Int J Performability Eng ›› 2019, Vol. 15 ›› Issue (1): 317325.doi: 10.23940/ijpe.19.01.p32.317325
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Yu Li^{a}^{b}, Qian Guo^{b}, and Jingsen Liu^{c}*()
Revised on
;
Accepted on
Contact:
Liu Jingsen
Email:ljs@henu.edu.cn
About author:
Yu Li received her PhD from University of Shanghai for Science and Technology. She is a professor of Institute of Management Science and Engineering, and Business School, Henan University. Her research interests include intelligence algorithms, electronic commerce, etc.Qian Guo is a master degree candidate of Business School, Henan University. Her research interest is intelligence algorithm.Jingsen Liu received his PhD from Northwestern Polytechnical University. He is a professor of Institute of Intelligent Network system, and College of Software, Henan University. His research interests include intelligence algorithm and network information security, etc.
Yu Li, Qian Guo, and Jingsen Liu. Improved Bat Algorithm for Vehicle Routing Problem [J]. Int J Performability Eng, 2019, 15(1): 317325.
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Bat algorithm
pseudo code"
Input: Initialize the bat population ${{x}_{i}}$, ${{f}_{i}}$, and ${{v}_{i}}$,$(i=1,2,\cdots ,n)$ 

1. While$(t<{{T}_{\max }})$; 
2. Update velocities and locations; 
3. If$(rand>{{r}_{i}})$; 
Select a current best solution randomly among the best solutions and generate a local solution around the selected best solution; 
5. End if; 
6. Generate a new solution randomly; 
7. If ($rand<{{A}_{i}}$and $f({{x}_{i}})<f({{x}_{*}})$); 
8. $f({{x}_{*}})=f({{x}_{i}})$; 
9. Increase ${{r}_{i}}$and reduce ${{A}_{i}}$; 
10. End if; 
11. Rank the bats and find the current best ${{x}_{*}}$; 
12. End while. 
Table 1
Distance and demand"
0  1  2  3  4  5  6  7  8  

0  0  4  6  7.5  9  20  10  16  8 
1  4  0  6.5  4  10  5  7.5  11  10 
2  6  6.5  0  7.5  10  10  7.5  7.5  7.5 
3  7.5  4  7.5  0  10  5  9  9  15 
4  9  10  10  10  0  10  7.5  7.5  10 
5  20  5  10  5  10  0  7  9  7.5 
6  10  7.5  7.5  9  7.5  7  0  7  10 
7  16  11  7.5  9  7.5  9  7  0  10 
8  8  10  7.5  15  10  7.5  10  10  0 
d  1  2  1  2  1  4  2  2 
Table 3
Solution by standard GA and doublepopulation GA for 10 times"
Algorithm  Times  

1  2  3  4  5  6  7  8  9  10  
standard GA  74.00  75.00  71.50  72.00  73.50  75.00  73.00  72.50  75.50  73.50 
doublepopulation GA  70.00  69.50  67.50  71.00  69.00  70.50  72.00  67.50  71.50  69.00 
11  12  13  14  15  16  17  18  19  20  
standard GA  72.00  69.00  73.00  75.50  72.00  73.00  75.00  73.50  71.50  75.00 
doublepopulation GA  67.50  69.00  71.00  70.00  67.50  70.50  69.00  69.50  71.00  69.00 
Table 4
Pn19k2 coordinate and demand"
Coordinate  Demand  Coordinate  Demand  

0  (30,40)  0  10  (42,57)  8 
1  (37,52)  19  11  (27,68)  7 
2  (49,43)  30  12  (43,67)  14 
3  (52,64)  16  13  (58,27)  19 
4  (31,62)  23  14  (37,69)  11 
5  (52,33)  11  15  (61,33)  26 
6  (42,41)  31  16  (62,63)  17 
7  (52,41)  15  17  (63,69)  6 
8  (57,58)  28  18  (45,35)  15 
9  (62,42)  14 
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