Solving the Traveling Salesman’s Problem Using the African Buffalo Optimization

Table 3

Comparative experimental result.

Problem	Number of cities	Optima	Method	Best	Mean	Rel. err. (%)	Time (s)
Berlin52			ABO	7542	7616	0%	0.002
			ACO	7548.99	7659.31	1.52	116.67
	52	7542	ABC	9479.11	10,390.26	37.72	2.17
			HA	7544.37	7544.37	0.03	60.64
St70			ABO	676	678.33	0.15	0.08
			ACO	696.05	709.16	4.73	226.06
	70	675	ABC	1162.12	1230.49	81.73	3.15
			HA	687.24	700.58	3.47	115.65
Eil76			ABO	538	563.04	0%	0.03
	76	538	ACO	554.46	561.98	3.04	271.98
			ABC	877.28	931.44	70.78	3.49
			HA	551.07	557.98	2.31	138.82
Pr76		108159	ABO	108167	108,396	0.007%	0.08
	76		ACO	115,166.66	116,321.22	7.55	272.41
			ABC	195,198.9	205,119.61	89.65	3.50
			HA	113,798.56	115,072.29	6.39	138.92
Kroa100		21282	ABO	21311	22163.8	0.4%	0.00
	100		ACO	22,455.89	22,880.12	7.49	615.06
			ABC	49,519.51	53,840.03	152.94	5.17
			HA	22,122.75	22,435.31	5.40	311.12
Eil101		629	ABO	640	640	1.7%	0.027
	101		ACO	678.04	693.42	7.96	527.42
			ABC	1237.31	1315.95	104.88	5.17
			HA	672.71	683.39	6.39	267.08
Ch150		6528	ABO	6532	6601	0.06%	0.032
	150		ACO	6648.51	6702.87	2.61	1387.65
			ABC	20,908.89	21,617.48	230.93	8.95
			HA	6641.69	6677.12	2.21	698.61
Tsp225		3916	ABO	3917	3982	0.03	0.09
	225		ACO	4112.35	4176.08	8.22	4038.75
			ABC	16,998.41	17,955.12	365.2792	16.68
			HA	4090.54	4157.85	7.74	2037.33