Annealing Ant Colony Optimization with Mutation Operator for Solving TSP

Table 4

A comparison of the proposed algorithm with Yousefikhoshbakht et al. [32] and Mahi et al. [31] according to the best solution, average solution, standard deviation, the percentage deviation of the average solution (), and the percentage deviation of the best solution () found by the algorithms.

Instance	Opt.	Method	Best	Average	Std. dev.
eil51	426	Proposed algorithm	426	426	0.000	0.000	0.000
		Yousefikhoshbakht et al. [32]	426	N/A	N/A	0.000	N/A
		Mahi et al. [31]	N/A	426.45	0.610	N/A	0.106
eil76	538	Proposed algorithm	538	538	0.000	0.000	0.000
		Yousefikhoshbakht et al. [32]	538	N/A	N/A	0.000	N/A
		Mahi et al. [31]	N/A	538.3	0.470	N/A	0.056
eil101	629	Proposed algorithm	629	629	0.000	0.000	0.000
		Yousefikhoshbakht et al. [32]	629	N/A	N/A	0.000	N/A
		Mahi et al. [31]	N/A	632.7	2.120	N/A	0.588
berlin52	7542	Proposed algorithm	7542	7542	0.000	0.000	0.000
		Yousefikhoshbakht et al. [32]	7542	N/A	N/A	0.000	N/A
		Mahi et al. [31]	N/A	7543.2	2.370	N/A	0.016
ch150	6528	Proposed algorithm	6528	6528	0.000	0.000	0.000
		Mahi et al. [31]	N/A	6563.95	27.580	N/A	0.551
lin105	14379	Proposed algorithm	14379	14379	0.000	0.000	0.000
		Yousefikhoshbakht et al. [32]	14379	N/A	N/A	0.000	N/A
		Mahi et al. [31]	N/A	14379.15	0.480	N/A	0.001
lin318	42029	Proposed algorithm	42029	42042.4	42.375	0.000	0.032
		Yousefikhoshbakht et al. [32]	42543	N/A	N/A	1.223	N/A
kroA100	21282	Proposed algorithm	21282	21282	0.000	0.000	0.000
		Yousefikhoshbakht et al. [32]	21282	N/A	N/A	0.000	N/A
		Mahi et al. [31]	N/A	21445.1	78.240	N/A	0.766
kroA150	26524	Proposed algorithm	26524	26524	0.000	0.000	0.000
		Yousefikhoshbakht et al. [32]	26611	N/A	N/A	0.328	N/A
kroA200	29368	Proposed algorithm	29368	29368	0.000	0.000	0.000
		Yousefikhoshbakht et al. [32]	29368	N/A	N/A	0.000	N/A
		Mahi et al. [31]	N/A	29646.05	114.710	N/A	0.947
kroB100	22141	Proposed algorithm	22141	22141	0.000	0.000	0.000
		Yousefikhoshbakht et al. [32]	22141	N/A	N/A	0.000	N/A
kroB150	26130	Proposed algorithm	26130	26130	0.000	0.000	0.000
		Yousefikhoshbakht et al. [32]	26202	N/A	N/A	0.276	N/A
kroB200	29437	Proposed algorithm	29437	29437	0.000	0.000	0.000
		Yousefikhoshbakht et al. [32]	29509	N/A	N/A	0.245	N/A
kroC100	20749	Proposed algorithm	20749	20749	0.000	0.000	0.000
		Yousefikhoshbakht et al. [32]	20754	N/A	N/A	0.024	N/A
kroD100	21294	Proposed algorithm	21294	21294	0.000	0.000	0.000
		Yousefikhoshbakht et al. [32]	21335	N/A	N/A	0.193	N/A
kroE100	22068	Proposed algorithm	22068	22068	0.000	0.000	0.000
		Yousefikhoshbakht et al. [32]	22068	N/A	N/A	0.000	N/A