一种适应度排序的高维多目标粒子群优化算法

doi:10.19665/j.issn1001-2400.2021.03.0010

Abstract

Abstract:

Due to the complexity and difficulty of solving the many-objective optimization problem,a many-objective particle swarm optimization algorithm for ensemble fitness ranking is proposed.In this algorithm,the nearest vector between the individual and reference points in the population is obtained,and the individuals in the population are sorted by the penalty-based boundary intersection approach.Then,the poor individuals in the population are deleted and the elite individuals are saved in the external archives.The four advanced many-objective evolutionary optimization algorithms are adopted to make comparisons on 5,8,10,15 objectives of 13 standard test sets.Experimental results show that the performance of the proposed algorithm is better than comparison algorithms in most of the test cases.It has also been proved that the algorithm has good convergence and diversity,and that it can effectively deal with many-objective optimization problems.

Key words: ensemble fitness ranking, many-objective optimization, particle swarm optimization, penalty-based boundary intersection approach

CLC Number:

TP18

YANG Wusi,CHEN Li,WANG Yi,ZHANG Maosheng. Many-objective particle swarm optimization algorithm for fitness ranking[J].Journal of Xidian University, 2021, 48(3): 78-84.

Figures/Tables 6

测试用例	目标维度	NSGAIII	EFRRR	MaOEAIGD	MOEAD	MaPSOEFR
DTLZ1	5	6.338 2×10^-2=	6.335 2×10^-2=	4.577 0×10^-1-	6.342 0×10^-2=	6.820 4×1 $0 - 2$
	8	1.067 7×10^-1=	1.029 8×10^-1=	1.568 8×10^-1-	9.569 1×10^-2=	9.746 1×1 $0 - 2$
	10	1.443 2×10^-1-	1.403 4×10^-1-	1.215 2×10^-1=	1.265 5×10^-1-	1.160 4×10^-1
	15	2.158 6×10^-1-	1.389 2×10^-1+	1.831 5×10^-1-	1.294 0×10^-1+	1.641 5×10^-1
DTLZ2	5	1.948 8×10^-1=	1.948 9×10^-1=	1.975 1×10^-1=	1.949 0×10^-1=	1.948 5×10^-1
	8	3.399 5×10^-1+	3.266 5×10^-1+	3.279 9×10^-1+	3.149 6×10^-1+	4.022 4×10^-1
	10	5.303 2×10^-1-	4.569 0×10^-1=	4.538 3×10^-1=	4.560 6×10^-1=	4.741 8×10^-1
	15	6.384 0×10^-1-	5.547 9×10^-1+	5.612 8×10^-1+	5.262 0×10^-1+	5.986 5×10^-1
DTLZ3	5	2.013 8×10^-1+	1.973 4×10^-1+	8.444 1×10⁰-	2.500 3×10^-1=	2.617 1×10^-1
	8	1.007 7×10⁰-	4.883 9×10^-1-	5.108 8×10⁰-	5.237 1×10^-1-	3.939 6×10^-1
	10	6.399 1×10⁰-	4.433 6×10⁰-	6.490 6×10⁰-	5.960 4×10^-1-	5.032 8×10^-1
	15	5.201 3×10¹-	7.218 2×10^-1+	1.934 8×10⁰-	1.233 7×10⁰-	7.688 8×10^-1
DTLZ4	5	2.176 6×10^-1-	1.955 1×10^-1=	2.838 8×10^-1-	3.529 5×10^-1-	1.950 8×10^-1
	8	3.482 1×10^-1=	3.364 4×10^-1=	3.348 2×10^-1=	5.544 1×10^-1-	3.417 8×10^-1
	10	4.559 0×10^-1-	4.583 3×10^-1-	4.537 2×10^-1=	6.300 7×10^-1-	4.534 5×10^-1
	15	6.045 4×10^-1=	5.896 0×10^-1=	5.770 0×10^-1+	7.255 0×10^-1-	5.936 3×10^-1
WFG4	5	1.172 7×10⁰-	1.294 3×10⁰-	6.739 6×10⁰-	1.865 2×10⁰-	1.167 3×10⁰
	8	3.112 4×10⁰=	3.192 0×10⁰-	9.751 3×10⁰-	6.962 5×10⁰-	3.028 4×10⁰
	10	4.782 4×10⁰=	4.837 5×10⁰=	1.204 6×10¹-	9.434 4×10⁰-	4.724 9×10⁰
	15	8.554 1×10⁰=	8.850 8×10⁰=	1.926 ×10¹-	1.623 5×10¹-	8.925 1×10⁰
WFG5	5	1.164 1×10⁰=	1.236 2×10⁰-	6.323 5×10⁰-	1.615 8×10⁰-	1.132 2×10⁰
	8	2.961 1×10⁰=	3.261 8×10⁰-	1.334 3×10¹-	6.533 4×10⁰-	2.954 7×10⁰
	10	4.725 5×10⁰-	5.539 9×10⁰-	1.757 5×10¹-	9.062 3×10⁰-	4.501 5×10⁰
	15	8.088 9×10⁰+	8.497 8×10⁰=	2.820 8×10¹-	1.591 9×10¹-	8.439 4×10⁰
WFG6	5	1.165 4×10⁰=	1.352 2×10⁰-	5.945 3×10⁰-	1.983 6×10⁰-	1.162 3×10⁰
	8	2.957 2×10⁰=	3.282 3×10⁰-	1.206 1×10¹-	7.092 3×10⁰-	3.053 4×10⁰
	10	4.784 4×10⁰=	5.311 4×10⁰-	1.304 4×10¹-	9.767 8×10⁰-	4.756 5×10⁰
	15	1.184 7×10¹-	8.835 3×10⁰=	2.449 0×10¹-	1.647 4×10¹-	8.775 1×10⁰
WFG7	5	1.178 7×10⁰=	1.238 8×10⁰=	5.923 7×10⁰-	2.110 5×10⁰-	1.177 6×10⁰
	8	2.976 3×10⁰=	3.273 2×10⁰-	1.008 2×10¹-	7.037 0×10⁰-	3.041 1×10⁰
	10	4.812 3×10⁰=	5.247 0×10⁰-	1.299 8×10¹-	9.579 8×10⁰-	4.721 1×10⁰
	15	1.049 4×10¹-	9.021 4×10⁰-	2.320 8×10¹-	1.664 7×10¹-	8.509 2×10⁰
WFG8	5	1.146 7×10⁰=	1.315 9×10⁰-	4.068 0×10⁰-	1.835 9×10⁰-	1.166 4×10⁰
	8	3.123 2×10⁰=	3.344 7×10⁰-	7.376 8×10⁰-	6.459 9×10⁰-	3.062 5×10⁰
	10	5.059 0×10⁰-	5.401 9×10⁰-	6.465 3×10⁰-	8.673 6×10⁰-	4.528 9×10⁰
	15	9.354 3×10⁰-	8.751 6×10⁰-	1.996 4×10¹-	1.473 2×10¹-	8.394 7×10⁰
WFG9	5	1.131 9×10⁰=	1.268 1×10⁰-	4.409 2×10⁰-	1.737 4×10⁰-	1.116 2×10⁰
	8	2.939 9×10⁰+	3.324 7×10⁰-	8.600 0×10⁰-	6.719 7×10⁰-	3.071 0×10⁰
	10	4.567 2×10⁰-	5.363 0×10⁰-	6.038 8×10⁰-	9.166 5×10⁰-	4.360 8×10⁰
	15	7.811 5×10⁰+	8.303 3×10⁰+	1.053 7×10¹=	1.594 6×10¹-	9.143 4×10⁰
+/-/=		5/14/21	6/21/13	3/31/6	3/32/5

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测试问题	目标数	决策变量数	参数k
DTLZ1	5,8,10,15	m+k-1	5
DTLZ2-DTLZ4	5,8,10,15	m+k-1	10
WFG4-WFG9	5,8,10,15	k+l	2 (m-1);l=20

目标数	种群数	进化次数
5	150	100 000
8	200	100 000
10	250	100 000
15	300	100 000

Many-objective particle swarm optimization algorithm for fitness ranking

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