3e-2-	3.751 0e-2+	4.549 7e-2
		300	4.843 9e-2≈	4.470 8e-2≈	5.076 4e-2-	4.671 3e-2≈	4.709 8e-2
		1 000	4.340 3e-2≈	4.587 4e-2≈	5.076 1e-2-	4.245 7e-2≈	4.561 3e-2
UF8	3	100	1.545 2e-1-	1.945 7e-1≈	5.958 1e-2≈	6.824 2e-2≈	6.890 8e-2
		300	2.698 0e-1≈	3.675 8e-1≈	1.500 0e-1≈	1.466 5e-1≈	2.106 8e-1
		1 000	3.627 1e-1≈	3.926 9e-1-	2.874 8e-1≈	2.024 1e-1≈	2.826 5e-1
UF9	3	100	1.502 3e-1-	3.607 4e-2≈	4.607 6e-2-	5.701 7e-2≈	4.564 6e-2
		300	2.745 4e-1-	1.644 5e-1≈	7.329 3e-2-	1.045 4e-1≈	4.724 0e-2
		1 000	3.219 4e-1-	3.547 6e-2≈	5.250 5e-2-	6.319 1e-2≈	5.148 6e-2
UF10	3	100	3.657 1e-1-	1.077 2e-1-	8.811 1e-2≈	9.594 0e-2-	8.773 1e-2
		300	3.362 9e-1-	1.168 3e-1+	1.183 8e-1≈	1.590 7e-1-	1.398 8e-1
		1 000	3.613 4e-1-	1.718 2e-1≈	7.816 7e-2+	1.447 5e-1-	9.729 3e-2
+/-/≈	-	-	1/12/35	5/10/33	10/28/10	1/11/36	-

Table 4

Table 5

References 32

1	CAO B , FAN S S , ZHAO J W , et al. Quantum-enhanced multiobjective large-scale optimization via parallelism[J]. Swarm and Evolutionary Computation, 2020, 57, 100697. doi: 10.1016/j.swevo.2020.100697
2	DEB K , PRATAP A , AGARWAL S , et al. A fast and elitist multiobjective genetic algorithm: NSGA-Ⅱ[J]. IEEE Trans.on Evolutionary Computation, 2002, 6 (2): 182- 197. doi: 10.1109/4235.996017
3	DEB K , JAIN H . An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints[J]. IEEE Trans.on Evolutionary Computation, 2014, 18 (4): 577- 601. doi: 10.1109/TEVC.2013.2281535
4	JAIN H , DEB K . An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part Ⅱ: handling constraints and extending to an adaptive approach[J]. IEEE Trans.on Evolutionary Computation, 2014, 18 (4): 602- 622. doi: 10.1109/TEVC.2013.2281534
5	周晶, 赵晓哲, 许震, 等. 基于D-NSGA-Ⅲ算法的无人机群高维多目标任务分配方法[J]. 系统工程与电子技术, 2021, 43 (5): 1240- 1247.
	ZHOU J , ZHAO X Z , XU Z , et al. Mang-objective task allocation method based on D-NSGA-Ⅲ algorithm for multi-UAVs[J]. Systems Engineering and Electronics, 2021, 43 (5): 1240- 1247.
6	ZHANG Q F , LI H . MOEA/D: a multiobjective evolutionary algorithm based on decomposition[J]. IEEE Trans.on Evolutionary Computation, 2007, 11 (6): 712- 731. doi: 10.1109/TEVC.2007.892759
7	马武彬, 王锐, 王威超, 等. 基于进化多目标优化的微服务组合部署与调度策略[J]. 系统工程与电子技术, 2020, 42 (1): 90- 100.
	MA W B , WANG R , WANG W C , et al. Micro-service composition deployment and scheduling strategy based on evolutionary multi-objective optimization[J]. Systems Engineering and Electronics, 2020, 42 (1): 90- 100.
8	毕晓君, 张永建, 沈继红. 高维多目标多方向协同进化算法[J]. 控制与决策, 2014, 29 (10): 1737- 1743.
	BI X J , ZHANG Y J , SHEN J H . High-dimensional multi-objective multi-directional co-evolutionary algorithm[J]. Control and Decision, 2014, 29 (10): 1737- 1743.
9	OMIDVAR M N , LI X D , MEI Y , et al. Cooperative co-evolution with differential grouping for large scale optimization[J]. IEEE Trans.on Evolutionary Computation, 2014, 18 (3): 378- 393. doi: 10.1109/TEVC.2013.2281543
10	MA X L , LI X D , ZHANG Q F , et al. A survey on cooperative co-evolutionary algorithms[J]. IEEE Trans on Evolutionary Computation, 2019, 23 (3): 421- 441. doi: 10.1109/TEVC.2018.2868770
11	刘立佳, 李相民, 颜骥. 基于高维多目标多约束分组优化的要地防空扇形优化部署[J]. 系统工程与电子技术, 2013, 35 (12): 2513- 2520. doi: 10.3969/j.issn.1001-506X.2013.12.12
	LIU L J , LI X M , YAN J . Key-point air defense fan-shaped deployment with large-dimensional multi-objective multi-constraint group divided optimization[J]. Systems Engineering and Electronics, 2013, 35 (12): 2513- 2520. doi: 10.3969/j.issn.1001-506X.2013.12.12
12	ZENG Z Q , ZHANG M , CHEN T , et al. A new selection ope-rator for differential evolution algorithm[J]. Knowledge-Based Systems, 2021, 226, 107150. doi: 10.1016/j.knosys.2021.107150
13	ZOU D , GONG D . Differential evolution based on migrating variables for the combined heat and power dynamic economic dispatch[J]. Energy, 2022, 238, 121664. doi: 10.1016/j.energy.2021.121664
14	ZOU D X , LI S , KONG X Y , et al. Solving the dynamic economicdispatchby a memory-based global differential evolution and a repair technique of constraint handling[J]. Energy, 2018, 147, 59- 80. doi: 10.1016/j.energy.2018.01.029
15	IORIO A W, LI X D. A cooperative coevolutionary multiobjective algorithm using non-dominated sorting[C]//Proc. of the Genetic and Evolutionary Computation Conference, 2004: 537-548.
16	MA X L , LIU F , QI Y , et al. A multiobjective evolutionary algorithm based on decision variable analyses for multiobjective optimization problems with large-scale variables[J]. IEEE Trans.on Evolutionary Computation, 2016, 20 (2): 275- 298. doi: 10.1109/TEVC.2015.2455812
17	ZHANG X Y , TIAN Y , CHENG R , et al. A decision variable clustering-based evolutionary algorithm for large-scale many-objective optimization[J]. IEEE Trans.on Evolutionary Computation, 2018, 22 (1): 97- 112. doi: 10.1109/TEVC.2016.2600642
18	刘建昌, 李飞, 王洪海, 等. 进化高维多目标优化算法研究综述[J]. 控制与决策, 2018, 33 (5): 879- 887.
	LIU J C , LI F , WANG H H , et al. Survey on evolutionary many-objective optimization algorithms[J]. Control and Decision, 2018, 33 (5): 879- 887.
19	DEL S J , OSABA E , MOLINA D , et al. Bio-inspired computation: where we stand and what's next[J]. Swarm and Evolutionary Computation, 2019, 48, 220- 250. doi: 10.1016/j.swevo.2019.04.008
20	ZILLE H , ISHIBUCHI H , MOSTAGHIM S , et al. A framework for large-scale multiobjective optimization based on problem transformation[J]. IEEE Trans.on Evolutionary Computation, 2018, 22 (2): 260- 275. doi: 10.1109/TEVC.2017.2704782
21	HE C , LI L H , TIAN Y , et al. Accelerating large-scale multiobjective optimization via problem reformulation[J]. IEEE Trans.on Evolutionary Computation, 2019, 23 (6): 949- 961. doi: 10.1109/TEVC.2019.2896002
22	LIU R C , REN R , LIU J , et al. A clustering and dimensionality reduction based evolutionary algorithm for large-scale multi-objective problems[J]. Applied Soft Computing, 2020, 89, 106120. doi: 10.1016/j.asoc.2020.106120
23	ZHANG Y , WANG G G , LI K Q , et al. Enhancing MOEA/D with information feedback models for large-scale many-objective optimization[J]. Information Sciences, 2020, 522, 1- 16. doi: 10.1016/j.ins.2020.02.066
24	CHENG R , JIN Y C , NARUKAWA K , et al. A multiobjective evolutionary algorithm using Gaussian process-based inverse modeling[J]. IEEE Trans.on Evolutionary Computation, 2015, 19 (6): 838- 856. doi: 10.1109/TEVC.2015.2395073
25	CAO B , ZHAO J W , LV Z H , et al. A distributed parallel cooperative coevolutionary multiobjective evolutionary algorithm for large-scale optimization[J]. IEEE Trans.on Industrial Informatics, 2017, 13 (4): 2030- 2038. doi: 10.1109/TII.2017.2676000
26	ZHANG Q F, ZHOU A, ZHAO S Z, et al. Multiobjective optimization test instances for the CEC special session and competition[EB/OL]. [2021-08-01]. http://www.al-roomi.org/multimedia/CEC_Database/CEC2009/MultiObjectiveEA/CEC2009_MultiObjectiveEA_TechnicalReport.pdf.
27	WANG H D , ZHANG Q F , JIAO L C , et al. Regularity model for noisy multiobjective optimization[J]. IEEE Trans.on Cybernetics, 2016, 46 (9): 1997- 2009. doi: 10.1109/TCYB.2015.2459137
28	CHENG R , JIN Y C , OLHOFER M , et al. Test problems for large-scale multiobjective and many-objective optimization[J]. IEEE Trans.on Cybernetics, 2017, 47 (12): 4108- 4121. doi: 10.1109/TCYB.2016.2600577
29	TIAN Y , CHENG R , ZHANG X Y , et al. A strengthened dominance relation considering convergence and diversityfor evolutionary many-objective optimization[J]. IEEE Trans.on Evolutionary Computation, 2019, 23 (2): 331- 345. doi: 10.1109/TEVC.2018.2866854
30	CHENG S X , ZHAN H , YAO H Q , et al. Large-scale many-objective particle swarm optimizer with fast convergence based on Alpha-stable mutation and logistic function[J]. Applied Soft Computing, 2021, 99, 106947. doi: 10.1016/j.asoc.2020.106947
31	LIU R C , LIU J , LI Y F , et al. A random dynamic grouping based weight optimization framework for large-scale multi-objective optimization problems[J]. Swarm and Evolutionary Computation, 2020, 55, 100486.
32	MA L B, HUANG M, YANG S X, et al. An adaptive localized decision variable analysis approach to large-scale multiobjective and many-objective optimization[J]. IEEE Trans. on Cybernetics. DOI: 10.1109/tcyb.2020.3041212.

问题	S=15 P_A=1 P_N=0.9	S=10 P_A=1 P_N=0.9	S=5 P_A=1 P_N=0.9	S=10 P_A=1 P_N=0.99	S=10 P_A=1 P_N=0.95	S=10 P_A=1 P_N=0.8	S=10 P_A=0.9 P_N=0.9
LSMOP1	4.194 1e-2	4.180 8e-2	4.241 9e-2	4.245 8e-2	4.190 1e-2	4.080 9e-2	4.153 6e-2
LSMOP2	7.768 4e-2	7.734 7e-2	7.747 8e-2	7.692 8e-2	7.771 7e-2	7.786 7e-2	7.784 7e-2
LSMOP3	3.910 5e-1	3.783 0e-1	3.971 8e-1	3.958 8e-1	3.929 4e-1	3.924 1e-1	3.997 7e-1
LSMOP4	6.687 1e-2	6.590 4e-2	6.552 4e-2	6.855 5e-2	6.565 8e-2	6.518 3e-2	6.780 2e-2
LSMOP5	5.715 6e-2	5.665 1e-2	5.752 5e-2	5.731 6e-2	5.740 0e-2	5.756 0e-2	5.660 4e-2
LSMOP6	9.141 8e-1	9.044 0e-1	8.876 7e-1	9.112 3e-1	8.894 5e-1	9.088 1e-1	9.173 3e-1
LSMOP7	7.838 2e-1	7.966 6e-1	8.034 1e-1	8.468 6e-1	8.117 3e-1	8.660 2e-1	7.777 1e-1
LSMOP8	6.030 0e-2	6.029 7e-2	6.143 4e-2	6.043 3e-2	6.075 1e-2	6.080 2e-2	6.056 7e-2
LSMOP9	1.229 0e-1	1.184 2e-1	1.209 9e-1	1.214 5e-1	1.225 7e-1	1.235 8e-1	1.238 4e-1

问题	NAS-PCA	NAS-MOEA
UF1	3.699 4e+4	3.258 8e+4
UF 2	4.962 8e+4	4.958 6e+4
UF 3	5.984 2e+4	6.800 8e+4
UF4	4.063 6e+4	4.074 4e+4
UF5	3.992 5e+4	3.839 1e+4

[1]	He TIAN, Chunzhu DONG, Hongcheng YIN. Radar target three-dimensional scattering centers inversion based on compressed sensing and frequency sparsity [J]. Systems Engineering and Electronics, 2022, 44(9): 2783-2790.
[2]	Chenrui SHI, Lu TIAN, Zhan XU, Ruxin ZHI, Jinhui CHEN. Effectiveness evaluation method of emergency communication and sensing equipment based on PSO-BP [J]. Systems Engineering and Electronics, 2022, 44(11): 3455-3462.
[3]	Lu GUO, Xiaodong LIU, Dongtao WEI, Pu ZHU. Extraction method of missile equipment health characterization parameters based on improved PCA [J]. Systems Engineering and Electronics, 2022, 44(10): 3275-3281.
[4]	Yunke SUN, Zhigeng FANG, Ding CHEN. Multi-time threat assessment based on dynamic grey principal component analysis [J]. Systems Engineering and Electronics, 2021, 43(3): 740-746.
[5]	Dongning FU, Guisheng LIAO, Yan HUANG, Jun LIU. ATI-RPCA GMTI method based on multi-channel SAR system [J]. Systems Engineering and Electronics, 2021, 43(1): 48-54.
[6]	Zhenzhen YANG, Jun LE, Yongpeng YANG, Lu FAN. Object detection algorithm of nonconvex motion-assisted low rank and sparse decomposition [J]. Systems Engineering and Electronics, 2020, 42(6): 1218-1225.
[7]	Yuzhao MA, Nan CHEN, Xinglong XIONG. Wind shear warning algorithm based on PCA and phase difference correction [J]. Systems Engineering and Electronics, 2020, 42(1): 52-60.
[8]	HUANG Chenxia, YIN Junjun, YANG Jian. Polarimetric SAR change detection with l1-norm principal component analysis [J]. Systems Engineering and Electronics, 2019, 41(10): 2214-2220.
[9]	JIAO Song, LI Wei, CHU Wei, MAO Shao-jie. Dynamic modification of online simulation system based on intelligence data-driven [J]. Systems Engineering and Electronics, 2016, 38(5): 1201-.
[10]	TIAN Zhongda， GAO Xianwen， LI Kun. Networked control system timedelay prediction method based on KPCA and LSSVM [J]. Journal of Systems Engineering and Electronics, 2013, 35(6): 1281-1285.
[11]	LIU Zhong-jie， ZHUANG Li-kui， CAO Yun-fen， DING Meng. Target recognition of SAR images using principal component analysis and sparse representation [J]. Journal of Systems Engineering and Electronics, 2013, 35(2): 282-286.
[12]	LIU Zhong-jie， CAO Yun-feng， ZHUANG Li-kui， DING Meng， WANG Xi-chao. Robust processing algorithm for SAR image target recognition [J]. Systems Engineering and Electronics, 2013, 35(12): 2489-2494.
[13]	ZHOU Xin， WU Ying. Signal modulation recognition based on KPCA and LDA [J]. Journal of Systems Engineering and Electronics, 2011, 33(7): 1611-1616.
[14]	CHEN Chuyao, ZHU Daqi. Sensor fault diagnosis method based on neural network principal component analysis [J]. Journal of Systems Engineering and Electronics, 2010, 32(7): 1549-1553.
[15]	WANG Yi-xiao, WANG Yi-ran. Similarity system theory of economic benefit estimation for satellite application industry [J]. Journal of Systems Engineering and Electronics, 2009, 31(8): 1897-1901.

Large-scale multi-objective algorithm based on neighborhood adaptive of differential evolution

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 25

References 32

Related Articles 15

Recommended Articles

Metrics

Comments