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Table 9 Comparison of the performance on the basis of absolute values of constitutional equations of problem 5

From: Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear systems arising in different physical models

Method Absolute values
\(f_{1} ({\mathbf{t}})\) \(f_{2} ({\mathbf{t}})\) \(f_{3} ({\mathbf{t}})\) \(f_{4} ({\mathbf{t}})\) \(f_{5} ({\mathbf{t}})\) \(f_{6} ({\mathbf{t}})\) \(f_{7} ({\mathbf{t}})\) \(f_{8} ({\mathbf{t}})\) \(f_{9} ({\mathbf{t}})\) \(f_{10} ({\mathbf{t}})\)
GA-1 2.34E−12 4.11E−12 1.33E−12 4.96E−13 3.16E−09 1.34E−09 4.15E−09 8.55E−12 1.38E−09 1.63E−15
GA-2 2.22E−13 2.55E−12 5.55E−13 1.33E−13 4.83E−09 5.90E−10 1.98E−09 2.14E−12 3.85E−09 6.43E−16
GA-3 3.21E−12 4.13E−12 3.70E−12 1.50E−12 6.53E−09 1.78E−10 9.56E−10 4.33E−12 1.93E−09 2.33E−15
GA-4 3.40E−12 1.54E−11 3.21E−12 1.53E−12 3.60E−09 4.19E−10 2.46E−09 2.81E−11 1.15E−08 2.98E−15
GA-5 1.43E−12 2.36E−13 6.44E−12 1.58E−12 1.67E−09 1.46E−10 1.00E−09 3.36E−12 5.68E−10 1.07E−15
GA-6 9.49E−14 1.24E−13 6.97E−14 9.58E−15 4.29E−10 3.29E−09 6.22E−10 4.71E−13 2.49E−09 2.95E−17
GA-7 2.63E−12 2.38E−12 3.20E−12 2.40E−12 6.10E−09 8.68E−10 1.75E−09 5.29E−13 8.11E−09 8.00E−16
GA-8 2.18E−12 3.48E−12 7.63E−12 2.96E−12 7.82E−09 3.49E−10 1.38E−09 1.43E−11 3.93E−10 8.13E−16
GA-9 8.43E−13 2.10E−12 9.20E−13 7.86E−12 2.71E−09 2.04E−11 2.43E−10 7.98E−12 7.34E−09 1.09E−15
GA-10 3.26E−12 5.36E−12 7.68E−12 4.39E−13 8.81E−10 3.05E−09 1.23E−09 1.81E−11 5.57E−10 5.88E−17
GA-11 2.34E−12 4.11E−12 1.33E−12 4.96E−13 3.16E−09 1.34E−09 4.15E−09 8.55E−12 1.38E−09 1.63E−15
GA-12 2.22E−13 2.55E−12 5.55E−13 1.33E−13 4.83E−09 5.90E−10 1.98E−09 2.14E−12 3.85E−09 6.43E−16
GA-SQP-1 3.21E−12 4.13E−12 3.70E−12 1.50E−12 6.53E−09 1.78E−10 9.56E−10 4.33E−12 1.93E−09 2.33E−15
GA-SQP-2 3.40E−12 1.54E−11 3.21E−12 1.53E−12 3.60E−09 4.19E−10 2.46E−09 2.81E−11 1.15E−08 2.98E−15
GA-SQP-3 1.43E−12 2.36E−13 6.44E−12 1.58E−12 1.67E−09 1.46E−10 1.00E−09 3.36E−12 5.68E−10 1.07E−15
GA-SQP-4 9.49E−14 1.24E−13 6.97E−14 9.58E−15 4.29E−10 3.29E−09 6.22E−10 4.71E−13 2.49E−09 2.95E−17
GA-SQP-5 2.63E−12 2.38E−12 3.20E−12 2.40E−12 6.10E−09 8.68E−10 1.75E−09 5.29E−13 8.11E−09 8.00E−16
GA-SQP-6 2.18E−12 3.48E−12 7.63E−12 2.96E−12 7.82E−09 3.49E−10 1.38E−09 1.43E−11 3.93E−10 8.13E−16
GA-SQP-7 8.43E−13 2.10E−12 9.20E−13 7.86E−12 2.71E−09 2.04E−11 2.43E−10 7.98E−12 7.34E−09 1.09E−15
GA-SQP-8 3.26E−12 5.36E−12 7.68E−12 4.39E−13 8.81E−10 3.05E−09 1.23E−09 1.81E−11 5.57E−10 5.88E−17
GA-SQP-9 2.34E−12 4.11E−12 1.33E−12 4.96E−13 3.16E−09 1.34E−09 4.15E−09 8.55E−12 1.38E−09 1.63E−15
GA-SQP-10 2.22E−13 2.55E−12 5.55E−13 1.33E−13 4.83E−09 5.90E−10 1.98E−09 2.14E−12 3.85E−09 6.43E−16
GA-SQP-11 3.21E−12 4.13E−12 3.70E−12 1.50E−12 6.53E−09 1.78E−10 9.56E−10 4.33E−12 1.93E−09 2.33E−15
GA-SQP-12 3.40E−12 1.54E−11 3.21E−12 1.53E−12 3.60E−09 4.19E−10 2.46E−09 2.81E−11 1.15E−08 2.98E−15