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

Table 3

Results of each of the best solutions obtained by conducting the GA experiments 100 times on an instance of the variant-onemax problem. (‘# of optima’ is the number of optima found during 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	# of optima	Average	SD				Time (mm:ss
20	Original	30	0.945	0.0452	0.900	0.950	1.000	0:44
	Meta	66	0.980	0.0302	0.950	1.000	1.000	3:07
	Epistasis-sq	64	0.982	0.0241	0.950	1.000	1.000	1:01
	Epistasis-cu	33	0.964	0.2760	0.950	0.950	1.000	3:11
30	Original	31	0.963	0.0329	0.930	0.970	1.000	1:09
	Meta	82	0.993	0.0155	1.000	1.000	1.000	12:15
	Epistasis-sq	47	0.979	0.0216	0.967	0.967	1.000	3:49
	Epistasis-cu	40	0.979	0.0187	0.967	0.967	1.000	7:03
50	Original	0	0.931	0.0257	0.920	0.940	0.940	2:58
	Meta	0	0.939	0.0240	0.920	0.940	0.960	136:46
	Epistasis-sq	2	0.934	0.0272	0.920	0.940	0.945	7:48
	Epistasis-cu	0	0.927	0.0272	0.900	0.920	0.940	67:59

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