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Table 4 Comparison of trained parameters along with their fitness for GA and GA-SQP algorithms in case of problem 2

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 1.95E−04 8.59E−05 8.04E−05 6.73E−05 2.14E−06 1.99E−04 2.03E−04 5.08E−05 2.38E−05 1.28E−04
GA-2 1.11E−04 6.11E−05 1.45E−04 1.64E−05 1.59E−04 3.00E−04 9.51E−05 1.51E−04 1.06E−04 3.37E−04
GA-3 7.70E−03 2.72E−03 7.92E−03 9.06E−03 8.95E−03 8.62E−04 3.63E−03 7.65E−03 6.87E−03 2.55E−03
GA-4 1.16E−03 8.85E−04 7.90E−04 5.93E−04 2.00E−03 8.81E−04 2.61E−04 4.13E−04 8.22E−05 1.26E−03
GA-5 6.24E−05 1.51E−06 1.10E−04 1.18E−04 3.31E−05 8.62E−06 1.83E−05 3.80E−05 9.69E−05 3.09E−05
GA-6 7.95E−05 1.03E−04 6.85E−05 1.35E−04 4.90E−05 2.66E−04 2.10E−04 2.02E−04 2.03E−04 8.51E−05
GA-7 1.15E−03 1.79E−03 1.38E−03 2.72E−04 2.27E−03 3.74E−03 2.23E−03 7.52E−04 6.01E−04 2.69E−03
GA-8 1.33E−04 4.64E−04 1.22E−04 8.29E−05 9.25E−04 5.37E−05 2.72E−05 3.39E−04 7.71E−04 7.23E−04
GA-9 4.50E−04 3.23E−05 3.72E−04 3.20E−04 8.02E−05 6.25E−04 1.68E−04 2.28E−04 5.79E−05 3.10E−04
GA-10 4.43E−04 1.85E−05 4.26E−04 7.06E−05 4.04E−05 2.16E−04 1.50E−04 2.12E−04 5.02E−04 5.50E−04
GA-11 1.13E−02 1.90E−03 2.95E−03 1.00E−02 2.57E−03 6.58E−03 4.03E−03 7.04E−03 4.98E−03 7.41E−03
GA-12 1.09E−03 7.57E−04 1.41E−03 1.54E−04 1.86E−03 1.98E−03 1.13E−03 4.83E−04 1.59E−04 4.41E−03
GA-SQP-1 3.51E−17 9.63E−17 8.33E−17 1.69E−17 2.21E−17 1.09E−16 5.20E−18 3.08E−17 1.52E−16 2.47E−17
GA-SQP-2 1.46E−16 1.65E−17 2.69E−17 1.78E−17 1.44E−16 8.24E−17 5.07E−17 3.69E−17 4.24E−17 2.58E−17
GA-SQP-3 9.06E−17 7.33E−17 7.98E−17 8.24E−18 1.32E−16 2.60E−18 5.64E−17 9.02E−17 4.36E−17 2.63E−17
GA-SQP-4 2.39E−17 1.65E−17 8.76E−17 8.67E−18 3.73E−17 3.17E−17 6.29E−17 6.11E−17 1.25E−16 7.98E−17
GA-SQP-5 8.89E−17 3.73E−17 2.69E−17 6.42E−17 3.51E−17 2.65E−17 5.29E−17 6.33E−17 9.89E−17 2.92E−17
GA-SQP-6 3.34E−17 7.16E−17 8.07E−17 3.77E−17 2.34E−17 8.24E−17 1.16E−16 9.11E−18 6.90E−17 3.01E−17
GA-SQP-7 3.43E−17 1.65E−17 2.60E−17 3.73E−17 2.17E−17 5.46E−17 6.07E−17 4.77E−18 4.23E−17 8.58E−17
GA-SQP-8 3.47E−17 1.69E−17 7.98E−17 6.42E−17 2.13E−17 4.34E−19 1.15E−16 2.17E−17 9.82E−17 2.57E−17
GA-SQP-9 3.47E−17 1.65E−17 3.21E−17 4.68E−17 9.11E−17 2.60E−18 1.17E−16 6.07E−18 4.23E−17 8.03E−17
GA-SQP-10 2.21E−17 1.69E−17 1.36E−16 6.64E−17 3.25E−17 8.67E−19 5.25E−17 5.07E−17 6.79E−17 2.96E−17
GA-SQP-11 2.13E−17 9.45E−17 2.78E−17 4.60E−17 8.98E−17 2.60E−17 6.07E−17 1.86E−17 6.87E−17 8.65E−17
GA-SQP-12 1.32E−16 1.47E−17 2.08E−17 4.38E−17 3.38E−17 2.95E−17 1.73E−18 9.41E−17 1.20E−17 3.01E−17