Epistasis-Based Basis Estimation Method for Simplifying the Problem Space of an Evolutionary Search in Binary Representation

Table 4

Results of each of the best solutions obtained by conducting the GA experiments 100 times on an instance of the -landscape problem. (‘Best’ is the best fitness among solutions found in 100 experiments, ‘Average’ is the average of 100 best solutions, and ‘SD’ is the standard deviation of 100 best solutions. , and are the first, second, and third quartiles, respectively. ‘Time’ is the sum of the time to search for the basis and that for the GA experiments.)

	Type	Best	Average	SD				Time (mm:ss
20, 3	Original	0.817	0.8135	0.0085	0.8170	0.8170	0.8170	1:02
	Meta	0.825	0.8226	0.0057	0.8250	0.8250	0.8250	5:52
	Epistasis	0.825	0.8200	0.0056	0.8170	0.8170	0.8250	1:32
20, 5	Original	0.761	0.7449	0.0157	0.7400	0.7405	0.7610	1:03
	Meta	0.761	0.7533	0.0131	0.7470	0.7610	0.7610	5:39
	Epistasis	0.761	0.7505	0.0109	0.7460	0.7470	0.7610	1:40
20, 10	Original	0.779	0.7306	0.0253	0.7020	0.7335	0.7520	1:10
	Meta	0.785	0.7572	0.0155	0.7660	0.7550	0.7660	7:13
	Epistasis	0.785	0.7558	0.0136	0.7460	0.7530	0.7653	2:16
30, 3	Original	0.776	0.7687	0.1373	0.7740	0.7760	0.7760	2:06
	Meta	0.776	0.7719	0.0109	0.7760	0.7760	0.7760	5:39
	Epistasis	0.776	0.7718	0.0090	0.7740	0.7760	0.7760	1:40
30, 5	Original	0.795	0.7725	0.0125	0.7638	0.7740	0.7870	2:06
	Meta	0.795	0.7661	0.0170	0.7540	0.7710	0.7770	32:28
	Epistasis	0.795	0.7706	0.0136	0.7623	0.7730	0.7830	2:50
30, 10	Original	0.779	0.7349	0.0181	0.7260	0.7310	0.7443	2:06
	Meta	0.805	0.7391	0.0179	0.7310	0.7370	0.7470	49:47
	Epistasis	0.796	0.7366	0.0198	0.7220	0.7335	0.7960	3:48
30, 20	Original	0.750	0.7039	0.0152	0.6938	0.7010	0.7113	2:51
	Meta	0.762	0.7181	0.0163	0.7070	0.7155	0.7243	49:47
	Epistasis	0.770	0.7220	0.0133	0.7120	0.7200	0.7300	3:48
50, 3	Original	0.776	0.7576	0.0102	0.7515	0.7590	0.7640	5:31
	Meta	0.776	0.7599	0.0119	0.7530	0.7585	0.7730	220:14
	Epistasis	0.776	0.7578	0.0096	0.7508	0.7590	0.7630	6:34

Intel (R) Core TM i7-6850K CPU @ 3.60GHz