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

Table 1

The contributions of the pheromone mechanism on ABC-MKP.

Instances	Best known	ABC-MKP			ABCPU-MKP			ABCPUD-MKP
		Best	Avg.	Num.	Best	Avg.	Num.	Best	Avg.	Num.
5.100.00	24381	24381	24381.0±0.0	238	24381	24381.0±0.0	220	24381	24381.0±0.0	178
5.100.01	24274	24274	24274.0±0.0	36	24274	24274.0±0.0	32	24274	24274.0±0.0	20
5.100.02	23551	23551	23539.3±4.1	4021	23551	23548.0±5.5	2251	23551	23550.0±3.9	354
5.100.03	23534	23534	23534.0±0.0	2356	23534	23527.0±3.5	2202	23534	23534.0±0.0	1538
5.100.04	23991	23991	23973.2±14.8	1746	23991	23982.4±13.7	1689	23991	23986.0±10.5	1622
5.100.05	24613	24613	24613.0±0.0	110	24613	24613.0±0.0	76	24613	24613.0±0.0	46
5.100.06	25591	25591	25591.0±0.0	252	25591	25591.0±0.0	224	25591	25591.0±0.0	65
5.100.07	23410	23410	23410.0±0.0	409	23410	23410.0±0.0	304	23410	23410.0±0.0	259
5.100.08	24216	24216	24216.0±0.0	1051	24216	24216.0±0.0	799	24216	24216.0±0.0	755
5.100.09	24411	24411	24411.0±0.0	189	24411	24411.0±0.0	97	24411	24411.0±0.0	81