计算机科学与探索 ›› 2022, Vol. 16 ›› Issue (5): 1169-1181.DOI: 10.3778/j.issn.1673-9418.2108067
收稿日期:
2021-07-08
修回日期:
2021-09-03
出版日期:
2022-05-01
发布日期:
2022-05-19
通讯作者:
+ E-mail: llqhjy@126.com作者简介:
刘立群(1982—),女,甘肃天水人,硕士,副教授,硕士生导师,主要研究方向为智能计算、图像处理等。基金资助:
Received:
2021-07-08
Revised:
2021-09-03
Online:
2022-05-01
Published:
2022-05-19
About author:
LIU Liqun, born in 1982, M.S., associate profe-ssor, M.S. supervisor. Her research interests in-clude intelligent computing, image processing, etc.Supported by:
摘要:
针对混合蛙跳算法(SFLA)青蛙个体当前位置提供的惯性以及跳跃步长引起的进化速度慢,易陷入局部收敛的缺陷,将青蛙个体跳跃进化行为定义为量子力学行为,提出一种核中心驱动混合蛙跳算法(NCSFLA)。在全局寻优中,以原子核为中心的同心圆作为电子轨道构成青蛙族群;在局部寻优中,分别以跃迁步长为半径向局部最优个体跳跃,以驱动步长为半径向全局最优个体跳跃,随机产生不重复的青蛙个体分量等三种不同的局部搜索策略对族群内最差个体进行更新。以电子轨道中心即局部最优个体为跃迁的惯性指导,使得族群内的收敛更加有利于寻找局部最优解,提升搜索能力;如果陷入局部最优,则以原子核中心即全局最优个体为驱动的惯性指导,使得青蛙个体尽可能聚集在原子核中心周围,从而加快收敛速度。将该算法应用于解决容量限制车辆路径问题(CVRP),提出一种核中心驱动混合蛙跳算法的容量限制车辆路径优化算法(NCSFLA-CVRP)。实验结果显示,在单峰值、多峰值函数以及复合函数等20个测试函数上,改进后的核中心驱动混合蛙跳算法相比其他五种算法具有收敛速度快、精度高的特点。Solomon算例标准测试数据测试结果表明该方法可有效提高容量限制车辆路径的优化性能。
中图分类号:
刘立群, 顾任远. 核中心驱动混合蛙跳算法及其应用[J]. 计算机科学与探索, 2022, 16(5): 1169-1181.
LIU Liqun, GU Renyuan. Shuffled Frog Leaping Algorithm Driven by Nuclear Center and Its Application[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(5): 1169-1181.
测试函数 | 公式 | 维数D | 范围 | | 峰值 |
---|---|---|---|---|---|
Sphere[ | | 30 | | 0 | 单峰 |
Griewank[ | | 30 | | 0 | 多峰 |
Bent Cigar[ | | 30 | | 0 | 单峰 |
Sumpower[ | | 30 | | 0 | 单峰 |
Zakharov[ | | 30 | | 0 | 单峰 |
Discus[ | | 30 | | 0 | 单峰 |
Weierstrass[ | | 30 | | 0 | 多峰 |
Katsuura[ | | 30 | | 0 | 多峰 |
HappyCat[ | | 30 | | | 多峰 |
HGBat[ | | 30 | | | 多峰 |
Schwefel222[ | | 30 | | 0 | 单峰 |
aa[ | | 30 | | 0 | 单峰 |
Schwefel221[ | | 30 | | 0 | 单峰 |
Step[ | | 30 | | 0 | 单峰 |
dd[ | | 30 | | 0 | 多峰 |
ee[ | | 30 | | 0 | 多峰 |
Rosenbrock[ | | 30 | | 0 | 多峰 |
Schwefel2_26[ | | 30 | | 0 | 多峰 |
cf01[ | | 30 | | | 复合 |
cf02[ | | 30 | | | 复合 |
表1 测试函数
Table 1 Benchmark functions
测试函数 | 公式 | 维数D | 范围 | | 峰值 |
---|---|---|---|---|---|
Sphere[ | | 30 | | 0 | 单峰 |
Griewank[ | | 30 | | 0 | 多峰 |
Bent Cigar[ | | 30 | | 0 | 单峰 |
Sumpower[ | | 30 | | 0 | 单峰 |
Zakharov[ | | 30 | | 0 | 单峰 |
Discus[ | | 30 | | 0 | 单峰 |
Weierstrass[ | | 30 | | 0 | 多峰 |
Katsuura[ | | 30 | | 0 | 多峰 |
HappyCat[ | | 30 | | | 多峰 |
HGBat[ | | 30 | | | 多峰 |
Schwefel222[ | | 30 | | 0 | 单峰 |
aa[ | | 30 | | 0 | 单峰 |
Schwefel221[ | | 30 | | 0 | 单峰 |
Step[ | | 30 | | 0 | 单峰 |
dd[ | | 30 | | 0 | 多峰 |
ee[ | | 30 | | 0 | 多峰 |
Rosenbrock[ | | 30 | | 0 | 多峰 |
Schwefel2_26[ | | 30 | | 0 | 多峰 |
cf01[ | | 30 | | | 复合 |
cf02[ | | 30 | | | 复合 |
函数 | 算法 | 平均最优值 | 标准差 | 最大值 | 最小值 | 运行时间/s | 函数 | 算法 | 平均最优值 | 标准差 | 最大值 | 最小值 | 运行时间/s |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| NCSFLA | 1.34E+03 | 5.34E+03 | 4.68E+04 | 6.25E-05 | 1.51E-01 | | NCSFLA | 4.91E+00 | 1.47E+01 | 1.18E+02 | 8.66E-05 | 1.98E-01 |
MSFLA | 1.34E+04 | 1.65E+04 | 4.68E+04 | 4.53E+02 | 1.85E-01 | MSFLA | 1.21E+01 | 1.55E+01 | 1.18E+02 | 1.98E+00 | 2.20E-01 | ||
GSF2LA | 6.37E+03 | 1.42E+04 | 4.68E+04 | 1.64E+01 | 1.76E-01 | GSF2LA | 4.57E+00 | 1.49E+01 | 1.18E+02 | 8.48E-01 | 1.78E-01 | ||
SFLA | 6.37E+03 | 1.41E+04 | 4.68E+04 | 4.24E+01 | 1.70E-01 | SFLA | 5.29E+00 | 1.29E+01 | 1.18E+02 | 1.56E+00 | 1.78E-01 | ||
HSA | 4.64E+04 | 3.01E+02 | 4.68E+04 | 4.54E+04 | 1.09E-01 | HSA | 1.07E+02 | 4.51E+00 | 1.18E+02 | 1.05E+02 | 1.17E-01 | ||
ABCA | 1.66E+04 | 2.01E+04 | 7.31E+04 | 1.45E+01 | 1.84E+00 | ABCA | 3.53E+08 | 3.92E+09 | 5.45E+10 | 6.03E-01 | 1.62E+00 | ||
| NCSFLA | 1.26E+01 | 4.82E+01 | 4.22E+02 | 2.97E-02 | 4.30E-01 | | NCSFLA | 2.19E+03 | 8.82E+03 | 8.35E+04 | 6.18E+00 | 3.05E-01 |
MSFLA | 4.14E+02 | 1.92E+01 | 4.22E+02 | 3.45E+02 | 2.71E-01 | MSFLA | 6.00E+04 | 1.95E+04 | 8.35E+04 | 3.33E+04 | 2.41E-01 | ||
GSF2LA | 3.20E+02 | 1.15E+02 | 4.22E+02 | 9.77E+01 | 2.47E-01 | GSF2LA | 2.79E+04 | 3.49E+04 | 8.35E+04 | 2.29E+02 | 2.15E-01 | ||
SFLA | 3.21E+02 | 1.15E+02 | 4.22E+02 | 9.81E+01 | 2.50E-01 | SFLA | 2.62E+04 | 3.45E+04 | 8.35E+04 | 2.63E+02 | 2.18E-01 | ||
HSA | 4.19E+02 | 1.98E+00 | 4.22E+02 | 4.18E+02 | 1.89E-01 | HSA | 8.35E+04 | 0.00E+00 | 8.35E+04 | 8.35E+04 | 7.60E-02 | ||
ABCA | 1.45E+02 | 1.88E+02 | 5.87E+02 | 1.44E+00 | 2.20E+00 | ABCA | 3.62E+04 | 1.51E+04 | 9.13E+04 | 2.52E+04 | 1.87E+00 | ||
| NCSFLA | 1.30E+07 | 5.75E+07 | 4.59E+08 | 2.12E-01 | 2.97E-01 | | NCSFLA | 5.38E-01 | 5.92E+00 | 8.20E+01 | 0.00E+00 | 2.28E-01 |
MSFLA | 1.83E+07 | 6.47E+07 | 4.59E+08 | 1.86E+05 | 2.76E-01 | MSFLA | 5.89E+01 | 6.94E+00 | 8.20E+01 | 5.40E+01 | 2.58E-01 | ||
GSF2LA | 8.61E+06 | 5.46E+07 | 4.59E+08 | 4.02E+04 | 2.10E-01 | GSF2LA | 8.07E+01 | 3.64E-01 | 8.20E+01 | 8.05E+01 | 1.85E-01 | ||
SFLA | 7.45E+06 | 4.87E+07 | 4.59E+08 | 1.20E+05 | 1.98E-01 | SFLA | 7.81E+01 | 3.70E+00 | 8.20E+01 | 7.20E+01 | 1.84E-01 | ||
HSA | 4.35E+08 | 1.53E+07 | 4.59E+08 | 4.25E+08 | 1.89E-01 | HSA | 8.20E+01 | 0.00E+00 | 8.20E+01 | 8.20E+01 | 1.50E-01 | ||
ABCA | 1.30E+08 | 2.10E+08 | 8.07E+08 | 4.88E+04 | 1.96E+00 | ABCA | 7.42E+01 | 9.04E+00 | 9.33E+01 | 6.07E+01 | 1.95E+00 | ||
| NCSFLA | 4.58E+43 | 6.45E+44 | 9.15E+45 | 5.20E+01 | 4.35E-01 | | NCSFLA | 1.28E+03 | 5.29E+03 | 4.67E+04 | 6.79E-06 | 2.02E-01 |
MSFLA | 1.04E+45 | 2.87E+45 | 9.15E+45 | 1.18E+18 | 2.87E-01 | MSFLA | 1.37E+04 | 1.63E+04 | 4.67E+04 | 6.04E+02 | 2.07E-01 | ||
GSF2LA | 9.69E+44 | 2.80E+45 | 9.15E+45 | 1.00E+00 | 2.24E-01 | GSF2LA | 6.36E+03 | 1.41E+04 | 4.67E+04 | 4.06E+01 | 1.75E-01 | ||
SFLA | 9.81E+44 | 2.81E+45 | 9.15E+45 | 1.30E+01 | 2.22E-01 | SFLA | 6.37E+03 | 1.41E+04 | 4.67E+04 | 3.73E+01 | 1.80E-01 | ||
HSA | 7.52E+45 | 1.49E+45 | 9.15E+45 | 6.16E+45 | 1.90E-01 | HSA | 4.67E+04 | 0.00E+00 | 4.67E+04 | 4.67E+04 | 1.46E-01 | ||
ABCA | 1.32E+48 | 4.79E+48 | 2.50E+49 | 4.98E+06 | 1.25E+00 | ABCA | 1.18E+04 | 1.94E+04 | 7.32E+04 | 9.36E-01 | 1.48E+00 | ||
| NCSFLA | 2.84E+04 | 3.99E+05 | 5.65E+06 | 4.16E-01 | 4.25E-01 | | NCSFLA | 5.07E+06 | 3.19E+07 | 3.19E+08 | -9.21E-01 | 5.57E-01 |
MSFLA | 1.72E+05 | 9.64E+05 | 5.65E+06 | 1.91E+02 | 4.11E-01 | MSFLA | 2.03E+07 | 7.02E+07 | 3.19E+08 | 2.31E-01 | 4.07E-01 | ||
GSF2LA | 2.16E+05 | 1.07E+06 | 5.65E+06 | 1.59E+01 | 3.30E-01 | GSF2LA | 1.31E+07 | 5.77E+07 | 3.19E+08 | -1.00E+00 | 2.47E-01 | ||
SFLA | 2.05E+05 | 1.02E+06 | 5.65E+06 | 1.10E+01 | 3.45E-01 | SFLA | 1.27E+07 | 5.68E+07 | 3.19E+08 | -9.92E-01 | 2.48E-01 | ||
HSA | 1.33E+06 | 2.40E+06 | 5.65E+06 | 5.80E+02 | 1.48E-01 | HSA | 3.19E+08 | 5.36E-07 | 3.19E+08 | 3.19E+08 | 1.97E-01 | ||
ABCA | 2.58E+07 | 1.89E+08 | 2.08E+09 | 2.79E+02 | 1.26E+00 | ABCA | 3.58E+07 | 7.76E+07 | 4.59E+08 | -9.07E-01 | 1.21E+00 | ||
| NCSFLA | 3.60E+01 | 1.33E+02 | 7.63E+02 | 4.61E-07 | 1.65E-01 | | NCSFLA | 1.23E+07 | 6.72E+07 | 6.09E+08 | 2.10E-05 | 6.63E-01 |
MSFLA | 9.07E+01 | 1.56E+02 | 7.63E+02 | 6.67E+00 | 1.76E-01 | MSFLA | 4.54E+07 | 1.44E+08 | 6.09E+08 | 2.19E+01 | 4.24E-01 | ||
GSF2LA | 1.85E+01 | 1.02E+02 | 7.63E+02 | 7.98E-01 | 1.67E-01 | GSF2LA | 2.82E+07 | 1.16E+08 | 6.09E+08 | 1.64E-01 | 2.69E-01 | ||
SFLA | 2.21E+01 | 1.08E+02 | 7.63E+02 | 1.43E+00 | 1.71E-01 | SFLA | 2.76E+07 | 1.15E+08 | 6.09E+08 | 2.39E-01 | 2.81E-01 | ||
HSA | 7.63E+02 | 2.16E-12 | 7.63E+02 | 7.63E+02 | 1.01E-01 | HSA | 6.09E+08 | 2.03E-06 | 6.09E+08 | 6.09E+08 | 1.55E-01 | ||
ABCA | 1.61E+04 | 5.40E+04 | 3.67E+05 | 1.21E+03 | 1.39E+00 | ABCA | 1.47E+08 | 2.63E+08 | 9.27E+08 | 3.90E-02 | 1.13E+00 | ||
| NCSFLA | 1.09E+01 | 1.10E+01 | 4.91E+01 | 3.99E+00 | 2.53E+01 | | NCSFLA | 2.18E+04 | 9.17E+04 | 8.17E+05 | 6.24E-01 | 8.17E-01 |
MSFLA | 2.32E+01 | 6.47E+00 | 4.91E+01 | 1.78E+01 | 3.54E+01 | MSFLA | 1.83E+04 | 8.60E+04 | 8.17E+05 | 1.36E+03 | 5.62E-01 | ||
GSF2LA | 8.67E+00 | 8.34E+00 | 4.91E+01 | 3.82E+00 | 1.36E+01 | GSF2LA | 1.75E+04 | 9.77E+04 | 8.17E+05 | 1.72E+03 | 2.94E-01 | ||
SFLA | 8.93E+00 | 8.17E+00 | 4.91E+01 | 2.99E+00 | 1.60E+01 | SFLA | 1.73E+04 | 8.45E+04 | 8.17E+05 | 3.80E+03 | 2.99E-01 | ||
HSA | 4.77E+01 | 1.40E+00 | 4.91E+01 | 4.55E+01 | 2.08E-01 | HSA | 8.17E+05 | 2.33E-10 | 8.17E+05 | 8.17E+05 | 1.56E-01 | ||
ABCA | 1.44E+01 | 1.28E+01 | 5.54E+01 | 2.61E+00 | 2.36E+00 | ABCA | 1.66E+05 | 3.60E+05 | 1.69E+06 | 1.72E+02 | 2.13E+00 | ||
| NCSFLA | 3.35E-01 | 2.47E-01 | 9.62E-01 | 9.74E-03 | 4.71E+01 | | NCSFLA | -2.69E+19 | 1.14E+19 | 9.46E+03 | -3.75E+19 | 1.58E+00 |
MSFLA | 5.32E-01 | 1.35E-01 | 9.62E-01 | 4.53E-01 | 6.72E+01 | MSFLA | 9.26E+03 | 3.58E+01 | 9.46E+03 | 9.25E+03 | 4.48E-01 | ||
GSF2LA | 4.82E-01 | 2.33E-01 | 9.62E-01 | 1.90E-01 | 3.40E+01 | GSF2LA | 9.38E+03 | 1.50E+02 | 9.46E+03 | 9.08E+03 | 4.48E-01 | ||
SFLA | 4.16E-01 | 1.71E-01 | 9.62E-01 | 2.42E-01 | 5.74E+01 | SFLA | 9.39E+03 | 2.02E+01 | 9.46E+03 | 9.38E+03 | 4.20E-01 | ||
HSA | 7.67E-01 | 1.59E-01 | 9.62E-01 | 6.37E-01 | 1.78E-01 | HSA | 9.25E+03 | 6.89E+01 | 9.46E+03 | 9.03E+03 | 1.57E-01 | ||
ABCA | 3.55E-01 | 1.22E+00 | 9.20E+00 | 6.02E-03 | 2.02E+00 | ABCA | 5.30E+03 | 2.25E+03 | 1.08E+04 | 2.36E+03 | 1.44E+00 | ||
| NCSFLA | 5.40E+01 | 8.83E+01 | 7.95E+02 | 2.15E+01 | 1.82E-01 | | NCSFLA | 1.30E+04 | 5.88E+03 | 7.64E+04 | 1.16E+04 | 2.32E+00 |
MSFLA | 7.72E+02 | 1.75E+01 | 7.95E+02 | 7.48E+02 | 1.92E-01 | MSFLA | 2.83E+04 | 1.73E+04 | 7.64E+04 | 1.29E+04 | 1.14E+00 | ||
GSF2LA | 5.65E+02 | 9.01E+01 | 7.95E+02 | 4.95E+02 | 1.80E-01 | GSF2LA | 3.43E+04 | 1.59E+04 | 7.64E+04 | 1.93E+04 | 1.79E+00 | ||
SFLA | 5.78E+02 | 8.68E+01 | 7.95E+02 | 5.07E+02 | 1.72E-01 | SFLA | 3.47E+04 | 1.35E+04 | 7.64E+04 | 1.75E+04 | 1.86E+00 | ||
HSA | 7.08E+02 | 5.50E+01 | 7.95E+02 | 6.73E+02 | 1.67E-01 | HSA | 6.58E+04 | 4.52E+03 | 7.64E+04 | 6.26E+04 | 1.54E-01 | ||
ABCA | 4.78E+02 | 2.75E+02 | 1.29E+03 | 2.28E+02 | 1.74E+00 | ABCA | 2.14E+04 | 1.53E+04 | 6.98E+04 | 1.19E+04 | 1.29E+00 | ||
| NCSFLA | 2.77E+03 | 5.60E+03 | 4.78E+04 | 9.31E+02 | 2.00E-01 | | NCSFLA | 1.24E+02 | 1.46E+01 | 2.45E+02 | 1.18E+02 | 1.25E+00 |
MSFLA | 4.69E+04 | 9.22E+02 | 4.78E+04 | 4.57E+04 | 1.91E-01 | MSFLA | 1.68E+02 | 4.36E+01 | 2.45E+02 | 1.29E+02 | 9.06E-01 | ||
GSF2LA | 3.50E+04 | 5.28E+03 | 4.78E+04 | 3.13E+04 | 1.76E-01 | GSF2LA | 1.80E+02 | 2.94E+01 | 2.45E+02 | 1.40E+02 | 1.15E+00 | ||
SFLA | 3.49E+04 | 5.33E+03 | 4.78E+04 | 3.06E+04 | 1.77E-01 | SFLA | 1.68E+02 | 3.64E+01 | 2.45E+02 | 1.30E+02 | 9.91E-01 | ||
HSA | 4.78E+04 | 1.31E-10 | 4.78E+04 | 4.78E+04 | 1.57E-01 | HSA | 2.45E+02 | 4.83E-13 | 2.45E+02 | 2.45E+02 | 1.50E-01 | ||
ABCA | 2.27E+04 | 1.48E+04 | 7.93E+04 | 1.34E+04 | 1.51E+00 | ABCA | 1.57E+02 | 4.27E+01 | 2.90E+02 | 1.24E+02 | 3.01E+00 |
表2 收敛精度和速度比较
Table 2 Comparison of convergence precision and convergence speed
函数 | 算法 | 平均最优值 | 标准差 | 最大值 | 最小值 | 运行时间/s | 函数 | 算法 | 平均最优值 | 标准差 | 最大值 | 最小值 | 运行时间/s |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| NCSFLA | 1.34E+03 | 5.34E+03 | 4.68E+04 | 6.25E-05 | 1.51E-01 | | NCSFLA | 4.91E+00 | 1.47E+01 | 1.18E+02 | 8.66E-05 | 1.98E-01 |
MSFLA | 1.34E+04 | 1.65E+04 | 4.68E+04 | 4.53E+02 | 1.85E-01 | MSFLA | 1.21E+01 | 1.55E+01 | 1.18E+02 | 1.98E+00 | 2.20E-01 | ||
GSF2LA | 6.37E+03 | 1.42E+04 | 4.68E+04 | 1.64E+01 | 1.76E-01 | GSF2LA | 4.57E+00 | 1.49E+01 | 1.18E+02 | 8.48E-01 | 1.78E-01 | ||
SFLA | 6.37E+03 | 1.41E+04 | 4.68E+04 | 4.24E+01 | 1.70E-01 | SFLA | 5.29E+00 | 1.29E+01 | 1.18E+02 | 1.56E+00 | 1.78E-01 | ||
HSA | 4.64E+04 | 3.01E+02 | 4.68E+04 | 4.54E+04 | 1.09E-01 | HSA | 1.07E+02 | 4.51E+00 | 1.18E+02 | 1.05E+02 | 1.17E-01 | ||
ABCA | 1.66E+04 | 2.01E+04 | 7.31E+04 | 1.45E+01 | 1.84E+00 | ABCA | 3.53E+08 | 3.92E+09 | 5.45E+10 | 6.03E-01 | 1.62E+00 | ||
| NCSFLA | 1.26E+01 | 4.82E+01 | 4.22E+02 | 2.97E-02 | 4.30E-01 | | NCSFLA | 2.19E+03 | 8.82E+03 | 8.35E+04 | 6.18E+00 | 3.05E-01 |
MSFLA | 4.14E+02 | 1.92E+01 | 4.22E+02 | 3.45E+02 | 2.71E-01 | MSFLA | 6.00E+04 | 1.95E+04 | 8.35E+04 | 3.33E+04 | 2.41E-01 | ||
GSF2LA | 3.20E+02 | 1.15E+02 | 4.22E+02 | 9.77E+01 | 2.47E-01 | GSF2LA | 2.79E+04 | 3.49E+04 | 8.35E+04 | 2.29E+02 | 2.15E-01 | ||
SFLA | 3.21E+02 | 1.15E+02 | 4.22E+02 | 9.81E+01 | 2.50E-01 | SFLA | 2.62E+04 | 3.45E+04 | 8.35E+04 | 2.63E+02 | 2.18E-01 | ||
HSA | 4.19E+02 | 1.98E+00 | 4.22E+02 | 4.18E+02 | 1.89E-01 | HSA | 8.35E+04 | 0.00E+00 | 8.35E+04 | 8.35E+04 | 7.60E-02 | ||
ABCA | 1.45E+02 | 1.88E+02 | 5.87E+02 | 1.44E+00 | 2.20E+00 | ABCA | 3.62E+04 | 1.51E+04 | 9.13E+04 | 2.52E+04 | 1.87E+00 | ||
| NCSFLA | 1.30E+07 | 5.75E+07 | 4.59E+08 | 2.12E-01 | 2.97E-01 | | NCSFLA | 5.38E-01 | 5.92E+00 | 8.20E+01 | 0.00E+00 | 2.28E-01 |
MSFLA | 1.83E+07 | 6.47E+07 | 4.59E+08 | 1.86E+05 | 2.76E-01 | MSFLA | 5.89E+01 | 6.94E+00 | 8.20E+01 | 5.40E+01 | 2.58E-01 | ||
GSF2LA | 8.61E+06 | 5.46E+07 | 4.59E+08 | 4.02E+04 | 2.10E-01 | GSF2LA | 8.07E+01 | 3.64E-01 | 8.20E+01 | 8.05E+01 | 1.85E-01 | ||
SFLA | 7.45E+06 | 4.87E+07 | 4.59E+08 | 1.20E+05 | 1.98E-01 | SFLA | 7.81E+01 | 3.70E+00 | 8.20E+01 | 7.20E+01 | 1.84E-01 | ||
HSA | 4.35E+08 | 1.53E+07 | 4.59E+08 | 4.25E+08 | 1.89E-01 | HSA | 8.20E+01 | 0.00E+00 | 8.20E+01 | 8.20E+01 | 1.50E-01 | ||
ABCA | 1.30E+08 | 2.10E+08 | 8.07E+08 | 4.88E+04 | 1.96E+00 | ABCA | 7.42E+01 | 9.04E+00 | 9.33E+01 | 6.07E+01 | 1.95E+00 | ||
| NCSFLA | 4.58E+43 | 6.45E+44 | 9.15E+45 | 5.20E+01 | 4.35E-01 | | NCSFLA | 1.28E+03 | 5.29E+03 | 4.67E+04 | 6.79E-06 | 2.02E-01 |
MSFLA | 1.04E+45 | 2.87E+45 | 9.15E+45 | 1.18E+18 | 2.87E-01 | MSFLA | 1.37E+04 | 1.63E+04 | 4.67E+04 | 6.04E+02 | 2.07E-01 | ||
GSF2LA | 9.69E+44 | 2.80E+45 | 9.15E+45 | 1.00E+00 | 2.24E-01 | GSF2LA | 6.36E+03 | 1.41E+04 | 4.67E+04 | 4.06E+01 | 1.75E-01 | ||
SFLA | 9.81E+44 | 2.81E+45 | 9.15E+45 | 1.30E+01 | 2.22E-01 | SFLA | 6.37E+03 | 1.41E+04 | 4.67E+04 | 3.73E+01 | 1.80E-01 | ||
HSA | 7.52E+45 | 1.49E+45 | 9.15E+45 | 6.16E+45 | 1.90E-01 | HSA | 4.67E+04 | 0.00E+00 | 4.67E+04 | 4.67E+04 | 1.46E-01 | ||
ABCA | 1.32E+48 | 4.79E+48 | 2.50E+49 | 4.98E+06 | 1.25E+00 | ABCA | 1.18E+04 | 1.94E+04 | 7.32E+04 | 9.36E-01 | 1.48E+00 | ||
| NCSFLA | 2.84E+04 | 3.99E+05 | 5.65E+06 | 4.16E-01 | 4.25E-01 | | NCSFLA | 5.07E+06 | 3.19E+07 | 3.19E+08 | -9.21E-01 | 5.57E-01 |
MSFLA | 1.72E+05 | 9.64E+05 | 5.65E+06 | 1.91E+02 | 4.11E-01 | MSFLA | 2.03E+07 | 7.02E+07 | 3.19E+08 | 2.31E-01 | 4.07E-01 | ||
GSF2LA | 2.16E+05 | 1.07E+06 | 5.65E+06 | 1.59E+01 | 3.30E-01 | GSF2LA | 1.31E+07 | 5.77E+07 | 3.19E+08 | -1.00E+00 | 2.47E-01 | ||
SFLA | 2.05E+05 | 1.02E+06 | 5.65E+06 | 1.10E+01 | 3.45E-01 | SFLA | 1.27E+07 | 5.68E+07 | 3.19E+08 | -9.92E-01 | 2.48E-01 | ||
HSA | 1.33E+06 | 2.40E+06 | 5.65E+06 | 5.80E+02 | 1.48E-01 | HSA | 3.19E+08 | 5.36E-07 | 3.19E+08 | 3.19E+08 | 1.97E-01 | ||
ABCA | 2.58E+07 | 1.89E+08 | 2.08E+09 | 2.79E+02 | 1.26E+00 | ABCA | 3.58E+07 | 7.76E+07 | 4.59E+08 | -9.07E-01 | 1.21E+00 | ||
| NCSFLA | 3.60E+01 | 1.33E+02 | 7.63E+02 | 4.61E-07 | 1.65E-01 | | NCSFLA | 1.23E+07 | 6.72E+07 | 6.09E+08 | 2.10E-05 | 6.63E-01 |
MSFLA | 9.07E+01 | 1.56E+02 | 7.63E+02 | 6.67E+00 | 1.76E-01 | MSFLA | 4.54E+07 | 1.44E+08 | 6.09E+08 | 2.19E+01 | 4.24E-01 | ||
GSF2LA | 1.85E+01 | 1.02E+02 | 7.63E+02 | 7.98E-01 | 1.67E-01 | GSF2LA | 2.82E+07 | 1.16E+08 | 6.09E+08 | 1.64E-01 | 2.69E-01 | ||
SFLA | 2.21E+01 | 1.08E+02 | 7.63E+02 | 1.43E+00 | 1.71E-01 | SFLA | 2.76E+07 | 1.15E+08 | 6.09E+08 | 2.39E-01 | 2.81E-01 | ||
HSA | 7.63E+02 | 2.16E-12 | 7.63E+02 | 7.63E+02 | 1.01E-01 | HSA | 6.09E+08 | 2.03E-06 | 6.09E+08 | 6.09E+08 | 1.55E-01 | ||
ABCA | 1.61E+04 | 5.40E+04 | 3.67E+05 | 1.21E+03 | 1.39E+00 | ABCA | 1.47E+08 | 2.63E+08 | 9.27E+08 | 3.90E-02 | 1.13E+00 | ||
| NCSFLA | 1.09E+01 | 1.10E+01 | 4.91E+01 | 3.99E+00 | 2.53E+01 | | NCSFLA | 2.18E+04 | 9.17E+04 | 8.17E+05 | 6.24E-01 | 8.17E-01 |
MSFLA | 2.32E+01 | 6.47E+00 | 4.91E+01 | 1.78E+01 | 3.54E+01 | MSFLA | 1.83E+04 | 8.60E+04 | 8.17E+05 | 1.36E+03 | 5.62E-01 | ||
GSF2LA | 8.67E+00 | 8.34E+00 | 4.91E+01 | 3.82E+00 | 1.36E+01 | GSF2LA | 1.75E+04 | 9.77E+04 | 8.17E+05 | 1.72E+03 | 2.94E-01 | ||
SFLA | 8.93E+00 | 8.17E+00 | 4.91E+01 | 2.99E+00 | 1.60E+01 | SFLA | 1.73E+04 | 8.45E+04 | 8.17E+05 | 3.80E+03 | 2.99E-01 | ||
HSA | 4.77E+01 | 1.40E+00 | 4.91E+01 | 4.55E+01 | 2.08E-01 | HSA | 8.17E+05 | 2.33E-10 | 8.17E+05 | 8.17E+05 | 1.56E-01 | ||
ABCA | 1.44E+01 | 1.28E+01 | 5.54E+01 | 2.61E+00 | 2.36E+00 | ABCA | 1.66E+05 | 3.60E+05 | 1.69E+06 | 1.72E+02 | 2.13E+00 | ||
| NCSFLA | 3.35E-01 | 2.47E-01 | 9.62E-01 | 9.74E-03 | 4.71E+01 | | NCSFLA | -2.69E+19 | 1.14E+19 | 9.46E+03 | -3.75E+19 | 1.58E+00 |
MSFLA | 5.32E-01 | 1.35E-01 | 9.62E-01 | 4.53E-01 | 6.72E+01 | MSFLA | 9.26E+03 | 3.58E+01 | 9.46E+03 | 9.25E+03 | 4.48E-01 | ||
GSF2LA | 4.82E-01 | 2.33E-01 | 9.62E-01 | 1.90E-01 | 3.40E+01 | GSF2LA | 9.38E+03 | 1.50E+02 | 9.46E+03 | 9.08E+03 | 4.48E-01 | ||
SFLA | 4.16E-01 | 1.71E-01 | 9.62E-01 | 2.42E-01 | 5.74E+01 | SFLA | 9.39E+03 | 2.02E+01 | 9.46E+03 | 9.38E+03 | 4.20E-01 | ||
HSA | 7.67E-01 | 1.59E-01 | 9.62E-01 | 6.37E-01 | 1.78E-01 | HSA | 9.25E+03 | 6.89E+01 | 9.46E+03 | 9.03E+03 | 1.57E-01 | ||
ABCA | 3.55E-01 | 1.22E+00 | 9.20E+00 | 6.02E-03 | 2.02E+00 | ABCA | 5.30E+03 | 2.25E+03 | 1.08E+04 | 2.36E+03 | 1.44E+00 | ||
| NCSFLA | 5.40E+01 | 8.83E+01 | 7.95E+02 | 2.15E+01 | 1.82E-01 | | NCSFLA | 1.30E+04 | 5.88E+03 | 7.64E+04 | 1.16E+04 | 2.32E+00 |
MSFLA | 7.72E+02 | 1.75E+01 | 7.95E+02 | 7.48E+02 | 1.92E-01 | MSFLA | 2.83E+04 | 1.73E+04 | 7.64E+04 | 1.29E+04 | 1.14E+00 | ||
GSF2LA | 5.65E+02 | 9.01E+01 | 7.95E+02 | 4.95E+02 | 1.80E-01 | GSF2LA | 3.43E+04 | 1.59E+04 | 7.64E+04 | 1.93E+04 | 1.79E+00 | ||
SFLA | 5.78E+02 | 8.68E+01 | 7.95E+02 | 5.07E+02 | 1.72E-01 | SFLA | 3.47E+04 | 1.35E+04 | 7.64E+04 | 1.75E+04 | 1.86E+00 | ||
HSA | 7.08E+02 | 5.50E+01 | 7.95E+02 | 6.73E+02 | 1.67E-01 | HSA | 6.58E+04 | 4.52E+03 | 7.64E+04 | 6.26E+04 | 1.54E-01 | ||
ABCA | 4.78E+02 | 2.75E+02 | 1.29E+03 | 2.28E+02 | 1.74E+00 | ABCA | 2.14E+04 | 1.53E+04 | 6.98E+04 | 1.19E+04 | 1.29E+00 | ||
| NCSFLA | 2.77E+03 | 5.60E+03 | 4.78E+04 | 9.31E+02 | 2.00E-01 | | NCSFLA | 1.24E+02 | 1.46E+01 | 2.45E+02 | 1.18E+02 | 1.25E+00 |
MSFLA | 4.69E+04 | 9.22E+02 | 4.78E+04 | 4.57E+04 | 1.91E-01 | MSFLA | 1.68E+02 | 4.36E+01 | 2.45E+02 | 1.29E+02 | 9.06E-01 | ||
GSF2LA | 3.50E+04 | 5.28E+03 | 4.78E+04 | 3.13E+04 | 1.76E-01 | GSF2LA | 1.80E+02 | 2.94E+01 | 2.45E+02 | 1.40E+02 | 1.15E+00 | ||
SFLA | 3.49E+04 | 5.33E+03 | 4.78E+04 | 3.06E+04 | 1.77E-01 | SFLA | 1.68E+02 | 3.64E+01 | 2.45E+02 | 1.30E+02 | 9.91E-01 | ||
HSA | 4.78E+04 | 1.31E-10 | 4.78E+04 | 4.78E+04 | 1.57E-01 | HSA | 2.45E+02 | 4.83E-13 | 2.45E+02 | 2.45E+02 | 1.50E-01 | ||
ABCA | 2.27E+04 | 1.48E+04 | 7.93E+04 | 1.34E+04 | 1.51E+00 | ABCA | 1.57E+02 | 4.27E+01 | 2.90E+02 | 1.24E+02 | 3.01E+00 |
算法 | 最短路径值 | 车辆1优化路径 | 车辆2优化路径 |
---|---|---|---|
NCSFLA-CVRP | 554.08 | 5-81-4-46-22-90-6-79 | 19-11-59-51-65-34-50-85 |
MSFLA-CVRP | 629.68 | 59-46-4-81-9-11-67-94 | 22-1-3-50-88-82-95-87 |
GSF2LA-CVRP | 634.21 | 98-16-4-17-58-67-53-65-82 | 38-59-11-75-32-69-8-12 |
SFLA-CVRP | 647.69 | 56-79-85-22-58-18-57-86-74 | 12-96-78-11-5-50-31-29 |
表3 各算法 K = 2Solomon算例数据车辆路径优化比较
Table 3 Comparison of vehicle routing optimization algorithms for Solomon example data while K = 2
算法 | 最短路径值 | 车辆1优化路径 | 车辆2优化路径 |
---|---|---|---|
NCSFLA-CVRP | 554.08 | 5-81-4-46-22-90-6-79 | 19-11-59-51-65-34-50-85 |
MSFLA-CVRP | 629.68 | 59-46-4-81-9-11-67-94 | 22-1-3-50-88-82-95-87 |
GSF2LA-CVRP | 634.21 | 98-16-4-17-58-67-53-65-82 | 38-59-11-75-32-69-8-12 |
SFLA-CVRP | 647.69 | 56-79-85-22-58-18-57-86-74 | 12-96-78-11-5-50-31-29 |
算法 | 最短路径值 | 车辆1优化路径 | 车辆2优化路径 | 车辆3优化路径 | 车辆4优化路径 |
---|---|---|---|---|---|
NCSFLA-CVRP | 479.75 | 69-40-41-49-11-5-46-12 | 71-4-76-96-24-83-61-13-86-98-60-64-47 | 33-65-9-38-55-77-44-19 | 34-63-22-20-17-10-91-66-78 |
MSFLA-CVRP | 552.85 | 87-97-17-68-36-89-85-57-65 | 12-58-16-27-34-95-33-30-35-83 | 90-64-74-46-60-75-28-21-53-98-18-80 | 11-86-94-56-22-26-38 |
GSF2LA-CVRP | 566.62 | 64-21-15-80-5-87-53-36-92-83-52 | 96-89-42-85-93-94-25-44-6-17 | 23-76-97-73-49-30-33-40-69-65 | 10-38-61-18-68-75-95 |
SFLA-CVRP | 578.84 | 86-7-85-11-82-45-90-50-8-3 | 95-36-49-34-22-93-66 | 78-21-73-96-57-62-87-24-23-48 | 38-26-46-13-97-61-35-70-91-68-55 |
表4 各算法 K = 4 Solomon算例数据车辆路径优化比较
Table 4 Comparison of vehicle routing optimization algorithms for Solomon example data while K = 4
算法 | 最短路径值 | 车辆1优化路径 | 车辆2优化路径 | 车辆3优化路径 | 车辆4优化路径 |
---|---|---|---|---|---|
NCSFLA-CVRP | 479.75 | 69-40-41-49-11-5-46-12 | 71-4-76-96-24-83-61-13-86-98-60-64-47 | 33-65-9-38-55-77-44-19 | 34-63-22-20-17-10-91-66-78 |
MSFLA-CVRP | 552.85 | 87-97-17-68-36-89-85-57-65 | 12-58-16-27-34-95-33-30-35-83 | 90-64-74-46-60-75-28-21-53-98-18-80 | 11-86-94-56-22-26-38 |
GSF2LA-CVRP | 566.62 | 64-21-15-80-5-87-53-36-92-83-52 | 96-89-42-85-93-94-25-44-6-17 | 23-76-97-73-49-30-33-40-69-65 | 10-38-61-18-68-75-95 |
SFLA-CVRP | 578.84 | 86-7-85-11-82-45-90-50-8-3 | 95-36-49-34-22-93-66 | 78-21-73-96-57-62-87-24-23-48 | 38-26-46-13-97-61-35-70-91-68-55 |
[1] | 颜腾威. 求解VRP问题的改进和声搜索算法的研究[D]. 金华: 浙江师范大学, 2015. |
YAN T W. Research of improved harmony search algori-thm for VRP[D]. Jinhua: Zhejiang Normal University, 2015. | |
[2] | LAU H C, CHAN T M, TSUI W T, et al. Application of ge-netic algorithms to solve the multidepot vehicle routing pro-blem[J]. IEEE Transactions on Automation Science & En-gineering, 2010, 7(2): 383-392. |
[3] |
PAVONE M, FRAZZOLI E, BULLO F. Adaptive and dis-tributed algorithms for vehicle routing in a stochastic and dynamic environment[J]. IEEE Transactions on Automatic Control, 2011, 56(6): 1259-1274.
DOI URL |
[4] | ZHAO Z X, WAN F C. The solving of vehicle routing prob-lem based on hybrid harmony search algorithm[C]// Procee-dings of the 3rd International Conference on Computa-tional Intelligence and Industrial Application, 2010: 379-382. |
[5] | EUSUFF M M, LANSEY K E. Optimization of water distri-bution network design using the shuffled frog leaping algo-rithm[J]. Journal of Water Resources Planning and Manage-ment, 2003, 129(3): 210. |
[6] | 姚应龙. 混合蛙跳算法及其应用研究[D]. 深圳: 深圳大学, 2015. |
YAO Y L. Research on shuffled frog leaping algorithm and its application[D]. Shenzhen: Shenzhen University, 2015. | |
[7] | 郑俊褒, 饶珊珊. 改进蛙跳算法的小波神经网络短时交通流预测[J]. 软件导刊, 2020, 19(4): 50-54. |
ZHENG J B, RAO S S. Short-term traffic flow prediction of wavelet neural network based on the improved shuffled flog leaping algorithm[J]. Software Guide, 2020, 19(4): 50-54. | |
[8] | 黄遥. 混合蛙跳算法及其在带容量约束的车辆路径问题中的应用研究[D]. 南京: 南京信息工程大学, 2020. |
HUANG Y. Shuffled frog leaping algorithm and its appli-cations on the capacitated vehicle routing problem[D]. Nan-jing: Nanjing University of Information Science and Tech-nology, 2020. | |
[9] | 骆剑平, 李霞, 陈泯融. 基于改进混合蛙跳算法的CVRP求解[J]. 电子与信息学报, 2011, 33(2): 429-434. |
LUO J P, LI X, CHEN M R. Improved shuffled frog leaping algorithm for solving CVRP[J]. Journal of Elec-tronics & Information Technology, 2011, 33(2): 429-434. | |
[10] | 万博, 卢昱, 陈立云, 等. 求解CVRP的改进混合蛙跳算法研究[J]. 计算机应用研究, 2011, 28(12): 4503-4506. |
WAN B, LU Y, CHEN L Y, et al. Study of modified shuf-fled frog leaping algorithm for solving CVRP[J]. Applica-tion Research of Computers, 2011, 28(12): 4503-4506. | |
[11] | 蔡延光, 王世豪, 戚远航, 等. 帝国竞争算法求解CVRP[J]. 计算机应用研究, 2021, 38(3): 782-786. |
CAI Y G, WANG S H, QI Y H, et al. Imperialist compe-titive algorithm for solving CVRP[J]. Application Research of Computers, 2021, 38(3): 782-786. | |
[12] | ZHU X N, ZHAO Z Q, YAN R. Low carbon logistics opti-mization for multi-depot CVRP with backhauls-model and solution[J]. Technical Gazette, 2020, 27(5): 1617-1624. |
[13] | KHACHAY M Y, OGORODNIKOV Y, KHACHAY D. Efficient approximation of the metric CVRP in spaces of fixed doubling dimension[J]. Journal of Global Optimiza-tion, 2021, 80(3): 679-710. |
[14] | 黄子峻, 曾楚祥, 戚远航. CVRP的改进离散蝙蝠算法[J]. 工业控制计算机, 2020, 33(8): 100-101. |
HUANG Z J, ZENG C X, QI Y H. Improve discrete bat algorithm for CVRP[J]. Industrial Control Computer, 2020, 33(8): 100-101. | |
[15] | 向明尚, 张强. 求解带容量约束车辆路径问题的离散布谷鸟算法[J]. 东北石油大学学报, 2021, 45(1): 95-101. |
XIANG M S, ZHANG Q. Discrete cuckoo algorithm for vehi-cle routing with capacity constraints[J]. Journal of Northeast Petroleum University, 2021, 45(1): 95-101. | |
[16] | 朱佳莹, 高茂庭. 融合粒子群与改进蚁群算法的AUV路径规划算法[J]. 计算机工程与应用, 2021, 57(6): 267-273. |
ZHU J Y, GAO M T. AUV path planning based on particle swarm optimization and improved ant colony optimization[J]. Computer Engineering and Applications, 2021, 57(6): 267-273. | |
[17] | 韩立钦, 张耀南, 秦其明. 深度学习自编码结合混合蛙跳算法提取农田高光谱影像端元[J]. 农业工程学报, 2019, 35(6): 167-173. |
HAN L Q, ZHANG Y N, QIN Q M. Endmember extraction of farmland hyperspectral image using deep learning auto-encoder and shuffled frog leaping algorithm[J]. Transa-ctions of the Chinese Society of Agricultural Engineering, 2019, 35(6): 167-173. | |
[18] |
MOHAN G S S S S V K, RAO Y S. An efficient design of fractional order differentiator using hybrid shuffled frog leaping algorithm for handling noisy electrocardiograms[J]. International Journal of Computers and Applications, 2021, 43(5): 494-500.
DOI URL |
[19] | 孟磊磊, 张彪, 任亚平, 等. 求解分布式柔性作业车间调度的混合蛙跳算法[J]. 机械工程学报, 2021, 57(17): 263-272. |
MENG L L, ZHANG B, REN Y P, et al. Hybrid shuffled frog-leaping algorithm for distributed flexible job shop schedu-ling[J]. Journal of Mechanical Engineering, 2021, 57(17): 263-272.
DOI URL |
|
[20] | 鲁建厦, 翟文倩, 李嘉丰, 等. 基于改进混合蛙跳算法的多约束车辆路径优化[J]. 浙江大学学报(工学版), 2021, 55(2): 259-270. |
LU J S, ZHAI W Q, LI J F, et al. Multi-constrained vehicle routing optimization based on improved hybrid shuffled frog leaping algorithm[J]. Journal of Zhejiang University (Engineering Science), 2021, 55(2): 259-270. | |
[21] | 任龙杰, 孙颖, 丁卫平, 等. 基于单种群蛙跳优化CNN的眼底图像多病变检测[J]. 计算机科学与探索, 2021, 15(9): 1762-1772. |
REN L J, SUN Y, DING W P, et al. Multiple lesions detec-tion of fundus images based on convolution neural network algorithm optimized by single population frog jumping algo-rithm[J]. Journal of Frontiers of Computer Science and Tech-nology, 2021, 15(9): 1762-1772. | |
[22] | 塔诺季, 迪于, 拉洛埃. 量子力学(第一卷)[M]. 刘家谟, 陈星奎, 译. 北京: 高等教育出版社, 2014. |
TANNOUDJI C C, DIU B, LALOE F. Mecanique quan-tique I[M]. LIU J M, CHEN X K. Beijing: Higher Education Press, 2014. | |
[23] | 代永强, 王联国. 带记忆功能的混合蛙跳算法[J]. 计算机工程与设计, 2011, 32(9): 3170-3173. |
DAI Y Q, WANG L G. Shuffled frog leaping algorithm with memory function[J]. Computer Engineering and Design, 2011, 32(9): 3170-3173. | |
[24] | 刘立群, 王联国, 韩俊英, 等. 基于全局共享因子的混合蛙跳算法[J]. 计算机工程, 2013, 39(10): 162-166. |
LIU L Q, WANG L G, HAN J Y, et al. Shuffled frog lea-ping algorithm based on global sharing factor[J]. Compu-ter Engineering, 2013, 39(10): 162-166. | |
[25] |
GEEM Z W, KIM J H, LOGANATHAN G V. A new heuristic optimization algorithm: harmony search[J]. Simulation, 2001, 76(2): 60-68.
DOI URL |
[26] | KARABOGA D, BASTURK B. A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm[J]. Journal of Global Optimi-zation, 2007, 39(3): 459-471. |
[27] |
MOUSAVIRAD S J, EBRAHIMPOUR-KOMLEH H. Hu-man mental search: a new population-based metaheuris-tic opti-mization algorithm[J]. Applied Intelligence, 2017, 47: 850-887.
DOI URL |
[28] | AWAD N H, ALI M Z, LIANG J J, et al. Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective bound constrained real-parameter numerical optimization[R]. Singapore: Nanyang Technological University, 2016. |
[1] | 任龙杰, 孙颖, 丁卫平, 鞠恒荣, 曹金鑫. 基于单种群蛙跳优化CNN的眼底图像多病变检测[J]. 计算机科学与探索, 2021, 15(9): 1762-1772. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||