A Multistrategy Artificial Bee Colony Algorithm Enlightened by Variable Neighborhood Search

Table 2

Objective values searched by ABC and ABCVNS for 30 and 100 ( and ) test problems.

No.	Dim	maxFEs	Methods	Best	Worst	Median	Mean	Std.	Sig.
	30	15e4	ABC	4.76e − 057	1.25e − 053	1.67e − 055	9.15e − 055	2.37e − 054	†
			ABCVNS	7.57e − 139	1.81e − 123	1.69e − 128	7.26e − 125	3.30e − 124
	30	15e4	ABC	6.66e − 048	1.15e − 044	2.82e − 046	1.43e − 045	2.67e − 045	†
			ABCVNS	3.22e − 137	7.26e − 121	5.32e − 126	2.77e − 122	1.33e − 121
	30	15e4	ABC	4.82e − 059	2.24e − 054	4.02e − 057	8.23e − 056	4.09e − 055	†
			ABCVNS	9.03e − 136	9.87e − 125	1.39e − 130	3.33e − 126	1.80e − 125
	30	15e4	ABC	1.84e − 067	1.71e − 056	1.45e − 061	6.48e − 058	3.12e − 057	†
			ABCVNS	0.00e + 00	1.43e − 160	7.01e − 216	4.76e − 162	2.61e − 161
	30	15e4	ABC	4.42e − 030	4.88e − 029	1.50e − 029	1.80e − 029	1.13e − 029	†
			ABCVNS	5.58e − 071	1.66e − 064	1.72e − 067	1.38e − 065	3.56e − 065
	30	15e4	ABC	2.78e − 001	1.55e + 000	6.44e − 001	7.15e − 001	3.04e − 001	†
			ABCVNS	4.61e − 003	1.58e − 002	1.06e − 002	1.03e − 002	2.88e − 003
	30	15e4	ABC	0	0	0	0	0
			ABCVNS	0	0	0	0	0
	30	15e4	ABC	1.72e − 123	2.49e − 117	5.55e − 120	1.74e − 118	5.92e − 118	†
			ABCVNS	3.38e − 279	4.20e − 255	1.26e − 263	1.87e − 256	0
	30	15e4	ABC	2.69e − 002	7.04e − 002	5.24e − 002	5.10e − 002	1.09e − 002	†
			ABCVNS	7.49e − 003	2.25e − 002	1.26e − 002	1.30e − 002	3.35e − 003
	30	15e4	ABC	2.92e − 004	5.32e − 001	1.24e − 002	6.99e − 002	1.28e − 001	-
			ABCVNS	1.59e − 003	7.69e + 001	2.51e + 000	1.34e + 001	2.19e + 001
	30	15e4	ABC	0	0	0	0	0
			ABCVNS	0	0	0	0	0
	30	15e4	ABC	0	0	0	0	0
			ABCVNS	0	0	0	0	0
	30	15e4	ABC	0	5.51e − 006	0	1.84e − 007	1.01e − 006
			ABCVNS	0	2.68e − 011	0	8.96e − 013	4.89e − 012
	30	15e4	ABC	0	0	0	0	0
			ABCVNS	0	0	0	0	0
	30	15e4	ABC	2.93e − 014	4.35e − 014	4.00e − 014	3.85e − 014	4.13e − 015	†
			ABCVNS	8.88e − 016	1.51e − 014	4.44e − 015	5.15e − 015	4.61e − 015
	30	15e4	ABC	1.57e − 032	1.57e − 032	1.57e − 032	1.57e − 032	5.57e − 048
			ABCVNS	1.57e − 032	1.57e − 032	1.57e − 032	1.57e − 032	5.57e − 048
	30	15e4	ABC	1.35e − 032	1.35e − 032	1.35e − 032	1.35e − 032	5.57e − 048
			ABCVNS	1.35e − 032	1.35e − 032	1.35e − 032	1.35e − 032	5.57e − 048
	30	15e4	ABC	7.37e − 014	6.54e − 009	1.65e − 011	4.13e − 010	1.34e − 009	†
			ABCVNS	3.07e − 085	3.47e − 068	1.19e − 075	1.24e − 069	6.33e − 069
	30	15e4	ABC	1.35e − 031	1.35e − 031	1.35e − 031	1.35e − 031	6.68e − 047
			ABCVNS	1.35e − 031	1.35e − 031	1.35e − 031	1.35e − 031	6.68e − 047
	30	15e4	ABC	0	7.11e − 015	0	7.11e − 016	2.17e − 015
			ABCVNS	0	0	0	0	0
	30	15e4	ABC	2.28e − 001	3.96e − 001	3.46e − 001	3.27e − 001	4.85e − 002	†
			ABCVNS	1.27e − 001	3.46e − 001	2.50e − 001	2.44e − 001	5.47e − 002
	100	15e4	ABC	−78.33233	−78.33233	−78.33233	−78.33233	2.77e − 013	-
			ABCVNS	−78.33233	−78.33233	−78.33233	−78.33233	1.36e − 009
	100	15e4	ABC	−97.03089	−95.93808	−96.36986	−96.40813		†
			ABCVNS	−9.96e + 001	−9.94e + 001	−9.95e + 001	−9.95e + 001	5.51e − 002
	30	15e4	ABC	0	0	0	0	0
			ABCVNS	0	0	0	0	0
	30	15e4	ABC	0	0	0	0	0
			ABCVNS	0	0	0	0	0
	30	15e4	ABC	0	7.26e − 004	0	2.42e − 005	1.33e − 004	†
			ABCVNS	0	1.11e − 016	0	3.70e − 018	2.03e − 017
	30	15e4	ABC	2.58e − 014	5.06e − 014	4.00e − 014	3.77e − 014	5.40e − 015	†
			ABCVNS	1.51e − 014	2.93e − 014	2.58e − 014	2.52e − 014	4.18e − 015
	30	15e4	ABC	7.44e − 012	8.57e − 007	2.11e − 009	7.05e − 008	1.90e − 007	†
			ABCVNS	6.25e − 017	1.97e − 015	9.97e − 017	2.88e − 016	4.22e − 016

“†” indicates ABCVNS is better than ABC by the Wilcoxon signed rank test at .“-” means that ABCVNS is inferior to ABC. “” means that there is no significant difference between ABCVNS and ABC.