Journal of Shandong University(Engineering Science) ›› 2019, Vol. 49 ›› Issue (3): 22-31.doi: 10.6040/j.issn.1672-3961.0.2017.418

• Machine Learning & Data Mining • Previous Articles     Next Articles

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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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

CLC Number: 

  • TP301.6

Table 1

8 Benchmark test functions"

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

Fig.1

Relationship curves of population size and optimization mean"

Table 2

Experimental results of 4 algorithms with lower iterations"

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

Fig.2

Optimization mean fitness evolutionary curves of test functions with lower iterations"

Table 3

Experimental results of 3 algorithms with higher iterations"

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

Fig.3

Optimization mean fitness evolutionary curve of test functions with higher iterations"

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