结合粒子群和单纯形的改进飞蛾优化算法

doi:10.13229/j.cnki.jdxbgxb20170066

摘要/Abstract

摘要：

为提高飞蛾优化算法求解实际问题的能力,提出了一种基于单存形的混合飞蛾优化算法。该算法通过粒子群优化获取飞蛾的初始最优位置,使其具有更佳丰富的种群;同时,引入单存形方法获取最优解。通过与其他4种算法在10个函数上测试比较,结果表明:本文算法收敛速度及解的质量优于其他算法,具有更好的求解能力和优化性能,可作为问题优化的有效工具。

关键词: 计算机应用, 单纯形法, 飞蛾优化算法, 粒子群优化, 函数优化

Abstract:

In order to improve the ability of moth optimization algorithm in solving practical problems, a novel hybrid moth optimization algorithm based on single storage is proposed. The algorithm uses particle swarm optimization to obtain the initial optimal location of the moths, so that it has a better and richer population. The optimal solution is also obtained by the simplex method. The proposed algorithm is compared with other four kinds of algorithms by tests on ten functions. Experimental results show that the convergence speed and solution quality of the proposed algorithm are better than other algorithms, it has better solving and optimizing performance, and can be used as an effective optimization tool.

Key words: computer application, simplex method, moth-flame optimization method, particle swarm optimization(PSO), function optimization

中图分类号:

TP393

赵东,孙明玉,朱金龙,于繁华,刘光洁,陈慧灵. 结合粒子群和单纯形的改进飞蛾优化算法[J]. 吉林大学学报(工学版), 2018, 48(6): 1867-1872.

ZHAO Dong,SUN Ming-yu,ZHU Jin-long,YU Fan-hua,LIU Guang-jie,CHEN Hui-ling. Improved moth-flame optimization method based on combination of particle swarm optimization and simplex method[J]. Journal of Jilin University(Engineering and Technology Edition), 2018, 48(6): 1867-1872.

图/表 7

图1

表1

基准函数"

函数	参数取值	最小值
$f 1 x = ∑ i = 1 n x i 2$	[-100,100]	0
$f 2 (x) = ∑ i = 1 n (∑ j = 1 i x j) 2$	[-100,100]	0
$f 3 (x) = ∑ i = 1 n ([x i + 0.5]) 2$	[-100,100]	0
$f 4 (x) = ∑ i = 1 n [x i 2 - 10 cos (2 π x i) + 10]$	[-5.12,5.12]	0
$f 5 (x) = - 20 exp - 0.2 1 n ∑ i = 1 n x i 2 - exp 1 n ∑ i = 1 n cos 2 π x i + 20 + e$	[-32,32]	0
$f 6 (x) = 14000 ∑ i = 1 n x i 2 - ∏ i = 1 n cos x i i + 1$	[-600,600]	0
$f 7 (x) = - ∑ i = 1 4 c i exp - ∑ j = 1 6 a ij x j - p ij 2$	[0,1]	-3.32
$f 8 (x) = - ∑ i = 1 5 X - a i X - a i T + c i - 1$	[0,10]	-10.1532
$f 9 (x) = - ∑ i = 1 7 X - a i X - a i T + c i - 1$	[0,10]	-10.4028
$f 10 (x) = - ∑ i = 1 10 X - a i X - a i T + c i - 1$	[0,10]	-10.5363

表1

表2

图2

图3

图4

图5

参考文献 19

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函数	评估指标	ASMFO算法	MFO算法	BA算法	DA算法	PSO算法
f₁	mean	6.61587×10^-7	1333.333611	14.41469608	1310.364321	128.8093818
	std	1.06073×10^-6	3457.459063	1.950027759	702.372311	16.73078547
	rank	1	5	2	4	3
f₂	mean	11.13415206	16890.85645	66.99110732	12941.56989	424.1775374
	std	5.154097921	11761.33616	15.65998979	9035.062058	91.97276795
	rank	1	5	2	4	3
f₃	mean	3.33979×10^-7	336.6754613	14.13230939	1206.616187	130.4472998
	std	3.80072×10^-7	1844.044846	2.021082608	556.6614262	13.69394367
	rank	1	4	2	5	3
f₄	mean	123.6179	161.0097	269.4918	159.1627	371.1542
	std	34.70155	29.88465	21.51611	35.78036	21.12408
	rank	1	3	4	2	5
f₅	mean	0.949335	13.62444	4.415123	9.1096	8.560911
	std	0.987226	7.940168	0.22009	1.792495	0.273829
	rank	1	5	2	4	3
f₆	mean	0.012629	15.08013	0.57143	12.63523	1.029492
	std	0.016012	34.26064	0.055542	6.425597	0.006695
	rank	1	5	2	4	3
f₇	mean	-3.28199	-3.211	-2.92727	-3.24876	-2.91484
	std	0.065413	0.062542	0.139138	0.095367	0.167127
	rank	1	3	4	2	5
f₈	mean	-8.9743	-5.47333	-6.01592	-7.66817	-3.76938
	std	2.173469	3.262726	2.988532	2.663623	1.264555
	rank	1	4	3	2	5
f₉	mean	-9.69972	-8.12273	-5.70277	-7.75656	-4.61679
	std	1.823505	3.337846	3.16243	3.087822	1.289141
	rank	1	2	4	3	5
f₁₀	mean	-10.3561	-8.3255	-5.95764	-7.71155	-4.64473
	std	0.987348	3.481528	3.131923	2.864567	1.056005
	rank	1	2	4	3	5
排名和		10	38	27	33	40
总体排名		1	4	2	3	5