Mathematical Problems in Engineering / 2014 / Article / Tab 2 / Research Article
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 variablesGlobal 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