An Algorithm for Global Optimization Inspired by Collective Animal Behavior

Table 3

Minimization result of benchmark functions in Table 12 with 𝑛=30. Maximum number of iterations = 1000.

		RGA	PSO	GSA	DE	CAB
𝑓1	Average best sofar	23.13	1.8×10^−3	7.3×10^−11	11.21	𝟐.𝟑×𝟏𝟎^−𝟐𝟗
	Median best sofar	21.87	1.2×10^−3	7.1×10^−11	13.21	𝟏.𝟏×𝟏𝟎^−𝟐𝟎
	Average mean fitness	23.45	1.2×10^−2	2.1×10^−10	11.78	𝟏.𝟐×𝟏𝟎^−𝟏𝟎
𝑓2	Average best sofar	1.07	2.0	4.03×10^−5	0.95	𝟓.𝟐𝟖×𝟏𝟎^−𝟐𝟎
	Median best sofar	1.13	1.9×10^−3	4.07×10^−5	1.05	𝟐.𝟖𝟖×𝟏𝟎^−𝟏𝟏
	Average mean fitness	1.07	2.0	6.9×10^−5	0.90	𝟏.𝟒𝟑×𝟏𝟎^−𝟗
𝑓3	Average best sofar	5.6×10^3	4.1×10^3	0.16×10^3	0.12	𝟕.𝟔𝟐×𝟏𝟎^−𝟑𝟏
	Median best sofar	5.6×10^3	2.2×10^3	0.15×10^3	0.09	𝟏.𝟐𝟖×𝟏𝟎^−𝟏𝟗
	Average mean fitness	5.6×10^3	2.9×10^3	0.16×10^3	0.11	𝟑.𝟓𝟏×𝟏𝟎^−𝟏𝟐
𝑓4	Average best sofar	11.78	8.1	3.7×10^−6	0.012	𝟐.𝟏𝟕×𝟏𝟎^−𝟏𝟕
	Median best sofar	11.94	7.4	3.7×10^−6	0.058	𝟓.𝟔𝟓×𝟏𝟎^−𝟏𝟐
	Average mean fitness	11.78	23.6	8.5×10^−6	0.013	𝟒.𝟗𝟔×𝟏𝟎^−𝟏𝟎
𝑓5	Average best sofar	1.1×10^3	3.6×10^4	25.16	0.25	𝟗.𝟎𝟐𝟓×𝟏𝟎^−𝟐𝟖
	Median best sofar	1.0×10^3	1.7×10^3	25.18	0.31	𝟑.𝟏𝟎×𝟏𝟎^−𝟏𝟖
	Average mean fitness	1.1×10^3	3.7×10^4	25.16	0.24	𝟔.𝟎𝟒×𝟏𝟎^−𝟏𝟒
𝑓6	Average best sofar	24.01	1.0×10^−3	8.3×10^−11	1.25×10^−3	𝟒.𝟒𝟕×𝟏𝟎^−𝟐𝟗
	Median best sofar	24.55	6.6×10^−3	7.7×10^−11	3.33×10^−3	𝟒.𝟐𝟔×𝟏𝟎^−𝟐𝟏
	Average mean fitness	24.52	0.02	2.6×10^−10	1.27×10^−3	𝟏.𝟎𝟑×𝟏𝟎^−𝟏𝟐
𝑓7	Average best sofar	0.06	0.04	0.018	6.87×10^−3	𝟑.𝟒𝟓×𝟏𝟎^−𝟓
	Median best sofar	0.06	0.04	0.015	4.72×10^−3	𝟕.𝟑𝟗×𝟏𝟎^−𝟒
	Average mean fitness	0.56	1.04	0.533	1.28×10^−2	𝟖.𝟕𝟓×𝟏𝟎^−𝟒