Research Article
Boosted Sine Cosine Algorithm with Application to Medical Diagnosis
Table 3
Results of ESCA_PSO versus other algorithms on 30 benchmark functions.
| | F1 | F2 | F3 | | Avg | Std | Avg | Std | Avg | Std |
| | ESCA_PSO | 8.77+06 | 3.47+06 | 7.49+07 | 7.38+06 | 9.44+03 | 2.27+03 | | SCADE | 4.23 +08 | 9.19+07 | 2.97+10 | 4.56+09 | 5.46+04 | 6.21+03 | | SCA | 2.52+08 | 7.02+07 | 1.76+10 | 2.68+09 | 3.72+04 | 5.71+03 | | SCA_PSO | 8.01+06 | 2.83+06 | 3.83+07 | 8.40+06 | 2.99+03 | 1.04+03 | | CGSCA | 2.85+08 | 8.98+07 | 1.82+10 | 4.06+09 | 4.15+04 | 5.63+03 | | GWO | 5.76+07 | 4.69+07 | 2.18+09 | 2.05+09 | 3.24+04 | 8.29+03 | | MFO | 8.50+07 | 1.06+08 | 1.22+10 | 7.01+09 | 1.10+05 | 6.34+04 | | BA | 7.40+05 | 2.88+05 | 5.24+05 | 2.80+05 | 4.11+02 | 1.40+02 | | PSO | 9.30+06 | 2.45+06 | 1.46+08 | 1.63+07 | 9.60+02 | 9.65+01 | | LSHADE | 4.41+03 | 7.34+03 | 2.00+02 | 3.77-14 | 3.00+02 | 1.74-11 |
| | F4 | F5 | F6 | | Avg | Std | Avg | Std | Avg | Std |
| | ESCA_PSO | 4.73+02 | 3.72+01 | 5.21+02 | 4.33-02 | 6.29+02 | 3.45+00 | | SCADE | 2.40+03 | 5.90+02 | 5.21+02 | 3.58-02 | 6.35+02 | 1.86+00 | | SCA | 1.43+03 | 2.20+02 | 5.21+02 | 4.98-02 | 6.34+02 | 2.32+00 | | SCA_PSO | 4.77+02 | 4.19+01 | 5.21+02 | 6.37-02 | 6.29+02 | 3.03+00 | | CGSCA | 1.63+03 | 2.92+02 | 5.21+02 | 5.14-02 | 6.34+02 | 2.33+00 | | GWO | 7.02+02 | 2.37+02 | 5.21+02 | 5.08-02 | 6.13+02 | 2.06+00 | | MFO | 1.34+03 | 8.51+02 | 5.20+02 | 1.59-01 | 6.24+02 | 3.73+00 | | BA | 4.40+02 | 3.98+01 | 5.21+02 | 5.19-02 | 6.34+02 | 3.36+00 | | PSO | 4.68+02 | 3.39+01 | 5.21+02 | 4.82-02 | 6.23+02 | 2.99+00 | | LSHADE | 4.04+02 | 1.61+01 | 5.20+02 | 1.00-03 | 6.11+02 | 2.23+00 |
| | F7 | F8 | F9 | | Avg | Std | Avg | Std | Avg | Std |
| | ESCA_PSO | 7.02+02 | 5.88-02 | 9.83+02 | 2.14+01 | 1.13+03 | 2.09+01 | | SCADE | 9.10+02 | 3.53+01 | 1.07+03 | 1.63+01 | 1.21+03 | 1.63+01 | | SCA | 8.43+02 | 2.36+01 | 1.04+03 | 2.05+01 | 1.18+03 | 1.64+01 | | SCA_PSO | 7.01+02 | 7.70-02 | 9.97+02 | 3.65+01 | 1.13+03 | 3.53+01 | | CGSCA | 8.67+02 | 2.74+01 | 1.06+03 | 1.61+01 | 1.18+03 | 1.59+01 | | GWO | 7.23+02 | 1.75+01 | 8.81+02 | 1.77+01 | 9.99+02 | 2.43+01 | | MFO | 8.15+02 | 7.39+01 | 9.36+02 | 2.91+01 | 1.12+03 | 5.57+01 | | BA | 7.01+02 | 1.55-01 | 1.03+03 | 4.75+01 | 1.20+03 | 6.92+01 | | PSO | 7.02+02 | 1.62-01 | 9.71+02 | 2.31+01 | 1.12+03 | 3.57+01 | | LSHADE | 7.00+02 | 1.17-02 | 8.00+02 | 1.82-01 | 9.36+02 | 1.36+01 |
| | F10 | F11 | F12 | | Avg | Std | Avg | Std | Avg | Std |
| | ESCA_PSO | 4.71+03 | 6.56+02 | 5.69+03 | 6.28+02 | 1.20+03 | 3.92-01 | | SCADE | 7.41+03 | 3.71+02 | 8.10+03 | 3.58+02 | 1.20+03 | 2.15-01 | | SCA | 6.93+03 | 4.80+02 | 8.10+03 | 3.38+02 | 1.20+03 | 2.81-01 | | SCA_PSO | 5.26+03 | 7.19+02 | 5.62+03 | 7.81+02 | 1.20+03 | 3.01-01 | | CGSCA | 7.19+03 | 3.88+02 | 8.05+03 | 3.20+02 | 1.20+03 | 2.86-01 | | GWO | 3.34+03 | 4.08+02 | 3.93+03 | 4.80+02 | 1.20+03 | 8.77-01 | | MFO | 4.56+03 | 9.40+02 | 5.40+03 | 8.30+02 | 1.20+03 | 2.55-01 | | BA | 5.16+03 | 6.27+02 | 5.43+03 | 6.13+02 | 1.20+03 | 3.10-01 | | PSO | 4.97+03 | 5.63+02 | 5.70+03 | 5.81+02 | 1.20+03 | 2.82-01 | | LSHADE | 1.00+03 | 7.66-01 | 2.91+03 | 4.12+02 | 1.20+03 | 3.80-02 |
| | F13 | F14 | F15 | | Avg | Std | Avg | Std | Avg | Std |
| | ESCA_PSO | 1.30+03 | 9.71-02 | 1.40+03 | 3.81-02 | 1.52+03 | 1.41+00 | | SCADE | 1.30+03 | 3.33-01 | 1.49+03 | 1.18+01 | 2.17+04 | 7.85+03 | | SCA | 1.30+03 | 3.27-01 | 1.45+03 | 8.31+00 | 5.16+03 | 3.72+03 | | SCA_PSO | 1.30+03 | 6.25-02 | 1.40+03 | 4.86-02 | 1.52+03 | 1.49+00 | | CGSCA | 1.30+03 | 3.16-01 | 1.45+03 | 1.06+01 | 8.10+03 | 5.63+03 | | GWO | 1.30+03 | 3.97-01 | 1.41+03 | 7.06+00 | 1.82+03 | 8.98+02 | | MFO | 1.30+03 | 1.45+00 | 1.43+03 | 2.16+01 | 1.28+05 | 3.08+05 | | BA | 1.30+03 | 1.38-01 | 1.40+03 | 4.97-02 | 1.53+03 | 6.26+00 | | PSO | 1.30+03 | 7.09-02 | 1.40+03 | 1.19-01 | 1.52+03 | 1.11+00 | | LSHADE | 1.30+03 | 7.43-02 | 1.40+03 | 9.17-02 | 1.51+03 | 1.76+00 |
| | F16 | F17 | F18 | | Avg | Std | Avg | Std | Avg | Std |
| | ESCA_PSO | 1.61+03 | 3.67-01 | 4.35+05 | 2.41+05 | 1.93+06 | 6.44+05 | | SCADE | 1.61+03 | 2.26-01 | 1.58+07 | 5.49+06 | 1.54+08 | 9.16+07 | | SCA | 1.61+03 | 2.37-01 | 5.52+06 | 2.43+06 | 1.74+08 | 7.49+07 | | SCA_PSO | 1.61+03 | 4.47-01 | 1.79+05 | 1.09+05 | 7.62+05 | 4.43+05 | | CGSCA | 1.61+03 | 2.29-01 | 6.77+06 | 3.75+06 | 1.43+08 | 7.47+07 | | GWO | 1.61+03 | 7.29-01 | 1.49+06 | 1.54+06 | 2.88+06 | 1.02+07 | | MFO | 1.61+03 | 4.74-01 | 2.40+06 | 3.10+06 | 2.64+07 | 9.98+07 | | BA | 1.61+03 | 2.59-01 | 1.09+05 | 8.01+04 | 9.42+04 | 4.63+04 | | PSO | 1.61+03 | 5.31-01 | 2.76+05 | 1.21+05 | 2.19+06 | 7.43+05 | | LSHADE | 1.61+03 | 3.85-01 | 1.49+04 | 6.33+04 | 1.95+03 | 5.46+01 |
| | F19 | F20 | F21 | | Avg | Std | Avg | Std | Avg | Std |
| | ESCA_PSO | 1.92+03 | 2.29+00 | 3.81+03 | 1.57+03 | 1.29+05 | 1.10+05 | | SCADE | 2.02+03 | 1.98+01 | 2.52+04 | 1.06+04 | 2.18+06 | 1.12+06 | | SCA | 1.99+03 | 2.80+01 | 1.56+04 | 3.39+03 | 1.23+06 | 6.00+05 | | SCA_PSO | 1.92+03 | 2.72+00 | 2.47+03 | 2.22+02 | 9.35+04 | 4.63+04 | | CGSCA | 1.99+03 | 1.65+01 | 1.88+04 | 5.54+03 | 1.67+06 | 7.22+05 | | GWO | 1.94+03 | 2.47+01 | 1.97+04 | 1.35+04 | 6.56+05 | 1.16+06 | | MFO | 1.96+03 | 4.95+01 | 7.19+04 | 8.18+04 | 8.20+05 | 1.10+06 | | BA | 1.92+03 | 1.83+01 | 2.36+03 | 1.13+02 | 5.26+04 | 3.10+04 | | PSO | 1.92+03 | 2.43+00 | 2.32+03 | 7.07+01 | 1.17+05 | 6.92+04 | | LSHADE | 1.91+03 | 1.84+00 | 3.11+03 | 3.51+03 | 2.78+03 | 2.77+02 |
| | F22 | F23 | F24 | | Avg | Std | Avg | Std | Avg | Std |
| | ESCA_PSO | 2.97+03 | 2.43+02 | 2.50+03 | 0.00+00 | 2.60+03 | 0.00+00 | | SCADE | 3.11+03 | 1.85+02 | 2.50+03 | 0.00+00 | 2.60+03 | 5.15-06 | | SCA | 2.99+03 | 1.42+02 | 2.67+03 | 1.07+01 | 2.60+03 | 1.00-01 | | SCA_PSO | 3.17+03 | 2.89+02 | 2.50+03 | 0.00+00 | 2.60+03 | 0.00+00 | | CGSCA | 3.07+03 | 1.26+02 | 2.50+03 | 0.00+00 | 2.60+03 | 3.55-06 | | GWO | 2.59+03 | 1.83+02 | 2.63+03 | 9.77+00 | 2.60+03 | 9.56-04 | | MFO | 3.12+03 | 2.90+02 | 2.66+03 | 2.48+01 | 2.68+03 | 2.64+01 | | BA | 3.33+03 | 3.17+02 | 2.62+03 | 3.12-03 | 2.67+03 | 3.46+01 | | PSO | 2.90+03 | 2.61+02 | 2.62+03 | 7.09-01 | 2.63+03 | 5.18+00 | | LSHADE | 2.43+03 | 9.48+01 | 2.62+03 | 1.88-12 | 2.64+03 | 6.32+00 |
| | F25 | F26 | F27 | | Avg | Std | Avg | Std | Avg | Std |
| | ESCA_PSO | 2.70+03 | 0.00+00 | 2.70+03 | 1.27-01 | 2.90+03 | 0.00+00 | | SCADE | 2.70+03 | 0.00+00 | 2.70+03 | 4.66-01 | 3.20+03 | 2.10+02 | | SCA | 2.73+03 | 8.20+00 | 2.70+03 | 5.56-01 | 3.57+03 | 3.51+02 | | SCA_PSO | 2.70+03 | 0.00+00 | 2.77+03 | 4.48+01 | 2.90+03 | 0.00+00 | | CGSCA | 2.70+03 | 0.00+00 | 2.70+03 | 3.72-01 | 2.90+03 | 0.00+00 | | GWO | 2.71+03 | 3.94+00 | 2.74+03 | 6.01+01 | 3.32+03 | 1.24+02 | | MFO | 2.72+03 | 8.77+00 | 2.70+03 | 1.42+00 | 3.66+03 | 1.76+02 | | BA | 2.73+03 | 1.44+01 | 2.70+03 | 1.35-01 | 3.91+03 | 4.20+02 | | PSO | 2.71+03 | 5.98+00 | 2.78+03 | 4.07+01 | 3.39+03 | 2.97+02 | | LSHADE | 2.71+03 | 3.23+00 | 2.71+03 | 3.04+01 | 3.25+03 | 9.56+01 |
| | F28 | F29 | F30 | | Avg | Std | Avg | Std | Avg | Std |
| | ESCA_PSO | 3.00+03 | 0.00+00 | 3.19+03 | 8.63+01 | 3.88+03 | 6.83+02 | | SCADE | 4.96+03 | 9.21+02 | 1.91+07 | 1.01+07 | 4.90+05 | 1.70+05 | | SCA | 4.84+03 | 2.97+02 | 1.37+07 | 7.32+06 | 2.39+05 | 7.38+04 | | SCA_PSO | 3.00+03 | 0.00+00 | 1.26+04 | 3.99+04 | 1.53+04 | 1.08+04 | | CGSCA | 3.00+03 | 0.00+00 | 3.10+03 | 0.00+00 | 3.20+03 | 0.00+00 | | GWO | 3.84+03 | 2.03+02 | 6.26+05 | 2.36+06 | 4.88+04 | 4.04+04 | | MFO | 3.98+03 | 2.29+02 | 3.06+06 | 3.58+06 | 5.65+04 | 4.66+04 | | BA | 5.29+03 | 6.59+02 | 3.13+07 | 3.38+07 | 1.30+04 | 1.23+04 | | PSO | 7.32+03 | 8.69+02 | 9.61+04 | 1.83+05 | 1.44+04 | 7.29+03 | | LSHADE | 3.73+03 | 7.27+01 | 3.68+03 | 4.12+01 | 5.47+03 | 1.26+03 |
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