
Artificial Bee Colony Algorithm Based on Multiple Information Guidance
ZHOU Xin-yu, LIU Ying, WU Yan-lin, GUO Jing-lei
ACTA ELECTRONICA SINICA ›› 2024, Vol. 52 ›› Issue (4) : 1349-1363.
Artificial Bee Colony Algorithm Based on Multiple Information Guidance
As one of the main ideas to improve the artificial bee colony (ABC) algorithm, the superior individuals are used to enhance the exploitative capability of the solution search equation. However, in the related works, the fitness information is often considered as the sole criterion for evaluating the individuals, which may easily cause some problems, e.g., the premature convergence. In this work, an improved ABC variant is proposed based on multiple information guidance, called ABC-MIG. In ABC-MIG, three different solution search equations are designed by using the fitness, position, and similarity information, respectively, and these new solution search equations are used in different ways for the employed bee phase and onlooker bee phase. Meanwhile, to save the search experience for the scout bee phase, a modified neighborhood search strategy is used to handle the abandoned food sources. To verify the effectiveness of ABC-MIG, extensive experiments are carried out on the CEC2013 test suite and one real-world optimization problem, and six derivative algorithms and five well-known improved ABC variants are included in the performance comparison. The results confirm that ABC-MIG has very competitive performance, in terms of the result accuracy and convergence speed.
artificial bee colony algorithm / superior individuals / multiple information / solution search equation / neighborhood search {{custom_keyword}} /
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输入:参数SN、limit、MaxFEs 输出:全局最优个体Gbest 1. 按 2. while (FEs≤MaxFEs) do 3. for 4. 按 5. 若 6. 否则,令trial i ++. 7. FEs++. 8. end for 9. for 10. 按 11. if 12. 按贪婪方式为 13. 若 14. 否则,令trial i ++. 15. FEs++. 16. end if 17. end for 18. for 19. if trial i >limit do 20. 按 21. 令trial i =0, FEs++. 22. end if 23. end for 24. end while |
表1 ABC⁃MIG采用不同limit取值的对比结果 |
函数 | 50 | 100 | 200 | |
---|---|---|---|---|
F01 | 2.27×10-13 | 0.00 | 0.00 | 0.00 |
F02 | 6.28×106 | 6.08×106 | 6.03×106 | 6.77×106 |
F03 | 5.76×107 | 3.50×107 | 4.16×107 | 4.54×107 |
F04 | 3.88×104 | 3.82×104 | 3.83×104 | 3.91×104 |
F05 | 8.38×10-13 | 2.08×10-13 | 1.10×10 - 13 | 1.14×10-13 |
F06 | 2.90×10 | 2.70×10 | 2.46×10 | 2.54×10 |
F07 | 6.31×10 | 5.32×10 | 5.29×10 | 5.24×10 |
F08 | 2.10×10 | 2.10×10 | 2.09×10 | 2.09×10 |
F09 | 2.56×10 | 2.52×10 | 2.54×10 | 2.53×10 |
F10 | 9.78×10-1 | 1.11 | 8.08×10 - 1 | 8.23×10-1 |
F11 | 5.50×10-14 | 0.00 | 0.00 | 0.00 |
F12 | 1.38×102 | 1.16×102 | 8.64×10 | 9.76×10 |
F13 | 2.00×102 | 1.66×102 | 1.48×102 | 1.48×102 |
F14 | 1.01×10 | 1.03×10 | 2.80 | 4.19 |
F15 | 2.93×103 | 2.97×103 | 3.17×103 | 3.31×103 |
F16 | 9.76×10 - 1 | 1.02 | 9.98×10-1 | 1.09 |
F17 | 3.06×10 | 3.05×10 | 3.04×10 | 3.04×10 |
F18 | 3.00×10 | 3.00×10 | 3.00×10 | 3.00×10 |
F19 | 6.31×10-1 | 4.39×10-1 | 3.56×10 - 1 | 4.42×10-1 |
F20 | 1.03×10 | 1.02×10 | 9.91 | 9.98 |
F21 | 3.27×102 | 3.00×102 | 3.20×102 | 3.03×102 |
F22 | 1.11×102 | 1.15×102 | 1.04×102 | 1.10×102 |
F23 | 4.42×103 | 4.30×103 | 4.24×103 | 4.09×103 |
F24 | 2.36×102 | 2.33×102 | 2.32×102 | 2.34×102 |
F25 | 2.58×102 | 2.71×102 | 2.80×102 | 2.78×102 |
F26 | 2.00×102 | 2.00×102 | 2.00×102 | 2.00×102 |
F27 | 8.16×102 | 7.05×102 | 5.24×102 | 6.02×102 |
F28 | 2.93×102 | 2.80×102 | 2.93×102 | 2.93×102 |
Fried. | 3.34 | 2.48 | 1.80 | 2.38 |
表2 算法有效性验证的实验结果 |
函数 | ABC-1 | ABC-2 | ABC-3 | ABC-4 | ABC-MIG |
---|---|---|---|---|---|
F01 | 1.06×10-13 | 2.12×10-13 | 2.27×10-13 | 0.00 | 0.00 |
F02 | 9.67×106 | 6.42×106 | 7.46×106 | 6.26×106 | 6.03×106 |
F03 | 1.93×108 | 6.00×107 | 7.11×107 | 6.57×107 | 4.16×107 |
F04 | 8.30×104 | 4.41×104 | 4.17×104 | 3.41×104 | 3.83×104 |
F05 | 1.78×10-13 | 4.55×10-13 | 6.33×10-13 | 1.10×10 - 13 | 1.10×10-13 |
F06 | 2.46×10 | 2.30×10 | 2.83×10 | 2.06×10 | 2.46×10 |
F07 | 9.20×10 | 5.90×10 | 5.80×10 | 5.17×10 | 5.29×10 |
F08 | 2.09×10 | 2.09×10 | 2.09×10 | 2.10×10 | 2.09×10 |
F09 | 2.92×10 | 2.40×10 | 2.50×10 | 2.64×10 | 2.54×10 |
F10 | 2.53×10 - 1 | 8.44×10-1 | 9.10×10-1 | 9.05×10-1 | 8.08×10-1 |
F11 | 1.89×10-15 | 5.31×10-14 | 5.50×10-14 | 0.00 | 0.00 |
F12 | 1.14×102 | 1.32×102 | 1.12×102 | 8.98×10 | 8.64×10 |
F13 | 1.64×102 | 1.94×102 | 1.61×102 | 1.39×102 | 1.48×102 |
F14 | 1.50 | 3.28 | 4.27 | 5.20 | 2.80 |
F15 | 3.69×103 | 3.48×103 | 3.58×103 | 3.38×103 | 3.17×103 |
F16 | 1.36 | 1.28 | 1.25 | 1.11 | 9.98×10-1 |
F17 | 3.05×10 | 3.05×10 | 3.05×10 | 3.05×10 | 3.04×10 |
F18 | 3.00×10 | 3.00×10 | 3.00×10 | 3.00×10 | 3.00×10 |
F19 | 4.74×10-1 | 5.00×10-1 | 5.05×10-1 | 5.14×10-1 | 3.56×10 - 1 |
F20 | 1.16×10 | 1.04×10 | 1.03×10 | 9.84 | 9.91 |
F21 | 2.99×102 | 3.07×102 | 3.17×102 | 3.12×102 | 3.20×102 |
F22 | 8.21×10 | 9.21×10 | 9.69×10 | 1.23×102 | 1.04×102 |
F23 | 4.62×103 | 4.63×103 | 4.38×103 | 4.29×103 | 4.24×103 |
F24 | 2.76×102 | 2.38×102 | 2.37×102 | 2.31×102 | 2.32×102 |
F25 | 3.05×102 | 2.77×102 | 2.92×102 | 2.63×102 | 2.80×102 |
F26 | 2.00×102 | 2.00×102 | 2.00×102 | 2.00×102 | 2.00×102 |
F27 | 5.84×102 | 6.46×102 | 4.93×102 | 5.88×102 | 5.24×102 |
F28 | 3.00×102 | 3.36×102 | 3.43×102 | 3.00×102 | 2.93×102 |
| 3/7/18 | 1/12/15 | 0/13/15 | 1/23/4 | — |
Friedman | 3.50 | 3.36 | 3.57 | 2.55 | 2.02 |
表3 随机选择对比自适应选择的实验结果 |
函数 | ABC | ABC-5 | ABC-6 | ABC-MIG |
---|---|---|---|---|
F01 | 5.15×10-13 | 0.00 | 0.00 | 0.00 |
F02 | 8.01×106 | 5.59×106 | 5.42×106 | 6.03×106 |
F03 | 3.88×108 | 3.19×107 | 4.83×107 | 4.16×107 |
F04 | 7.08×104 | 3.82×104 | 3.96×104 | 3.83×104 |
F05 | 7.54×10-13 | 2.24×10-13 | 2.16×10-13 | 1.10×10-13 |
F06 | 1.31×10 | 2.23×10 | 2.22×10 | 2.46×10 |
F07 | 1.01×102 | 5.50×10 | 5.69×10 | 5.29×10 |
F08 | 2.09×10 | 2.10×10 | 2.10×10 | 2.09×10 |
F09 | 2.90×10 | 2.44×10 | 2.55×10 | 2.54×10 |
F10 | 1.71 | 1.17 | 1.13 | 8.08×10-1 |
F11 | 8.91×10-14 | 0.00 | 0.00 | 0.00 |
F12 | 2.45×102 | 1.13×102 | 1.11×102 | 8.64×10 |
F13 | 3.00×102 | 1.72×102 | 1.66×102 | 1.48×102 |
F14 | 1.95 | 7.88 | 6.48 | 2.80 |
F15 | 3.56×103 | 3.01×103 | 3.07×103 | 3.17×103 |
F16 | 1.39 | 1.06 | 1.04 | 9.98×10-1 |
F17 | 3.06×10 | 3.05×10 | 3.05×10 | 3.04×10 |
F18 | 3.00×10 | 3.00×10 | 3.00×10 | 3.00×10 |
F19 | 4.18×10-1 | 4.95×10-1 | 5.08×10-1 | 3.56×10 - 1 |
F20 | 1.18×10 | 1.02×10 | 1.01×10 | 9.91 |
F21 | 1.77×102 | 3.23×102 | 3.10×102 | 3.2×102 |
F22 | 2.95×10 | 1.18×102 | 8.83×10 | 1.04×102 |
F23 | 4.67×103 | 4.28×103 | 4.30×103 | 4.24×103 |
F24 | 2.85×102 | 2.33×102 | 2.32×102 | 2.32×102 |
F25 | 3.12×102 | 2.71×102 | 2.73×102 | 2.80E+02 |
F26 | 2.01×102 | 2.00×102 | 2.00×102 | 2.00×102 |
F27 | 4.00×102 | 6.20×102 | 7.10×102 | 5.24×102 |
F28 | 2.21×102 | 3.00×102 | 2.93×102 | 2.93×102 |
| 3/5/20 | 0/19/9 | 0/19/9 | — |
Fried. | 3.14 | 2.55 | 2.41 | 1.89 |
表4 与相关改进ABC的对比结果( |
函数 | GABC | ECABC | ABCVSS | LLABC | NABC | ABC-MIG |
---|---|---|---|---|---|---|
F01 | 3.33×10-13 | 1.06×10-13 | 2.35×10-13 | 5.15×10-13 | 4.62×10-13 | 0.00 |
F02 | 9.41×106 | 9.67×106 | 1.04×107 | 8.07×106 | 7.99×106 | 6.03×106 |
F03 | 2.47×108 | 1.93×108 | 3.85×108 | 2.82×108 | 1.00×108 | 4.16×107 |
F04 | 6.40×104 | 8.30×104 | 8.50×104 | 7.14×104 | 4.62×104 | 3.83×104 |
F05 | 5.31×10-13 | 1.78×10-13 | 4.21×10-13 | 6.59×10-13 | 7.16×10-13 | 1.10×10-13 |
F06 | 1.54×10 | 2.46×10 | 1.65×10 | 1.46×10 | 1.98×10 | 2.46×10 |
F07 | 8.41×10 | 9.20×10 | 9.91×10 | 1.04×102 | 6.32×10 | 5.29×10 |
F08 | 2.09×10 | 2.09×10 | 2.09×10 | 2.09×10 | 2.10×10 | 2.09×10 |
F09 | 2.82×10 | 2.92×10 | 2.96×10 | 2.96×10 | 2.75×10 | 2.54×10 |
F10 | 1.53 | 2.53×10-1 | 2.51 | 1.42 | 1.01 | 8.08×10-1 |
F11 | 6.06×10-14 | 1.89×10-15 | 5.68×10-14 | 5.87×10-14 | 9.66×10-14 | 0.00 |
F12 | 1.36×102 | 1.14×102 | 1.51×102 | 2.38×102 | 1.52×102 | 8.64×10 |
F13 | 2.03×102 | 1.64×102 | 2.26×102 | 2.96×102 | 1.87×102 | 1.48×102 |
F14 | 3.69×10-1 | 1.50 | 2.08×10-2 | 2.10 | 1.08 | 2.80 |
F15 | 3.95×103 | 3.69×103 | 3.79×103 | 3.64×103 | 3.09×103 | 3.17×103 |
F16 | 1.72 | 1.36 | 1.26 | 1.37 | 1.04 | 9.98×10-1 |
F17 | 2.96×10 | 3.05×10 | 2.98×10 | 3.01×10 | 3.05×10 | 3.04×10 |
F18 | 3.00×10 | 3.00×10 | 2.95×10 | 2.94×10 | 3.00×10 | 3.00×10 |
F19 | 5.12×10--1 | 4.74×10-1 | 3.61×10-1 | 3.39×10-1 | 4.14×10-1 | 3.56×10-1 |
F20 | 1.16×10 | 1.16×10 | 1.18×10 | 1.19×10 | 1.02×10 | 9.91 |
F21 | 2.07×102 | 2.99×102 | 2.04×102 | 1.75×102 | 3.17×102 | 3.20×102 |
F22 | 9.15×10 | 8.21×10 | 1.52×10 | 5.92×10 | 1.08×102 | 1.04×102 |
F23 | 4.92×103 | 4.62×103 | 4.74×103 | 4.72×103 | 4.82×103 | 4.24×103 |
F24 | 2.77×102 | 2.76×102 | 2.83×102 | 2.82×102 | 2.38×102 | 2.32×102 |
F25 | 3.02×102 | 3.05×102 | 3.02×102 | 3.08×102 | 2.81×102 | 2.80×102 |
F26 | 2.01×102 | 2.00×102 | 2.01×102 | 2.01×102 | 2.00×102 | 2.00×102 |
F27 | 4.22×102 | 5.84×102 | 4.64×102 | 4.00×102 | 5.92×102 | 5.24×102 |
F28 | 2.62×102 | 3.00×102 | 2.46×102 | 2.01×102 | 3.00×102 | 2.93×102 |
| 4/5/19 | 3/7/18 | 7/3/18 | 4/6/18 | 2/10/16 | — |
Friedman | 3.80 | 3.59 | 3.79 | 3.80 | 3.70 | 2.32 |
表5 与相关改进ABC的对比结果( |
函数 | GABC | ECABC | ABCVSS | LLABC | NABC | ABC-MIG |
---|---|---|---|---|---|---|
F01 | 7.96×10-13 | 2.43×10-13 | 6.21×10-13 | 1.08×10-12 | 1.09×10-12 | 1.74×10 - 13 |
F02 | 1.39×107 | 1.58×107 | 1.85×107 | 1.25×107 | 8.05×106 | 7.39×106 |
F03 | 1.37×109 | 1.51×109 | 1.84×109 | 1.46×109 | 2.41×108 | 1.52×108 |
F04 | 1.28×105 | 1.50×105 | 1.57×105 | 1.37×105 | 6.92×104 | 6.33×104 |
F05 | 1.14×10-12 | 3.60×10-13 | 9.28×10-13 | 1.32×10-12 | 1.63×10-12 | 2.92×10-13 |
F06 | 4.30×10 | 4.61×10 | 4.32×10 | 4.26×10 | 4.57×10 | 4.51×10 |
F07 | 1.27×102 | 1.26×102 | 1.40×102 | 1.47×102 | 8.58×10 | 8.20×10 |
F08 | 2.11×10 | 2.11×10 | 2.11×10 | 2.11×10 | 2.11×10 | 2.11×10 |
F09 | 5.68×10 | 5.79×10 | 5.89×10 | 5.84×10 | 5.44×10 | 5.23×10 |
F10 | 2.03 | 7.08×10-1 | 3.16 | 1.67 | 1.64 | 1.43 |
F11 | 1.74×10-13 | 5.50×10-14 | 1.46×10-13 | 1.33×10-13 | 2.86×10-13 | 2.65×10-14 |
F12 | 4.44×102 | 3.49×102 | 4.39×102 | 6.19×102 | 3.07×102 | 2.56×102 |
F13 | 5.37×102 | 4.64×102 | 5.87×102 | 7.05×102 | 4.37×102 | 3.77×102 |
F14 | 3.19 | 2.48 | 3.17×10-2 | 5.89 | 4.45 | 8.88 |
F15 | 8.27×103 | 7.75×103 | 7.68×103 | 7.81×103 | 7.21×103 | 7.11×103 |
F16 | 2.38 | 1.66 | 1.61 | 1.83 | 1.41 | 1.35 |
F17 | 5.08×10 | 5.08×10 | 5.08×10 | 5.09×10 | 5.09×10 | 5.08×10 |
F18 | 5.02×10 | 5.02×10 | 5.02×10 | 4.94×10 | 5.02×10 | 5.02×10 |
F19 | 1.16 | 7.99×10-1 | 7.61×10-1 | 8.75×10-1 | 9.86×10-1 | 7.08×10-1 |
F20 | 2.08×10 | 2.07×10 | 2.11×10 | 2.10×10 | 1.86×10 | 1.84×10 |
F21 | 2.79×102 | 3.06×102 | 2.37×102 | 2.42×102 | 3.00×102 | 3.20×102 |
F22 | 3.98×10 | 3.84×10 | 9.47 | 2.33×10 | 1.28×10 | 6.10×10 |
F23 | 9.81×103 | 9.65×103 | 9.91×103 | 9.65×103 | 1.02×104 | 9.10×103 |
F24 | 3.59×102 | 3.58×102 | 3.59×102 | 3.64×102 | 3.10×102 | 3.07×102 |
F25 | 4.05×102 | 4.14×102 | 4.10×102 | 4.17×102 | 4.16×102 | 4.08×102 |
F26 | 2.02×102 | 2.02×102 | 2.02×102 | 2.02×102 | 2.01×102 | 2.01×102 |
F27 | 9.47×102 | 1.54×103 | 1.26×103 | 7.09×102 | 1.51×103 | 1.33×103 |
F28 | 4.00×102 | 4.00×102 | 4.00×102 | 4.00×102 | 4.00×102 | 4.00×102 |
| 4/5/19 | 2/7/19 | 5/6/17 | 4/4/20 | 2/12/14 | — |
Friedman | 3.88 | 3.55 | 3.84 | 4.09 | 3.46 | 2.18 |
表6 与相关改进ABC的CPU运行时间对比结果 (时间:s) |
函数 | GABC | ECABC | ABCVSS | LLABC | NABC | ABC-MIG |
---|---|---|---|---|---|---|
F01 | 0.81 | 0.59 | 0.86 | 0.83 | 0.90 | 2.26 |
F02 | 0.77 | 0.87 | 0.77 | 0.77 | 0.81 | 2.66 |
F03 | 1.17 | 1.06 | 1.18 | 1.20 | 1.23 | 2.96 |
F04 | 0.52 | 0.48 | 0.51 | 0.54 | 0.55 | 2.24 |
F05 | 0.35 | 0.34 | 0.36 | 0.38 | 0.39 | 1.93 |
F06 | 0.47 | 0.44 | 0.46 | 0.48 | 0.49 | 2.23 |
F07 | 1.94 | 1.84 | 1.93 | 1.97 | 2.05 | 3.69 |
F08 | 1.57 | 1.50 | 1.58 | 1.61 | 1.67 | 3.32 |
F09 | 25.31 | 24.92 | 25.42 | 25.79 | 25.57 | 26.78 |
F10 | 0.87 | 0.83 | 0.87 | 0.88 | 0.89 | 2.66 |
F11 | 0.77 | 0.72 | 0.77 | 0.78 | 0.79 | 2.36 |
F12 | 1.55 | 1.49 | 1.59 | 1.61 | 1.57 | 3.29 |
F13 | 1.69 | 1.58 | 1.72 | 1.76 | 1.71 | 3.38 |
F14 | 0.91 | 0.96 | 0.85 | 1.00 | 1.01 | 2.83 |
F15 | 1.29 | 1.24 | 1.39 | 1.31 | 1.25 | 3.03 |
F16 | 7.66 | 7.58 | 8.20 | 7.98 | 7.66 | 9.29 |
F17 | 0.58 | 0.54 | 0.60 | 0.62 | 0.59 | 2.26 |
F18 | 1.22 | 1.14 | 1.26 | 1.27 | 1.23 | 2.90 |
F19 | 0.58 | 0.56 | 0.62 | 0.61 | 0.60 | 2.40 |
F20 | 1.19 | 1.16 | 1.21 | 1.28 | 1.19 | 2.89 |
F21 | 3.48 | 3.27 | 3.53 | 3.80 | 3.50 | 5.01 |
F22 | 3.25 | 3.16 | 3.36 | 3.89 | 3.25 | 4.96 |
F23 | 4.08 | 4.06 | 4.49 | 4.64 | 4.05 | 5.77 |
F24 | 29.21 | 29.45 | 30.44 | 31.20 | 29.22 | 30.69 |
F25 | 28.83 | 28.74 | 30.48 | 31.11 | 29.20 | 30.59 |
F26 | 32.21 | 32.04 | 33.14 | 33.25 | 32.95 | 33.83 |
F27 | 31.96 | 31.66 | 32.44 | 32.51 | 32.13 | 33.19 |
F28 | 7.97 | 7.70 | 8.00 | 8.13 | 7.99 | 9.23 |
平均时间 | 6.86 | 6.78 | 7.07 | 7.18 | 6.94 | 8.52 |
排名 | 2 | 1 | 4 | 5 | 3 | 6 |
表7 求解实际优化问题的实验结果 |
算法 | D=19 | D=20 |
---|---|---|
GABC | 1.01E+00 | 1.00E+00 |
ECABC | 1.08E+00 | 1.05E+00 |
ABCVSS | 1.02E+00 | 1.01E+00 |
LLABC | 9.45E-01 | 9.49E-01 |
NABC | 9.23E-01 | 9.73E-01 |
ABC-MIG | 8.93E-01 | 9.05E-01 |
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陈健瑞, 王景璟, 侯向往, 等. 挺进深蓝: 从单体仿生到群体智能[J]. 电子学报, 2021, 49(12): 2458-2467.
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