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. 2021 Aug 16;23(8):1053. doi: 10.3390/e23081053

Table 13.

Performance analysis on absolute errors in terms of minimum and mean values obtained by the proposed algorithm during 100 independent executions for different cases of problem 2.

ε1=0.0 ε1=0.2 ε1=0.4 ε1=0.6 ε1=0.8 ε1=1.0
Min Mean Min Mean Min Mean Min Mean Min Mean Min Mean
0.00 6.47 × 110−15 5.90 × 110−9 5.74 × 110−15 1.44 × 110−10 2.27 × 110−15 7.09 × 110−11 6.78 × 110−17 2.14 × 110−12 1.60 × 110−16 2.55 × 110−11 5.15 × 110−17 2.07 × 110−11
0.05 4.96 × 110−14 8.77 × 110−10 2.92 × 110−14 6.22 × 110−11 5.49 × 110−14 1.80 × 110−11 4.83 × 110−15 3.30 × 110−12 4.92 × 110−17 5.22 × 110−12 3.13 × 110−18 3.94 × 110−12
0.10 4.55 × 110−16 5.52 × 110−9 6.15 × 110−14 1.97 × 110−10 3.24 × 110−14 8.33 × 110−11 6.04 × 110−16 6.15 × 110−12 1.21 × 110−15 3.09 × 110−11 1.35 × 110−18 2.46 × 110−11
0.15 5.05 × 110−15 7.32 × 110−9 2.66 × 110−16 2.09 × 110−10 3.24 × 110−16 1.00 × 110−10 4.16 × 110−18 3.65 × 110−12 8.90 × 110−17 3.72 × 110−11 4.05 × 110−17 3.08 × 110−11
0.20 1.34 × 110−14 5.51 × 110−9 2.69 × 110−14 1.28 × 110−10 3.28 × 110−16 7.00 × 110−11 1.60 × 110−15 1.18 × 110−12 7.29 × 110−16 2.40 × 110−11 1.11 × 110−20 2.09 × 110−11
0.25 6.70 × 110−14 2.63 × 110−9 3.46 × 110−15 5.65 × 110−11 3.09 × 110−14 3.16 × 110−11 2.49 × 110−16 1.28 × 110−12 1.75 × 110−18 7.66 × 110−12 5.14 × 110−19 7.45 × 110−12
0.30 7.65 × 110−16 7.92 × 110−10 2.96 × 110−14 4.76 × 110−11 2.09 × 110−14 1.12 × 110−11 9.12 × 110−16 2.69 × 110−12 3.68 × 110−16 5.08 × 110−13 1.54 × 110−17 6.84 × 110−13
0.35 2.11 × 110−14 7.35 × 110−10 2.76 × 110−15 9.45 × 110−11 2.90 × 110−15 1.56 × 110−11 2.36 × 110−16 3.34 × 110−12 8.84 × 110−16 4.68 × 110−12 1.97 × 110−18 3.38 × 110−12
0.40 9.78 × 110−15 2.02 × 110−9 5.98 × 110−15 1.56 × 110−10 2.10 × 110−15 3.66 × 110−11 1.28 × 110−15 2.59 × 110−12 1.44 × 110−17 1.49 × 110−11 4.07 × 110−16 1.20 × 110−11
0.45 8.60 × 110−14 3.64 × 110−9 2.84 × 110−14 1.88 × 110−10 9.73 × 110−18 5.98 × 110−11 4.84 × 110−15 1.38 × 110−12 6.72 × 110−18 2.34 × 110−11 1.05 × 110−17 2.01 × 110−11
0.50 1.69 × 110−14 4.60 × 110−9 1.77 × 110−14 1.73 × 110−10 1.95 × 110−14 7.17 × 110−11 1.46 × 110−18 1.05 × 110−12 4.92 × 110−16 2.48 × 110−11 2.42 × 110−15 2.26 × 110−11
0.55 1.53 × 110−14 4.36 × 110−9 2.03 × 110−14 1.18 × 110−10 1.89 × 110−14 6.54 × 110−11 4.47 × 110−16 2.04 × 110−12 1.04 × 110−16 1.85 × 110−11 6.02 × 110−17 1.79 × 110−11
0.60 1.52 × 110−14 3.02 × 110−9 1.50 × 110−15 5.93 × 110−11 2.16 × 110−15 4.35 × 110−11 8.93 × 110−17 3.42 × 110−12 5.36 × 110−16 8.51 × 110−12 2.87 × 110−19 9.02 × 110−12
0.65 1.37 × 110−14 1.35 × 110−9 6.68 × 110−15 3.67 × 110−11 3.27 × 110−15 1.86 × 110−11 1.40 × 110−15 3.75 × 110−12 6.08 × 110−18 1.31 × 110−12 5.79 × 110−16 1.66 × 110−12
0.70 1.04 × 110−13 5.02 × 110−10 2.98 × 110−14 7.84 × 110−11 1.56 × 110−15 8.80 × 110−12 4.93 × 110−15 2.45 × 110−12 5.96 × 110−20 2.30 × 110−12 1.70 × 110−16 1.47 × 110−12
0.75 5.99 × 110−15 1.41 × 110−9 3.68 × 110−14 1.79 × 110−10 7.64 × 110−15 2.81 × 110−11 5.43 × 110−15 8.43 × 110−13 1.22 × 110−17 1.22 × 110−11 3.13 × 110−18 1.03 × 110−11
0.80 3.48 × 110−14 3.99 × 110−9 3.83 × 110−15 2.89 × 110−10 3.49 × 110−15 7.28 × 110−11 3.54 × 110−18 1.37 × 110−12 3.13 × 110−17 2.54 × 110−11 5.81 × 110−18 2.35 × 110−11
0.85 2.11 × 110−15 6.49 × 110−9 1.67 × 110−15 3.21 × 110−10 5.44 × 110−16 1.12 × 110−10 4.28 × 110−16 4.87 × 110−12 5.17 × 110−16 3.12 × 110−11 1.31 × 110−16 3.06 × 110−11
0.90 1.84 × 110−13 5.90 × 110−9 4.48 × 110−14 2.05 × 110−10 5.37 × 110−16 9.68 × 110−11 6.94 × 110−15 7.63 × 110−12 9.87 × 110−18 2.08 × 110−11 1.06 × 110−15 2.15 × 110−11
0.95 2.97 × 110−13 1.39 × 110−9 6.44 × 110−14 2.73 × 110−11 3.00 × 110−15 2.02 × 110−11 8.93 × 110−15 3.60 × 110−12 1.23 × 110−16 1.97 × 110−12 4.64 × 110−16 2.27 × 110−12
1.00 1.71 × 110−14 4.21 × 110−9 4.50 × 110−15 3.37 × 110−10 1.76 × 110−16 7.82 × 110−11 7.44 × 110−16 2.97 × 110−12 3.28 × 110−17 2.42 × 110−11 9.92 × 110−17 2.33 × 110−11