Research Article

Artificial Bee Colony Algorithm Merged with Pheromone Communication Mechanism for the 0-1 Multidimensional Knapsack Problem

Table 2

The results for two algorithms on some instances.

Instance statistic Algoritm
ABC-MKP ABCPUD-MKP

5.100.01 Best24274 (24274)24274 (24274)
Avg.24274 ± 0.024274 ± 0.0
Num. (53) 87.60 ± 74.02 (35)
Hit.1010
Time (s) (4.88) 7.44 ± 6.56 (2.70)

5.100.03 Best23534 (23534)23534 (23534)
Avg.23534 ± 0.023534 ± 0.0
Num. (2356) 2571.0 ± 551.54 (2181)
Hit.1010
Time (s) (223.03) 216.21 ± 51.11 (197.92)

5.100.05 Best24613 (24613)24613 (24613)
Avg.24613 ± 0.024613 ± 0.0
Num. (110) 96.0 ± 21.74 (74)
Hit.10 10
Time (s) (8.67) 8.03 ± 1.80 (5.89)

10.100.01 Best22801 (22801)22801 (22801)
Avg.22801 ± 0.022801 ± 0.0
Num. (844) 3161.79 ± 2331.48 (103)
Hit.1010
Time (s) (88.52) 276.22 ± 244.62 (10.41)

10.100.03 Best22772 (22772)22772 (22772)
Avg.22772 ± 0.022772 ± 0.0
Num. (4483) 4441.5 ± 1469.34 (2855)
Hit.1010
Time (s) (400.33) 399.15 ± 133.47 (254.10)

10.100.05 Best22777 (22777)22777 (22777)
Avg. 22771.3 ± 19.30
Num. (585) 3706.8 ± 2345.87 (258)
Hit. 7 9
Time (s) (65.16) 338.09 ± 209.85 (23.07)