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山东大学学报 (工学版) ›› 2019, Vol. 49 ›› Issue (3): 22-31.doi: 10.6040/j.issn.1672-3961.0.2017.418

• 机器学习与数据挖掘 • 上一篇    下一篇

一种新的双策略进化果蝇优化算法

方波1,2(),陈红梅1,2,*()   

  1. 1. 西南交通大学信息科学与技术学院, 四川 成都 611756
    2. 云计算与智能技术高校重点实验室(西南交通大学), 四川 成都 611756
  • 收稿日期:2017-08-24 出版日期:2019-06-20 发布日期:2019-06-27
  • 通讯作者: 陈红梅 E-mail:fangbo@my.swjtu.edu.cn;hmchen@swjtu.edu.cn
  • 作者简介:方波(1991-),男,浙江杭州人,硕士研究生,主要研究方向为数据挖掘,机器学习. fangbo@my.swjtu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(61572406)

A novel double strategies evolutionary fruit fly optimization algorithm

Bo FANG1,2(),Hongmei CHEN1,2,*()   

  1. 1. School of Information Science and Technology, Southwest Jiaotong University, Chengdu 611756, Sichuan, China
    2. Key Laboratory of Cloud Computing and Intelligent Technology (Southwest Jiaotong University), Chengdu 611756, Sichuan, China
  • Received:2017-08-24 Online:2019-06-20 Published:2019-06-27
  • Contact: Hongmei CHEN E-mail:fangbo@my.swjtu.edu.cn;hmchen@swjtu.edu.cn
  • Supported by:
    国家自然科学基金资助项目(61572406)

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摘要：

标准果蝇优化算法(fruit fly optimization algorithm, FOA)在迭代寻优的过程中,整个果蝇群体只向最优个体靠近,这导致算法极易陷入局部最优,从而引起早熟收敛的问题。针对该问题,提出一种新的双策略进化果蝇优化算法(a novel double strategies evolutionary fruit fly optimization algorithm, DSEFOA)。提出的一种新的群体分割策略,将果蝇群体动态地划分为精英子群和普通子群;对于精英子群,引入混沌变量引导果蝇个体在其附近搜索食物,优化其局部搜索能力;对于普通子群,引入权重因子改进标准FOA的随机搜索方式,执行全局搜索,加快收敛速度。DSEFOA算法针对不同进化水平的果蝇个体采用不同的策略更新进化,充分地提升了整个群体的寻优搜索能力。8个测试函数的仿真试验结果表明, DSEFOA算法有比标准FOA算法更好的优化性能。

关键词: 果蝇优化算法, 群体分割策略, 混沌变量, 权重因子

Abstract:

The problem of premature convergence caused by trapping into local optimum, which resulted form the fact that all the individuals were only attracted by the best one in the standard fruit fly optimization algorithm (FOA), was common. In order to overcome this demerit, a novel double strategies evolutionary fruit fly optimization algorithm (DSEFOA) was proposed. The whole group was divided into elite subgroup and ordinary subgroup dynamically based on a proposed new group partitioning strategy. Then an improved searching method with chaotic variable was used in the elite subgroup to improve the individual's local searching capability. Meanwhile, an improved standard FOA-based random searching method with weighting factors was used in the ordinary subgroup to enhance its global searching capability, as well accelerated the convergence. The searching capability of both superior and inferior individuals could be effectively improved in DSEFOA by using different strategies on different evolutionary levels of these individuals. The experimental results showed that DSEFOA had better optimization performance than the standard FOA.

Key words: fruit fly optimization algorithm, group partitioning strategy, chaotic variable, weighting factor

中图分类号: 

  • TP301.6

表1

8个基准测试函数"

函数 函数形式 搜索区间 最优值
Sphere ${f_1}(x) = \sum\limits_{i = 1}^n {x_i^2} $ [-100, 100] 0
Schwefels problem 2.22 ${f_2}(x) = \sum\limits_{i = 1}^n {\left| {{x_i}} \right|} + \prod\limits_{i = 1}^n {\left| {{x_i}} \right|} $ [-10, 10] 0
Exponential problem ${f_3}(x) = 1- \exp \left({ - 0.5\sum\limits_{i = 1}^n {x_i^2} } \right)$ [-1, 1] 0
Sum of different power ${f_4}(x) = \sum\limits_{i = 1}^n {{{\left| {{x_i}} \right|}^{i + 1}}} $ [-1, 1] 0
Rastrigin ${f_5}(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 ${f_6}(x) = 1 + \frac{1}{{4000}}\sum\limits_{i = 1}^n {x_i^2} - \prod\limits_{i = 1}^n {\cos } \left({\frac{{{x_i}}}{{\sqrt i }}} \right)$ [-600, 600] 0
Diff griewank ${f_7}(x) = |\sum\limits_{i = 1}^n {{{\left[{\sin \left({{x_i}} \right)} \right]}^2}} - 0.1\prod\limits_{i = 1}^n {\exp } \left({ - x_i^2} \right) + 0.1$ [-10, 10] 0
Ackley $\begin{array}{l}{f_8}(x) = 20 + e - 20\exp \left({ - 0.2\sqrt {\frac{1}{n}\sum\limits_{i = 1}^n {x_i^2} } } \right) - \\\; \; \; \; \; \; \; \; \; \; \; \; \exp \left[{- \frac{1}{n}\sum\limits_{i = 1}^n {\cos } \left({2\pi {x_i}} \right)} \right]\end{array}$ [-32, 32] 0

图1

群体规模与函数优化均值关系曲线"

表2

较低迭代次数下算法试验结果"

函数 维数 算法 最优值 优化均值 标准差
] f1 30 DSEFOA 4.906 4×10-05 7.583 3×10-05 1.576 6×10-05
FOA 1.332 8×10-03 2.001 4×10-03 5.161 1×10-04
CFOA 2.769 6×10-04 3.685 5×10-04 9.093 3×10-05
PSO 0.524 8 2.523 6 1.916 6
f2 30 DSEFOA 1.876 0×10-02 2.128 1×10-02 1.719 0×10-03
FOA 0.176 2 0.218 4 2.496 4×10-02
CFOA 7.514 7×10-02 9.291 0×10-02 1.146 2×10-02
PSO 2.215 0 6.540 9 2.862 9
f3 30 DSEFOA 2.101 7×10-05 4.174 4×10-05 1.229 3×10-05
FOA 5.276 6×10-04 9.409 7×10-04 2.027 9×10-04
CFOA 1.409 1×10-04 2.136 4×10-04 5.749 3×10-05
PSO 2.923 9×10-03 1.309 6×10-02 9.455 6×10-03
f4 30 DSEFOA 6.084 6×10-04 9.523 1×10-04 2.930 3×10-04
FOA 2.595 0×10-03 4.555 1×10-03 1.609 3×10-03
CFOA 1.296 7×10-02 2.215 1×10-02 7.545 1×10-03
PSO 1.463 7×10-06 1.017 3×10-03 1.805 7×10-03
f5 30 DSEFOA 1.121 2×10-02 1.792 3×10-02 4.067 9×10-03
FOA 0.265 7 0.394 1 8.265 5×10-02
CFOA 0.143 1 0.293 3 8.938 3×10-02
PSO 36.601 0 104.530 2 34.715 6
f6 30 DSEFOA 6.140 6×10-10 1.379 0×10-09 3.207 5×10-10
FOA 8.604 7×10-06 1.32 37×10-05 2.982 0×10-06
CFOA 2.936 3×10-09 5.800 9×10-09 2.573 8×10-09
PSO 0.713 4 1.036 9 0.149 5
f7 30 DSEFOA 1.306 3×10-05 2.3402×10-05 5.3770×10-06
FOA 1.092 4×10-03 2.137 4×10-03 6.1559×10-04
CFOA 2.602 8×10-04 4.572 8×10-04 1.0832×10-04
PSO 2.191 5 4.571 0 1.478 0
f8 30 DSEFOA 7.922 2×10-04 1.031 9×10-03 1.530 3×10-04
FOA 2.856 8×10-02 3.627 5×10-02 4.780 2×10-03
CFOA 3.241 4×10-03 4.454 3×10-03 7.805 0×10-04
PSO 4.414 2 6.001 1 1.056 1

图2

较低迭代次数下函数优化均值进化曲线"

表3

较高迭代次数下算法试验结果"

函数 维数 算法 最优值 优化均值 标准差
f1 30 DSEFOA 9.330 2×10-06 1.363 3×10-05 3.008 6×10-06
FOA 2.091 4×10-04 3.501 9×10-04 8.792 5×10-05
CFOA 3.290 5×10-05 5.741 7×10-05 1.366 6×10-05
f2 30 DSEFOA 7.266 0×10-03 8.570 6×10-03 5.729 2×10-04
FOA 7.252 9×10-02 8.982 6×10-02 1.023 5×10-02
CFOA 3.004 6×10-02 3.992 1×10-02 4.257 0×10-03
f3 30 DSEFOA 4.794 0×10-06 6.722 9×10-06 1.307 9×10-06
FOA 9.663 5×10-05 1.583 8×10-04 4.095 6×10-05
CFOA 2.058 8×10-05 3.228 9×10-05 8.965 8×10-06
f4 30 DSEFOA 1.812 1×10-04 3.712 5×10-04 1.364 7×10-04
FOA 9.584 0×10-04 1.875 9×10-03 5.559 2×10-04
CFOA 5.035 8×10-03 8.204 6×10-03 3.094 1×10-03
f5 30 DSEFOA 1.724 8×10-03 2.801 3×10-03 5.114 3×10-04
FOA 4.317 4×10-02 6.579 5×10-02 1.197 3×10-02
CFOA 2.700 4×10-02 4.679 4×10-02 1.574 7×10-02
f6 30 DSEFOA 1.304 7×10-10 2.330 6×10-10 9.277 2×10-11
FOA 5.150 0×10-06 9.087 3×10-06 1.991 0×10-06
CFOA 5.904 7×10-10 8.880 0×10-10 2.358 6×10-10
f7 30 DSEFOA 2.564 2×10-06 3.969 3×10-06 1.161 8×10-06
FOA 1.994 6×10-04 3.592 8×10-04 9.645 4×10-05
CFOA 4.327 5×10-05 7.419 0×10-05 1.858 5×10-05
f8 30 DSEFOA 3.382 7×10-04 4.384 4×10-04 6.702 1×10-05
FOA 1.061 5×10-02 1.365 9×10-02 1.635 3×10-03
CFOA 1.270 0×10-03 1.838 4×10-03 2.723 4×10-04

图3

较高迭代次数下函数优化均值进化曲线"

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