Advanced Harmony Search with Ant Colony Optimization for Solving the Traveling Salesman Problem

Table 2

Results of our algorithm (AHS-ACO) for 20 TSP instances from the TSPLIB.

TSPLIB	Known best solutions	Solution				Running Time	Relative error (%)
		Best	Worst	Mean	STDEV	Second (s)	Best
berlin52	7542	7542	7542	7542	0.000	15.12	0.000
st70	675	675	677	675.375	0.812	19.45	0.000
eil76	538	538	542	540.494	1.473	22.27	0.000
kroA100	21282	21282	21378	21307.554	34.983	40.97	0.000
kroB100*	22141	𝟐𝟐𝟏𝟑𝟗^∗	22271	22193.114	53.678	42.87	−0.009
kroC100	20749	20749	20868	20770	34.937	39.62	0.000
kroD100	21294	21294	21467	21338.03	63.797	41.24	0.000
kroE100	22068	22068	22117	22093.099	14.819	42.38	0.000
eil101	629	629	643	634.355	4.479	49.47	0.000
lin105	14379	14379	14541	14434.947	59.097	56.27	0.000
ch130	6110	6110	6200	6173.038	24.544	69.24	0.000
pr144*	58537	𝟓𝟖𝟓𝟑𝟒^∗	58902	58659.283	144.807	80.27	−0.003
ch150	6528	6528	6586	6554.589	17.303	97.34	0.000
pr152	73682	73682	74754	73846.437	325.185	111.59	0.000
d198	15780	15780	15963	15876.892	70.497	180.27	0.000
tsp225	3919	3859	4013.724	3977.047	26.516	208.48	0.000
pr226	80369	80369	80882	80558.519	174.915	213.78	0.000
pr264	49135	49135	49379	49205.87	75.675	279.69	0.000
a280	2579	2579	2726	2641.61	44.91	303.36	0.000
pr299	48191	48195	49989	49121.289	577.831	367.72	0.016