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山东大学学报 (工学版) ›› 2020, Vol. 50 ›› Issue (2): 34-43.doi: 10.6040/j.issn.1672-3961.0.2019.294

• 机器学习与数据挖掘 • 上一篇    下一篇

基于混合决策的改进鸟群算法

闫威(),张达敏*(),张绘娟,辛梓芸,陈忠云   

  1. 贵州大学大数据与信息工程学院, 贵州 贵阳 550025
  • 收稿日期:2019-06-10 出版日期:2020-04-20 发布日期:2020-04-16
  • 通讯作者: 张达敏 E-mail:349552812@qq.com;1203813362@qq.com
  • 作者简介:闫威(1993—)，男，贵州贵阳人，硕士研究生，主要研究方向为网络通信，优化计算. E-mail：349552812@qq.com
  • 基金资助:
    贵州省自然科学基金资助项目(黔科合基础[2017]1047号)

Improved bird swarm algorithms based on mixed decision making

Wei YAN(),Damin ZHANG*(),Huijuan ZHANG,Ziyun XI,Zhongyun CHEN   

  1. College of Big Data and Information Engineering, Guizhou University, Guiyang 550025, Guiyang, China
  • Received:2019-06-10 Online:2020-04-20 Published:2020-04-16
  • Contact: Damin ZHANG E-mail:349552812@qq.com;1203813362@qq.com
  • Supported by:
    贵州省自然科学基金资助项目(黔科合基础[2017]1047号)

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摘要：

针对鸟群算法(bird swarm algorithms, BSA)在求解复杂函数问题时存在的精度低、易陷入局部最优等问题,在保留BSA简单性的同时,提出一种基于混合决策的改进鸟群算法(improved bird swarm algorithms based on mixed decision making, IBSA)。应用重心反向学习机制初始化鸟群,维持鸟群较好的空间解分布。为了有效平衡算法在寻优过程中全局探索能力和局部发觉能力,动态调整鸟群飞往另外区域的周期。引入自适应余弦函数权重策略和加权平均思想对生产者觅食公式进行改进,增加算法在陷入局部最优后的脱困能力。在9个测试函数的基础上通过仿真试验对比基于IBSA、BSA、粒子群算法(particle swarm optimization, PSO)性能。结果表明,改进算法在单峰函数和多峰函数的测试中,寻优精度和寻优速度得到了较大程度上的提升。

关键词: 鸟群算法, 重心反向学习, 自适应余弦函数权重, 混合决策, 重心反向学习机制

Abstract:

Aiming at the problems of low precision and easy to fall into local optimum in solving complex function problems of traditional bird swarm algorithm (BSA), an improved bird swarm algorithm based on mixed decision-making was proposed while retaining the simplicity of BSA. The centroid opposition-based learning was used to initialize the bird population and maintain the better spatial solution distribution of the bird flock. In order to balance the global search ability and local detection ability of the algorithm in the optimization process, the period time of the birds flying to another area was dynamically adjusted. The weighting strategy of adaptive cosine function and weighted averaging idea were introduced to improve the producer's foraging formula, so as to increase the ability of the algorithm to get rid of difficulties after falling into local optimum. The performance of improved bird swarm algorithm based on mixed decision-making, bird swarm algorithm and particle swarm optimization were compared on the basis of nine test functions. The results showed that the accuracy and speed of the improved algorithm were greatly improved in the test of single-peak and multi-peak functions.

Key words: bird swarm algorithm, centroid opposition-based learning, the weighting strategy of adaptive cosine function, mixed decision making, the centroid opposition-based learning

中图分类号: 

  • TP391

图1

S型函数曲线"

图2

变换后的S型函数曲线"

表1

试验设置参数"

算法 参数设置
IBSA c1=c2=1.5, a1=a2=1, FQ=[4, 10], ω=[4, 9], a=12
BSA c1=c2=1.5, a1=a2=1, FQ=10
PSO ω=0.729, c1=c2=1.494 45,

表2

标准测试函数基本信息"

函数名 表达式 范围 最优值
Schwefel 1.2 $F_{1}(x)=\sum\limits_{i=1}^{n}\left(\sum\limits_{j=1}^{i} x_{j}^{2}\right)^{2}$ [-10, 10] 0
Tablet $F_{2}(x)=10^{6} x_{1}^{2}+\sum\limits_{i=2}^{n} x_{i}^{2}$ [-100, 100] 0
Schwefel 2.22 $F_{3}(x)=\sum\limits_{i=1}^{n}\left|x_{i}\right|+\prod\limits_{i=1}^{n}\left|x_{i}\right|$ [-10, 10] 0
Sphere $F_{4}(x)=\sum\limits_{i=1}^{n} x_{i}^{2}$ [-100, 100] 0
Alpine $F_{5}(x)=\sum\limits_{i=1}^{n}\left|x_{i} \sin \left(x_{i}\right)+0.1 x_{i}\right|$ [-10, 10] 0
Rastrigin $F_{6}(x)=\sum\limits_{i=1}^{n}\left(x_{i}^{2}-10 \cos \left(2 \pi x_{i}\right)+10\right)$ [-5.12, 5.12] 0
Griewank $F_{7}(x)=\sum\limits_{i=1}^{n} \frac{x_{i}^{2}}{4000}-\prod\limits_{i=1}^{n} \cos \left(\frac{x_{i}}{\sqrt{i}}\right)+1$ [-600, 600] 0
Powell $F_{8}(x)=\sum\limits_{i=1}^{n / 4}\left[\left(x_{4 i-3}+10 x_{4 i-2}\right)^{2}+5\left(x_{4 i-1}-x_{4 i}\right)^{2}+\left(x_{4 i-2}-2 x_{4 i-1}\right)^{4}+10\left(x_{4 i-3}-x_{4 i}\right)^{4}\right]$ [-4, 5] 0
Zakharov $F_{9}(x)=\sum\limits_{i=1}^{n} x_{i}^{2}+\left(\sum\limits_{i=1}^{n} 0.5 i x_{i}\right)^{2}+\left(\sum\limits_{i=1}^{n} 0.5 i x_{i}\right)^{4}$ [-5, 10] 0

表3

不同算法之间的性能对比"

函数 维数 算法 最优值 最差值 平均值 标准差 成功率/% 平均耗时/s
IBSA 0 0 0 0 100 1.464 4
10 BSA 0 0 0 0 100 1.865 5
PSO 1.670×10-134 6.565×10-45 6.565×10-47 6.565×10-46 97 1.187 2
IBSA 0 0 0 0 100 1.440 7
F1 20 BSA 0 0 0 0 100 1.826 9
PSO 5.522×10-7 3.037×10-3 2.129×10-4 4.340×10-4 0 1.217 4
IBSA 0 0 0 0 100 1.510 2
50 BSA 0 0 0 0 100 1.914 6
PSO 0.841 2.251×101 6.463 4.061 0 1.302 9
IBSA 0 0 0 0 100 1.829 9
10 BSA 2.579×10-252 5.409×10-187 7.623×10-189 0 100 2.230 9
PSO 7.388×10-53 1.621×10-4 4.465×10-6 2.167×10-5 0 1.596 4
IBSA 0 0 0 0 100 2.263 6
F2 20 BSA 3.363×10-247 3.795×10-165 4.579×10-167 0 100 2.712 6
PSO 1.359×10-2 2.687 3.255 3.694 0 2.081 7
IBSA 0 0 0 0 100 3.615 9
50 BSA 1.157×10-251 1.243×10-170 1.243×10-172 0 100 3.995 4
PSO 2.576 2.461 7.731 3.557 0 3.313 6
IBSA 4.303×10-221 7.367×10-195 1.539×10-196 0 100 1.833 9
10 BSA 7.813×10-112 2.020×10-77 2.102×10-79 2.020×10-78 20 2.299 6
PSO 7.269×10-5 1.331×10-1 1.326×10-2 2.201×10-2 0 1.617 4
IBSA 1.892×10-223 2.538×10-179 2.538×10-181 0 100 1.897 8
F3 20 BSA 7.098×10-110 6.962×10-74 6.962×10-76 6.962×10-75 15 2.317 0
PSO 2.199×10-1 3.028 1.029 0.597 0 1.581 6
IBSA 5.854×10-220 4.740×10-187 4.740×10-189 0 100 2.022 0
50 BSA 1.339×10-111 1.445×10-77 1.704×10-79 1.466×10-78 14 2.353 3
PSO 6.468 1.965×101 1.309×101 3.204 0 1.689 1
IBSA 0 0 0 0 100 1.453 1
10 BSA 5.489×10-247 7.667×10-182 7.669×10-184 0 100 1.822 3
PSO 1.066×10-56 6.109×10-5 6.113×10-7 6.109×10-6 0 1.160 9
IBSA 0 0 0 0 100 1.495 3
F4 20 BSA 4.011×10-247 1.652×10-183 1.808×10-185 0 100 1.858 1
PSO 0.108×10-1 0.762 0.161 0.150 0 1.235 4
IBSA 0 0 0 0 100 1.553 3
50 BSA 3.162×10-249 4.535×10-191 4.538×10-193 0 100 1.905 1
PSO 2.018 1.120×101 5.751 1.798 0 1.287 4
IBSA 1.067×10-216 5.371×10-194 5.510×10-196 0 100 1.940 5
10 BSA 1.331×10-106 8.476×10-84 1.415×10-85 9.703×10-85 24 2.368 1
PSO 4.454×10-7 0.331 0.017 0.042 0 1.722 3
IBSA 2.531×10-225 1.234×10-190 1.234×10-192 0 100 2.323 3
F5 20 BSA 1.036×10-105 7.532×10-74 7.532×10-76 7.532×10-75 21 2.812 9
PSO 9.482×10-3 2.922 0.408 0.551 0 2.064 9
IBSA 1.103×10-222 7.117×10-186 7.117×10-188 0 100 3.563 3
50 BSA 8.997×10-110 8.052×10-82 9.490×10-84 8.125×10-83 19 3.994 9
PSO 1.985 1.801×101 7.424 2.804 0 3.412 2
IBSA 0 0 0 0 100 1.847 6
10 BSA 0 0 0 0 100 2.264 0
PSO 1.990 2.288×101 8.467 3.793 0 1.613 9
IBSA 0 0 0 0 100 2.284 7
F6 20 BSA 0 0 0 0 100 2.688 4
PSO 6.236 4.507×101 1.817×101 5.829 0 2.073 9
IBSA 0 0 0 0 100 3.611 0
50 BSA 0 0 0 0 100 4.151 3
PSO 7.070×101 1.611×102 1.108×102 1.833×101 0 3.481 4
IBSA 0 0 0 0 100 2.261 9
10 BSA 0 0 0 0 100 2.673 1
PSO 0.832 5.868 2.435 0.899 0 2.102 7
IBSA 0 0 0 0 100 2.6604
F7 20 BSA 0 0 0 0 100 3.064 9
PSO 5.983 1.495×101 9.993 2.020 0 2.553 7
IBSA 0 0 0 0 100 3.882 9
50 BSA 0 0 0 0 100 4.294 4
PSO 2.518×101 5.273×101 3.723×101 4.637 0 3.970 0
IBSA 0 0 0 0 100 1.330 2
10 BSA 0 2.020×10-189 2.020×10-191 0 100 1.771 2
PSO 1.765×10-32 1.690×10-6 1.929×10-8 1.693×10-7 0 1.045 5
IBSA 0 0 0 0 100 1.462 0
F8 20 BSA 3.849×10-255 2.245×10-181 2.286×10-183 0 100 1.887 2
PSO 6.275×102 1.441×101 1.555 2.132 0 1.222 7
IBSA 0 0 0 0 100 1.903 9
50 BSA 8.628×10-250 4.011×10-189 4.011×10-191 0 100 2.340 6
PSO 1.284×101 8.807×101 4.002×101 1.65 0 1.672 1
IBSA 0 0 0 0 100 1.329 4
10 BSA 1.186×10-247 2.661×10-171 2.661×10-173 0 100 1.755 7
PSO 5.982×10-67 9.092×10-6 1.244×10-7 9.287×10-07 0 0.994 7
IBSA 0 0 0 0 100 1.327 4
F9 20 BSA 7.775×10-247 5.183×10-187 5.183×10-189 0 100 1.786 3
PSO 0.076 9 2.947×101 1.267 4.044 0 1.081 5
IBSA 0 0 0 0 100 1.705 5
50 BSA 2.081×10-250 6.203 9×10-168 6.203 9×10-170 0 100 2.080 3
PSO 1.158×101 4.111×102 6.729×101 5.663×101 0 1.407 0

图3

各测试函数平均收敛曲线"

表4

文献[7]算法与本文改进算法的性能对比"

文献[7]中的函数 算法
 最优值 最差值 平均值 方差
F2 IBSA 0 0 0 0
AIBSO 1.051 6×10-24 1.006 4×102 1.634 4 1.052 7×101
F3 IBSA 0 0 0 0
AIBSO 1.509 7×10-18 1.463 1×10-1 5.072 8×10-3 2.187 9×10-2
F7 IBSA 0 0 0 0
AIBSO 0 1.400 4×10-8 3.545 1×10-10 2.030 6×10-9

表5

文献[9]算法与本研究改进算法的性能对比"

文献[9]中的函数 算法 最优值 最差值 平均值 标准差
F1 IBSA 0 0 0 0
LFSABSA 3.47×10-200 8.44×10-152 8.44×10-153 2.67×10-152
F2 IBSA 0 0 0 0
LFSABSA 1.27×10-176 3.55×10-155 2.97×10-156 0
F3 IBSA 0 0 0 0
LFSABSA 7.92×10-12 1.19×10-7 1.42×10-8 3.72×10-8

表6

文献[10]算法与本研究改进算法的性能对比"

文献[10]中的函数
算法		 最优值 最差值 平均值 标准差
F1 IBSA 0 0 0 0
MMSBSA 2.629 4×10-278 1.867 5×10-214 6.225 0×10-216 4.314 7×10-215
F3 IBSA 3.349 1×10-232 2.146 7×10-190 7.155 6×10-192 0
MMSBSA 1.081 5×10-10 1.523 5×10-5 1.281 9×10-6 3.004 1×10-6
F4 IBSA 1.781 0×10-226 2.521 5×10-191 8.404 9×10-193 0
MMSBSA 3.818 3×10-4 0.133 6 0.013 5 0.034 0
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