Gradient-Based Cuckoo Search for Global Optimization

Table 2

Values of the mean minima and standard deviations obtained by the CS and GBCS algorithms compared with the value of the global minima of the twenty-four benchmark problems.

Number	Benchmark function	Number of; variables	Global; min.	Number of iterations	GBCS		CS
					Mean	Std. Dev.	Mean	Std. Dev.
1	Ackley	2	0	1000	0	0	2.2204E-16	6.7752E-16
2	Beale	2	0	1000	0	0	5.7891E-30	1.2165E-29
3	Booth	2	0	1000	0	0	0	0
4	Cross-leg table	2	−1	1000	−1.1463E-2	7.672E-3	−6.2704E-3	3.6529E-3
5	Himmelblau	2	0	1000	1.7058E-28	2.836E-28	2.5958E-19	5.3451E-19
6	Levy 13	2	0	1000	1.3498E-31	6.6809E-47	1.3498E-31	6.6809E-47
7	Matyas	2	0	1000	2.7691E-54	4.728E-54	2.0407E-38	5.0616E-38
8	Schaffer	2	0	3000	0	0	7.4015E-18	1.9193E-17
9	Powell	4	0	1000	1.8694E-8	3.5848E-8	1.6296E-13	3.4802E-13
10	Power sum	4	0	1000	1.8328E-4	1.6761E-4	2.5432E-4	1.8167E-4
11	Shekel 5	4	−10.536	200	−10.536	1.6289E-5	−10.536	1.8421E-2
12	Wood	4	0	1000	2.3726	2.2208	0.40838	0.337
13	Cube	5	0	5000	1.2567	0.86542	5.782E-8	2.5596E-7
14	Stochastic cube	5	0	5000	7.7438	6.9815	6.4369	5.0292
15	Sphere	5	0	1000	2.5147E-38	5.1577E-38	1.1371E-21	1.2967E-21
16	Hartmann	6	−3.3224	200	−3.3224	4.3959E-10	−3.3215	6.0711E-4
17	Dixon-price	50	0	5000	4.7094E-2	1.6904E-1	6.6667E-1	2.6103E-6
18	Griewank	50	0	5000	0	0	3.3651E-10	9.4382E-10
19	Stochastic Griewank	50	0	5000	7.2758E-13	2.8579E-12	6.9263	2.0451
20	Michaelwicz	50		5000	−32.263	1.3729	−27.383	1.3551
21	Rosenbrock	50	0	5000	0.97368	0.5885	35.286	3.7012
22	Stochastic Rosenbrock	50	0	5000	58.599	19.122	4894.4	4678.3
23	Trigonometric	50	0	5000	5356.0	4536.0	19435	4033.7
24	Zacharov	50	0	5000	6.5769	1.3288	27.031	5.2748