分段搜索的果蝇算法及其对纺织企业资源配置

doi:10.3778/j.issn.1673-9418.2203112

计算机科学与探索 ›› 2022, Vol. 16 ›› Issue (10): 2330-2344.DOI: 10.3778/j.issn.1673-9418.2203112

分段搜索的果蝇算法及其对纺织企业资源配置

白晓波¹^,²^,⁺(), 邵景峰¹, 王铁山¹, 李勃¹^,²

1.西安工程大学管理学院,西安 710048
2.“一带一路”纺织发展研究院,西安 710048

收稿日期:2022-03-25 修回日期:2022-06-08 出版日期:2022-10-01 发布日期:2022-10-14
通讯作者: + E-mail: baixiaobo@xpu.edu.cn
作者简介:白晓波（1983—）,男,陕西勉县人,硕士,高级工程师,硕士生导师,CCF专业会员,主要研究方向为信息融合、智能信息处理等。
邵景峰（1980—）,男,甘肃定西人,博士,教授,硕士生导师,CCF专业会员,主要研究方向为智能信息处理、纺织质量控制等。
王铁山（1974—）,男,河北唐山人,博士,副教授,硕士生导师,主要研究方向为信息化与人工智能、智能信息处理等。
李勃（1986—）,男,甘肃平凉人,博士,副教授,硕士生导师,主要研究方向为信息融合、智能信息处理等。
基金资助:
国家自然科学基金(71802155);陕西青年科技创新团队项目(70);陕西省教育厅智库项目(20JT027);咸阳市重点研发计划项目(S2021ZDYF-GY-0715)

Fruit Fly Optimization Algorithm Based on Segmented Search and Resource Allo-cation to Textile Enterprise

BAI Xiaobo¹^,²^,⁺(), SHAO Jingfeng¹, WANG Tieshan¹, LI Bo¹^,²

1. School of Management, Xi’an Polytechnic University, Xi’an 710048, China
2. Textile Development Research Institute of “One Belt and One Road”, Xi’an 710048, China

Received:2022-03-25 Revised:2022-06-08 Online:2022-10-01 Published:2022-10-14
About author:BAI Xiaobo, born in 1983, M.S., senior engineer, M.S. supervisor, professional member of CCF. His research interests include information fusion, intelligent information processing, etc.
SHAO Jingfeng, born in 1980, Ph.D., professor, M.S. supervisor, professional member of CCF. His research interests include intelligent information processing, textile quality control, etc.
WANG Tieshan, born in 1974, Ph.D., associate professor, M.S. supervisor. His research interests include informatization and artificial intelligence, intelligent information processing, etc.
LI Bo, born in 1986, Ph.D., associate professor, M.S. supervisor. His research interests include information fusion, intelligent information processing, etc.
Supported by:
National Natural Science Foundation of China(71802155);Think Tank Project of Shaanxi Provincial Department of Education(70);Key Research and Development Plan Project of Xianyang(20JT027);Project of Youth Science and Technology Innovation Team of Shaanxi Province(S2021ZDYF-GY-0715)

摘要/Abstract

摘要：

为了解决纺织企业智能化资源配置中的多参数多目标优化问题,提出了Multi-P-LevyFOA。首先,建立纺织企业智能化转型的多参数多目标资源配置模型。然后,在迭代次数小于等于2/3总迭代数时,基于Levy飞行的随机数更新种群位置,扩大搜寻范围,避免陷入局部最优。在迭代大于2/3总次数时,使用均匀分布的随机数更新种群位置,缩小搜寻范围,避免跳出最优值范围。对算法在不同迭代时刻全局和局部寻优能力进行了分析,对Multi-P-LevyFOA的算法时间复杂度进行了分析并与标准FOA和5个改进的FOA进行比较,并证明了其收敛性。将Multi-P-LevyFOA与其他4种改进的FOA进行了性能对比,重点分析了算法阈值SEP在22个benchmark函数上的影响,研究了Levy飞行中 $β$ 参数对寻优效果的影响规律。最后,以陕西某纺织企业的智能化资源配置为例,验证了Multi-P-LevyFOA的可行性。实验结果表明,Multi-P-LevyFOA能够有效地解决多参数多目标优化问题,为纺织企业智能化资源配置提供参考。

结果

关键词: 多参数多目标, Levy飞行, 果蝇算法, 智能化

Abstract:

To solve the multi-parameter and multi-objective optimization problem in the intelligent resource allocation of textile enterprises, Multi-P-LevyFOA is proposed. Firstly, a multi-parameter and multi-objective resource allocation model for intelligent transformation of textile enterprises is established. Then, if the number of iterations is less than or equal to 2/3 of the total number of iterations, based on the random number of Levy flight, the population position is updated to expand the search range and avoid falling into local optimization. When the number of iterations is greater than 2/3 of the total number, the population position is updated with random numbers of uniform distribution, and the search range is narrowed to avoid jumping out of the optimal value range. The global and local optimization ability of the algorithm at different iteration times are analyzed, and the time complexity of Multi-P-LevyFOA algorithm is analyzed and compared with standard FOA and five improved FOA, and its convergence is proven. The performance of Multi-P-LevyFOA is compared with other four improved FOA, the influence of threshold SEP of the algorithm on the 22 benchmark functions is analyzed, and the influence law of $β$ parameter on the optimization effect of the algorithm in Levy flight is studied. Finally, taking the intelligent resource allocation of a textile enterprise in Shaanxi province as an example, the feasibility of Multi-P-LevyFOA is verified. Experimental results show that the Multi-P-LevyFOA can effectively solve the multi-parameter and multi-objective optimization problem under appropriate $β$ parameters, which provides a reference for the intelligent resource allocation of textile enterprises.

Key words: multi-parameter and multi-objective, Levy flight, fruit fly algorithm, intelligent

中图分类号:

TP391

白晓波, 邵景峰, 王铁山, 李勃. 分段搜索的果蝇算法及其对纺织企业资源配置[J]. 计算机科学与探索, 2022, 16(10): 2330-2344.

BAI Xiaobo, SHAO Jingfeng, WANG Tieshan, LI Bo. Fruit Fly Optimization Algorithm Based on Segmented Search and Resource Allo-cation to Textile Enterprise[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(10): 2330-2344.

图/表 14

图1 Multi-P-LevyFOA流程图

Fig.1 Diagram of Multi-P-LevyFOA

图2 F8三维效果图

Fig.2 3D figure of F8

表1 不同阈值 S E P对寻优结果的影响

Table 1 Influence of different S E P on search results

$S E P$	均值（Avg）	标准差（Std）	最好值（Best）	最差值（Worst）
0	-319.40	178.16	-421.14	-3.95
1/5	-1 582.15	199.72	-2 236.40	-1 141.24
1/4	-1 585.57	195.66	-2 163.92	-1 180.22
1/3	-1 550.14	195.56	-2 271.48	-1 263.22
2/5	-1 595.62	203.36	-2 250.27	-1 198.90
1/2	-1 580.25	209.15	-2 366.24	-1 228.63
3/5	-1 599.31	222.23	-2 240.62	-1 253.24
2/3	-1 598.84	182.73	-2 178.72	-1 277.98
3/4	-1 594.96	214.57	-2 584.38	-1 134.37
4/5	-1 549.62	171.49	-2 031.10	-1 137.61
1	-1 556.10	181.97	-2 058.19	-1 169.58

表1 不同阈值 S E P对寻优结果的影响

Table 1 Influence of different S E P on search results

$S E P$	均值（Avg）	标准差（Std）	最好值（Best）	最差值（Worst）
0	-319.40	178.16	-421.14	-3.95
1/5	-1 582.15	199.72	-2 236.40	-1 141.24
1/4	-1 585.57	195.66	-2 163.92	-1 180.22
1/3	-1 550.14	195.56	-2 271.48	-1 263.22
2/5	-1 595.62	203.36	-2 250.27	-1 198.90
1/2	-1 580.25	209.15	-2 366.24	-1 228.63
3/5	-1 599.31	222.23	-2 240.62	-1 253.24
2/3	-1 598.84	182.73	-2 178.72	-1 277.98
3/4	-1 594.96	214.57	-2 584.38	-1 134.37
4/5	-1 549.62	171.49	-2 031.10	-1 137.61
1	-1 556.10	181.97	-2 058.19	-1 169.58

图3 50个种群在不同迭代次数时的搜索历史

Fig.3 Search history of 50 fruit flies at different iterations

表2 时间复杂度对比

Table 2 Comparison of time complexity

算法	时间复杂度
Multi-P-LevyFOA	$O (N T)$
标准FOA	$O (N T)$
CSFOA^[15]	$O (N T)$
QTFOA^[16]	$O (T (2 N d + d))$
TEFOA^[17]	$O (N T)$
MSAD-FOA^[21]	$O (T N (2 d + l b N))$
HarmonyFOA^[27]	$O (T N (d + 1))$

表2 时间复杂度对比

Table 2 Comparison of time complexity

算法	时间复杂度
Multi-P-LevyFOA	$O (N T)$
标准FOA	$O (N T)$
CSFOA^[15]	$O (N T)$
QTFOA^[16]	$O (T (2 N d + d))$
TEFOA^[17]	$O (N T)$
MSAD-FOA^[21]	$O (T N (2 d + l b N))$
HarmonyFOA^[27]	$O (T N (d + 1))$

表3 普通单峰函数

Table 3 Universal unimodal functions

名称	函数	搜索区间	维数
Shpere	$f 1 (x) = ∑ i = 1 n x i 2$	[-100,100]	30
Schwefel’s function 2.21	$f 2 (x) = ∑ i = 1 n \| x i \| + ∏ i = 1 n \| x i \|$	[-10,10]	30
Schwefel’s function 1.2	$f 3 (x) = ∑ i = 1 n ∑ j = 1 i x i 2$	[-100,100]	30
Schwefel’s function 2.22	$f 4 (x) = m a x {\| x i \|, 1 ≤ i ≤ n}$	[-100,100]	30
Ellipsoid	$f 5 (x) = ∑ i = 1 n i x i 2$	[-100,100]	30
Sum of different powers	$f 6 (x) = ∑ i = 1 n \| x i \| i + 1$	[-1,1]	30
Dejong’s noisy	$f 7 (x) = ∑ i = 1 n i x i 4 + r a n d (0,1)$	[-1.28,1.28]	30
Zakharow	$f 8 (x) = ∑ i = 1 n x i 2 + ∑ i = 1 n 0.5 i x i 2 + ∑ i = 1 n 0.5 i x i 4$	[-5,10]	30

表3 普通单峰函数

Table 3 Universal unimodal functions

名称	函数	搜索区间	维数
Shpere	$f 1 (x) = ∑ i = 1 n x i 2$	[-100,100]	30
Schwefel’s function 2.21	$f 2 (x) = ∑ i = 1 n \| x i \| + ∏ i = 1 n \| x i \|$	[-10,10]	30
Schwefel’s function 1.2	$f 3 (x) = ∑ i = 1 n ∑ j = 1 i x i 2$	[-100,100]	30
Schwefel’s function 2.22	$f 4 (x) = m a x {\| x i \|, 1 ≤ i ≤ n}$	[-100,100]	30
Ellipsoid	$f 5 (x) = ∑ i = 1 n i x i 2$	[-100,100]	30
Sum of different powers	$f 6 (x) = ∑ i = 1 n \| x i \| i + 1$	[-1,1]	30
Dejong’s noisy	$f 7 (x) = ∑ i = 1 n i x i 4 + r a n d (0,1)$	[-1.28,1.28]	30
Zakharow	$f 8 (x) = ∑ i = 1 n x i 2 + ∑ i = 1 n 0.5 i x i 2 + ∑ i = 1 n 0.5 i x i 4$	[-5,10]	30

表4 低维度单峰函数

Table 4 Low-dimensional unimodal functions

名称	函数	搜索区间	维数	最小值
Easom	$f 9 (x) = - c o s x 1 c o s x 2 e x p (- (x 1 - π) 2 - (x 2 - π) 2)$	[-100,100]	2	0
Matyas	$f 10 (x) = 0.26 (x 12 + x 22) - 0.48 x 1 x 2$	[-10,10]	2	0

表4 低维度单峰函数

Table 4 Low-dimensional unimodal functions

名称	函数	搜索区间	维数	最小值
Easom	$f 9 (x) = - c o s x 1 c o s x 2 e x p (- (x 1 - π) 2 - (x 2 - π) 2)$	[-100,100]	2	0
Matyas	$f 10 (x) = 0.26 (x 12 + x 22) - 0.48 x 1 x 2$	[-10,10]	2	0

表5 普通多峰函数

Table 5 Universal multimodal functions

名称	函数	搜索区间	维数	最小值
Schwefel	$f 11 (x) = ∑ i = 1 n - x i s i n \| x i \|$	[-500,500]	30	-418.982 9 $×$ 5
Rastringin	$f 12 (x) = ∑ i = 1 n [x i 2 - 10 c o s (2 π x i) + 10]$	[-5.12,5.12]	30	0
Ackley	$f 13 (x) = - 20 e x p - 0.2 1 n ∑ i = 1 n x i 2 - e x p 1 n ∑ i = 1 n c o s (2 π x i) + 20 + e$	[-32,32]	30	0
Griewank	$f 14 (x) = 1 4 000 ∑ i = 1 n x i 2 - ∏ i = 1 n c o s (x i / i) + 1$	[-600,600]	30	0
Levy	$f 15 (x) = s i n 2 (π x 1) + ∑ i = 1 n - 1 (x i - 1) 2 [1 + 10 s i n 2 (π x i + 1)] + (x n - 1) 2 [1 + s i n 2 (2 π x d)]$	[-10,10]	30	0
Powell	$f 16 (x) = ∑ i = 1 n / 4 [(x 4 i - 3 + 10 x 4 i - 2) 2 + 5 (x 4 i - 1 + x 4 i) 2 + (x 4 i - 2 - 2 x 4 i - 1) 4 + 10 (x 4 i - 3 - x 4 i) 4]$	[-4,5]	30	0
Syblinski-Tang	$f 17 (x) = 12 ∑ i = 1 n (x i 4 - 16 x i 2 + 5 x i)$	[-5,5]	30	-39.165 99

表5 普通多峰函数

Table 5 Universal multimodal functions

名称	函数	搜索区间	维数	最小值
Schwefel	$f 11 (x) = ∑ i = 1 n - x i s i n \| x i \|$	[-500,500]	30	-418.982 9 $×$ 5
Rastringin	$f 12 (x) = ∑ i = 1 n [x i 2 - 10 c o s (2 π x i) + 10]$	[-5.12,5.12]	30	0
Ackley	$f 13 (x) = - 20 e x p - 0.2 1 n ∑ i = 1 n x i 2 - e x p 1 n ∑ i = 1 n c o s (2 π x i) + 20 + e$	[-32,32]	30	0
Griewank	$f 14 (x) = 1 4 000 ∑ i = 1 n x i 2 - ∏ i = 1 n c o s (x i / i) + 1$	[-600,600]	30	0
Levy	$f 15 (x) = s i n 2 (π x 1) + ∑ i = 1 n - 1 (x i - 1) 2 [1 + 10 s i n 2 (π x i + 1)] + (x n - 1) 2 [1 + s i n 2 (2 π x d)]$	[-10,10]	30	0
Powell	$f 16 (x) = ∑ i = 1 n / 4 [(x 4 i - 3 + 10 x 4 i - 2) 2 + 5 (x 4 i - 1 + x 4 i) 2 + (x 4 i - 2 - 2 x 4 i - 1) 4 + 10 (x 4 i - 3 - x 4 i) 4]$	[-4,5]	30	0
Syblinski-Tang	$f 17 (x) = 12 ∑ i = 1 n (x i 4 - 16 x i 2 + 5 x i)$	[-5,5]	30	-39.165 99

表6 低维度多峰函数

Table 6 Low-dimensional multimodal functions

名称	函数	搜索区间	维数	最小值
Cross-in-tray	$f 18 (x) = 0.000 1 [\| s i n x 1 s i n x 2 e x p (\| 100 - (x 12 + x 22 / π) \|) \| + 1] 0.1$	[-10,10]	2	-2.062 60
Drop-wave	$f 19 (x) = - (1 + c o s (12 x 12 + x 22) / 0.5 (x 12 + x 22) + 2)$	[-5.12,5.12]	2	-1.000 00
Schaffer function N.2	$f 20 (x) = 0.5 + {s i n 2 (x 12 - x 22) - 0.5 / [1 + 0.001 (x 12 + x 22)] 2}$	[-100,100]	2	0
Hartman1	$f 21 (x) = - ∑ i = 1 4 c i e x p - ∑ j = 1 3 a i j (x j - p i j) 2$	[1,3]	3	-3.860 00
Hartman2	$f 22 (x) = - ∑ i = 1 4 c i e x p - ∑ j = 1 6 a i j (x j - p i j) 2$	[0,1]	6	-3.320 00

表6 低维度多峰函数

Table 6 Low-dimensional multimodal functions

名称	函数	搜索区间	维数	最小值
Cross-in-tray	$f 18 (x) = 0.000 1 [\| s i n x 1 s i n x 2 e x p (\| 100 - (x 12 + x 22 / π) \|) \| + 1] 0.1$	[-10,10]	2	-2.062 60
Drop-wave	$f 19 (x) = - (1 + c o s (12 x 12 + x 22) / 0.5 (x 12 + x 22) + 2)$	[-5.12,5.12]	2	-1.000 00
Schaffer function N.2	$f 20 (x) = 0.5 + {s i n 2 (x 12 - x 22) - 0.5 / [1 + 0.001 (x 12 + x 22)] 2}$	[-100,100]	2	0
Hartman1	$f 21 (x) = - ∑ i = 1 4 c i e x p - ∑ j = 1 3 a i j (x j - p i j) 2$	[1,3]	3	-3.860 00
Hartman2	$f 22 (x) = - ∑ i = 1 4 c i e x p - ∑ j = 1 6 a i j (x j - p i j) 2$	[0,1]	6	-3.320 00

表7 Multi-P-LevyFOA与4个算法结果对比

Table 7 Multi-P-LevyFOA compared with 4 algorithms

函数	Multi-P-LevyFOA		CSFOA^[15]		QTFOA^[16]		TEFOA^[17]		HarmonyFOA^[27]
函数	Avg	Std	Avg	Std	Avg	Std	Avg	Std	Avg	Std
$f 1$	0	0	1.69E-03	1.69E-03	0	0	5.82E-03	2.71E-03	1.50E-03	1.51E-07
$f 2$	0	0	2.26E+00	2.26E+00	0	0	2.66E+00	3.70E-01	2.11E+00	9.31E-04
$f 3$	0	0	5.32E-01	5.32E-01	0	0	1.23E+00	2.67E-01	4.72E-01	5.50E-05
$f 4$	0	0	9.06E-03	9.06E-03	0	0	5.14E-02	4.40E-02	7.07E-03	1.76E-18
$f 5$	0	0	0.026 7	0.002 4	0	0	0.138 1	0.232 3	0.023 2	0
$f 6$	0	3.26E-05	1.71E+00	6.78E-16	0	0	1.71E+00	6.78E-16	1.34E+00	5.92E-02
$f 7$	3.21E-04	5.05E-04	4.33E+01	2.58E-05	1.40E-05	1.47E-05	1.00E+02	1.49E+02	3.93E+01	3.68E-01
$f 8$	0	0	332 844.189 6	211 786.588 2	0	0	174 426.286 9	166 459.09	72 042.38	165.013 3
$f 9$	-0.904 2	0.204 4	-3.17E-09	2.08E-10	1	2.92E-08	-2.49E-06	1.27E-05	-6.29E-07	4.24E-07
$f 10$	0	0	2.38E-04	4.16E-05	2.23E-231	0	1.25E-03	1.91E-03	1.85E-04	3.28E-06
$f 11$	-1.71E+03	147.142 0	-4.18E-03	3.00E-03	1.25E+01	3.56E-02	-2.40E+00	11.610 0	-3.62E+01	7.744 0
$f 12$	0	0	125.095 7	12.962 6	0	0	143.584 7	27.998 6	102.523 5	0.836 5
$f 13$	8.88E-16	0	1.26E-01	7.69E-03	8.88E-16	0	2.24E-01	9.05E-02	1.14E-01	2.14E-05
$f 14$	6.12E-07	2.52E-06	3.18E-06	3.13E-07	0	0	2.36E-05	3.40E-05	2.78E-06	1.03E-10
$f 15$	130.885 0	11.028 6	211.326 0	9.876 9	2.726 0	0.104 0	168.895 0	13.018 8	110.509 2	39.082 9
$f 16$	0	0	28.055 4	4.071 8	0	0	62.960 7	79.915 1	19.214 5	0.098 2
$f 17$	-289.503 6	39.322 6	-34.022 4	14.724 9	-10.780 0	8.015 0	-105.477 8	19.792 5	-148.658 3	88.187 8
$f 18$	-2.062 2	0.000 4	-0.142 9	0.134 9	-1.809 0	9.03E-02	-0.617 7	0.739 3	-2.182 8	0.061 7
$f 19$	-4.000 0	0	3.827 0	0.157 8	0	0	3.724 0	0.141 3	-4.000 0	0
$f 20$	0	0	1.08E-07	1.21E-08	0	0	5.44E-07	1.59E-06	9.93E-08	2.98E-10
$f 21$	-3.856 9	0.401 1	-0.727 5	0.408 7	0.357 0	0.272 0	-2.305 3	0.439 6	-3.713 8	0.039 2
$f 22$	-3.065 5	0.606 9	-0.000 9	0.002 1	0.986 0	0.439 0	-0.014 1	0.001 9	-0.343 1	0.214 8
	胜: 18, 败: 4				胜: 15, 败: 7

表7 Multi-P-LevyFOA与4个算法结果对比

Table 7 Multi-P-LevyFOA compared with 4 algorithms

函数	Multi-P-LevyFOA		CSFOA^[15]		QTFOA^[16]		TEFOA^[17]		HarmonyFOA^[27]
函数	Avg	Std	Avg	Std	Avg	Std	Avg	Std	Avg	Std
$f 1$	0	0	1.69E-03	1.69E-03	0	0	5.82E-03	2.71E-03	1.50E-03	1.51E-07
$f 2$	0	0	2.26E+00	2.26E+00	0	0	2.66E+00	3.70E-01	2.11E+00	9.31E-04
$f 3$	0	0	5.32E-01	5.32E-01	0	0	1.23E+00	2.67E-01	4.72E-01	5.50E-05
$f 4$	0	0	9.06E-03	9.06E-03	0	0	5.14E-02	4.40E-02	7.07E-03	1.76E-18
$f 5$	0	0	0.026 7	0.002 4	0	0	0.138 1	0.232 3	0.023 2	0
$f 6$	0	3.26E-05	1.71E+00	6.78E-16	0	0	1.71E+00	6.78E-16	1.34E+00	5.92E-02
$f 7$	3.21E-04	5.05E-04	4.33E+01	2.58E-05	1.40E-05	1.47E-05	1.00E+02	1.49E+02	3.93E+01	3.68E-01
$f 8$	0	0	332 844.189 6	211 786.588 2	0	0	174 426.286 9	166 459.09	72 042.38	165.013 3
$f 9$	-0.904 2	0.204 4	-3.17E-09	2.08E-10	1	2.92E-08	-2.49E-06	1.27E-05	-6.29E-07	4.24E-07
$f 10$	0	0	2.38E-04	4.16E-05	2.23E-231	0	1.25E-03	1.91E-03	1.85E-04	3.28E-06
$f 11$	-1.71E+03	147.142 0	-4.18E-03	3.00E-03	1.25E+01	3.56E-02	-2.40E+00	11.610 0	-3.62E+01	7.744 0
$f 12$	0	0	125.095 7	12.962 6	0	0	143.584 7	27.998 6	102.523 5	0.836 5
$f 13$	8.88E-16	0	1.26E-01	7.69E-03	8.88E-16	0	2.24E-01	9.05E-02	1.14E-01	2.14E-05
$f 14$	6.12E-07	2.52E-06	3.18E-06	3.13E-07	0	0	2.36E-05	3.40E-05	2.78E-06	1.03E-10
$f 15$	130.885 0	11.028 6	211.326 0	9.876 9	2.726 0	0.104 0	168.895 0	13.018 8	110.509 2	39.082 9
$f 16$	0	0	28.055 4	4.071 8	0	0	62.960 7	79.915 1	19.214 5	0.098 2
$f 17$	-289.503 6	39.322 6	-34.022 4	14.724 9	-10.780 0	8.015 0	-105.477 8	19.792 5	-148.658 3	88.187 8
$f 18$	-2.062 2	0.000 4	-0.142 9	0.134 9	-1.809 0	9.03E-02	-0.617 7	0.739 3	-2.182 8	0.061 7
$f 19$	-4.000 0	0	3.827 0	0.157 8	0	0	3.724 0	0.141 3	-4.000 0	0
$f 20$	0	0	1.08E-07	1.21E-08	0	0	5.44E-07	1.59E-06	9.93E-08	2.98E-10
$f 21$	-3.856 9	0.401 1	-0.727 5	0.408 7	0.357 0	0.272 0	-2.305 3	0.439 6	-3.713 8	0.039 2
$f 22$	-3.065 5	0.606 9	-0.000 9	0.002 1	0.986 0	0.439 0	-0.014 1	0.001 9	-0.343 1	0.214 8
	胜: 18, 败: 4				胜: 15, 败: 7

表8 S E P对Multi-P-LevyFOA的影响

Table 8 Influence of value of S E P on Multi-P-LevyFOA

函数	$S E P = 0$		$S E P = 1 / 5$		$S E P = 1 / 2$		$S E P = 2 / 3$		$S E P = 4 / 5$		$S E P = 1$
函数	Avg	Std	Avg	Std	Avg	Std	Avg	Std	Avg	Std	Avg	Std
$f 1$	8.79E-03	4.17E-03	2.62E-82	8.29E-82	2.42E-234	0	0	0	0	0	0	0
$f 2$	4.37E+00	8.53E-01	8.87E-08	1.20E-07	2.35E-27	8.30E-27	1.38E-55	2.50E-56	2.11E-104	7.79E-105	4.44E-83	1.14E-82
$f 3$	1.14E-01	7.33E-02	1.70E-80	2.67E-80	1.19E-221	0	1.35E-303	0	0	0	0	0
$f 4$	3.59E-02	1.20E-02	4.09E-37	1.29E-36	1.18E-117	5.10E-117	0	0	0	0	0	0
$f 5$	0.145 9	0.084 3	9.35E-83	2.81E-82	9.35E-240	0	0	0	0	0	0	0
$f 6$	1.76E+01	2.108 8	2.40E-07	5.25E-07	6.61E-53	1.37E-52	2.13E-113	3.63E-113	1.51E-211	0	6.25E-40	1.98E-39
$f 7$	4.28E+02	9.93E+01	9.73E-05	1.13E-04	1.16E-04	1.66E-04	1.83E-04	1.81E-04	3.79E-04	3.79E-04	1.69E-03	9.21E-04
$f 8$	9.705 0	3.598 3	7.29E-10	1.28E-09	7.28E-51	1.10E-50	3.47E-110	1.84E-110	8.36E-208	0	1.99E-145	6.30E-145
$f 9$	-0.960 9	0.028 9	-0.802 0	0.204 1	-0.896 8	0.063 1	-0.821 8	0.152 0	-0.880 2	0.119 4	-0.792 3	0.128 1
$f 10$	1.68E-05	0	1.49E-14	0	5.04E-54	0	1.48E-115	0	5.15E-213	0	4.79E-208	0
$f 11$	-421.000 0	190.410 0	-1.70E+03	228.786 2	-1.56E+03	217.547 1	-1.57E+03	215.110 3	-1.75E+03	223.040 6	-1.64E+03	203.394 7
$f 12$	207.505 6	12.216 5	0.000 1	0.000 1	0	0	0	0	0	0	0	0
$f 13$	4.05E-01	1.68E-01	8.88E-16	0	8.88E-16	0	8.88E-16	0	8.88E-16	0	8.88E-16	0
$f 14$	2.70E-05	3.19E-05	0	0	0	0	0	0	0	0	0	0
$f 15$	118.384 2	11.392 9	137.824 4	5.903 0	137.706 9	10.395 7	134.767 1	7.342 8	139.537 1	6.340 3	137.607 3	11.121 9
$f 16$	9.23E+01	42.264 3	1.26E-05	1.51E-05	7.71E-48	1.96E-48	1.45E-109	6.20E-110	9.09E-207	0	6.86E-82	1.18E-81
$f 17$	-278.258 9	23.256 9	-276.207 7	27.140 6	-269.071 6	16.207 1	-296.682 5	30.174 1	-280.231 0	31.588 4	-275.674 7	30.631 2
$f 18$	-2.061 8	0.000 9	-2.062 2	0.000 3	-2.061 6	0.001 1	-2.062 1	0.000 5	-2.061 8	0.000 7	-2.061 4	0.000 8
$f 19$	-4.000 0	0	-4.000 0	0	-4.000 0	0	-4.000 0	0	-4.000 0	0	-4.000 0	0
$f 20$	5.92E-09	3.78E-09	0	0	0	0	0	0	0	0	0	0
$f 21$	-2.517 2	0.629 9	-3.844 4	0.025 5	-3.817 0	0.143 9	-3.818 6	0.130 1	-3.824 7	0.113 0	-3.860 0	0.002 9
$f 22$	-0.945 2	0.994 3	-2.775 6	0.585 9	-2.780 7	0.454 7	-2.780 2	0.543 7	-2.912 6	0.345 7	-3.020 2	0.279 2
	胜:3,败:19,波动:1		胜:6,败:16,波动:5		胜:5,败:17,波动:6		胜: 9,败:13,波动:7		胜:15,败:9,波动:6		胜:11,败:11,波动:4

表8 S E P对Multi-P-LevyFOA的影响

Table 8 Influence of value of S E P on Multi-P-LevyFOA

函数	$S E P = 0$		$S E P = 1 / 5$		$S E P = 1 / 2$		$S E P = 2 / 3$		$S E P = 4 / 5$		$S E P = 1$
函数	Avg	Std	Avg	Std	Avg	Std	Avg	Std	Avg	Std	Avg	Std
$f 1$	8.79E-03	4.17E-03	2.62E-82	8.29E-82	2.42E-234	0	0	0	0	0	0	0
$f 2$	4.37E+00	8.53E-01	8.87E-08	1.20E-07	2.35E-27	8.30E-27	1.38E-55	2.50E-56	2.11E-104	7.79E-105	4.44E-83	1.14E-82
$f 3$	1.14E-01	7.33E-02	1.70E-80	2.67E-80	1.19E-221	0	1.35E-303	0	0	0	0	0
$f 4$	3.59E-02	1.20E-02	4.09E-37	1.29E-36	1.18E-117	5.10E-117	0	0	0	0	0	0
$f 5$	0.145 9	0.084 3	9.35E-83	2.81E-82	9.35E-240	0	0	0	0	0	0	0
$f 6$	1.76E+01	2.108 8	2.40E-07	5.25E-07	6.61E-53	1.37E-52	2.13E-113	3.63E-113	1.51E-211	0	6.25E-40	1.98E-39
$f 7$	4.28E+02	9.93E+01	9.73E-05	1.13E-04	1.16E-04	1.66E-04	1.83E-04	1.81E-04	3.79E-04	3.79E-04	1.69E-03	9.21E-04
$f 8$	9.705 0	3.598 3	7.29E-10	1.28E-09	7.28E-51	1.10E-50	3.47E-110	1.84E-110	8.36E-208	0	1.99E-145	6.30E-145
$f 9$	-0.960 9	0.028 9	-0.802 0	0.204 1	-0.896 8	0.063 1	-0.821 8	0.152 0	-0.880 2	0.119 4	-0.792 3	0.128 1
$f 10$	1.68E-05	0	1.49E-14	0	5.04E-54	0	1.48E-115	0	5.15E-213	0	4.79E-208	0
$f 11$	-421.000 0	190.410 0	-1.70E+03	228.786 2	-1.56E+03	217.547 1	-1.57E+03	215.110 3	-1.75E+03	223.040 6	-1.64E+03	203.394 7
$f 12$	207.505 6	12.216 5	0.000 1	0.000 1	0	0	0	0	0	0	0	0
$f 13$	4.05E-01	1.68E-01	8.88E-16	0	8.88E-16	0	8.88E-16	0	8.88E-16	0	8.88E-16	0
$f 14$	2.70E-05	3.19E-05	0	0	0	0	0	0	0	0	0	0
$f 15$	118.384 2	11.392 9	137.824 4	5.903 0	137.706 9	10.395 7	134.767 1	7.342 8	139.537 1	6.340 3	137.607 3	11.121 9
$f 16$	9.23E+01	42.264 3	1.26E-05	1.51E-05	7.71E-48	1.96E-48	1.45E-109	6.20E-110	9.09E-207	0	6.86E-82	1.18E-81
$f 17$	-278.258 9	23.256 9	-276.207 7	27.140 6	-269.071 6	16.207 1	-296.682 5	30.174 1	-280.231 0	31.588 4	-275.674 7	30.631 2
$f 18$	-2.061 8	0.000 9	-2.062 2	0.000 3	-2.061 6	0.001 1	-2.062 1	0.000 5	-2.061 8	0.000 7	-2.061 4	0.000 8
$f 19$	-4.000 0	0	-4.000 0	0	-4.000 0	0	-4.000 0	0	-4.000 0	0	-4.000 0	0
$f 20$	5.92E-09	3.78E-09	0	0	0	0	0	0	0	0	0	0
$f 21$	-2.517 2	0.629 9	-3.844 4	0.025 5	-3.817 0	0.143 9	-3.818 6	0.130 1	-3.824 7	0.113 0	-3.860 0	0.002 9
$f 22$	-0.945 2	0.994 3	-2.775 6	0.585 9	-2.780 7	0.454 7	-2.780 2	0.543 7	-2.912 6	0.345 7	-3.020 2	0.279 2
	胜:3,败:19,波动:1		胜:6,败:16,波动:5		胜:5,败:17,波动:6		胜: 9,败:13,波动:7		胜:15,败:9,波动:6		胜:11,败:11,波动:4

表9 测试数据

Table 9 Test data

项1	项2	项3	项4	项5	结果
0.157	0.166	0.435	1.026	0.019	0
1.084	0.180	0.223	0.728	0.833	1
0.223	0.200	0.516	0.385	0.020	1
1.215	0.213	0.317	1.040	1.033	1
0.384	0.223	0.256	0.947	0.994	1
1.606	0.228	0.273	1.063	1.007	1
1.168	0.245	0.333	0.938	0.968	0
0.342	0.262	0.338	0.189	0.967	0
0.868	0.259	0.261	0.998	0.996	0
0.519	0.265	0.238	0.889	0.005	1

表10 β对Multi-P-LevyFOA的影响

Table 10 Influence of value of βon Multi-P-LevyFOA

迭代次数	种群数	$R M S E$ 均值
迭代次数	种群数	$β$ = 1.0	$β$ = 1.3	$β$ = 1.5
2	2	0.320 9	0.566 0	0.715 4
3	3	0.194 3	0.328 6	0.376 6
4	4	0.172 8	0.245 6	0.324 4
5	5	0.166 1	0.180 8	0.242 4
10	10	0.155 7	0.157 3	0.158 8
20	20	0.154 7	0.154 6	0.155 6
30	30	0.153 5	0.153 7	0.154 3
40	40	0.153 3	0.153 4	0.153 9
50	50	0.153 1	0.153 2	0.153 7
60	60	0.153 2	0.153 0	0.153 2
70	70	0.153 0	0.153 2	0.153 1
80	80	0.153 0	0.153 1	0.153 0
90	90	0.153 1	0.152 9	0.153 1

表10 β对Multi-P-LevyFOA的影响

Table 10 Influence of value of βon Multi-P-LevyFOA

迭代次数	种群数	$R M S E$ 均值
迭代次数	种群数	$β$ = 1.0	$β$ = 1.3	$β$ = 1.5
2	2	0.320 9	0.566 0	0.715 4
3	3	0.194 3	0.328 6	0.376 6
4	4	0.172 8	0.245 6	0.324 4
5	5	0.166 1	0.180 8	0.242 4
10	10	0.155 7	0.157 3	0.158 8
20	20	0.154 7	0.154 6	0.155 6
30	30	0.153 5	0.153 7	0.154 3
40	40	0.153 3	0.153 4	0.153 9
50	50	0.153 1	0.153 2	0.153 7
60	60	0.153 2	0.153 0	0.153 2
70	70	0.153 0	0.153 2	0.153 1
80	80	0.153 0	0.153 1	0.153 0
90	90	0.153 1	0.152 9	0.153 1

图4 β取值对Multi-P-LevyFOA的影响

Fig.4 Influence of value of β on Multi-P-LevyFOA

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分段搜索的果蝇算法及其对纺织企业资源配置

Fruit Fly Optimization Algorithm Based on Segmented Search and Resource Allo-cation to Textile Enterprise

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