Table 9 Results for further validation.
From: A novel meta-heuristic algorithm based on candidate cooperation and competition
Function | Statistic | CCCA | ESC | ODO | SBOA | Function | CCCA | ESC | ODO | SBOA |
|---|---|---|---|---|---|---|---|---|---|---|
\({{{F}}_{1}}(x)\) | Best | 1.17E−06 | 2.70E+01 | 4.27E+00 | 8.27E+03 | \({{{F}}_{13}}(x)\) | 1.10E+00 | 3.64E+00 | 1.26E+00 | 1.03E+06 |
Ave | 2.59E−06 | 4.87E+01 | 6.88E+01 | 1.09E+04 | 7.47E+00 | 2.59E+01 | 4.56E+00 | 2.68E+06 | ||
Std | 1.04E−06 | 2.11E+01 | 7.09E+01 | 1.77E+03 | 8.16E+00 | 1.69E+01 | 3.53E+00 | 1.24E+06 | ||
Least | 4.66E−06 | 9.25E+01 | 2.34E+02 | 1.34E+04 | 2.81E+01 | 6.17E+01 | 1.21E+01 | 5.42E+06 | ||
Time(s) | 1.54 | 4.11 | 0.66 | 1.07 | 2.34 | 4.55 | 0.88 | 1.48 | ||
\({{{F}}_{2}}(x)\) | Best | 1.01E+00 | 1.14E+00 | 1.92E+00 | 4.26E+01 | \({{{F}}_{14}}(x)\) | 0.2759 | 0.2759 | 0.2759 | 0.2759 |
Ave | 1.83E+00 | 2.02E+00 | 4.37E+00 | 6.13E+01 | 0.2759 | 0.2759 | 0.2759 | 0.7990 | ||
Std | 3.63E−01 | 5.63E−01 | 2.08E+00 | 1.77E+01 | 0.0000 | 0.0000 | 0.0000 | 0.3448 | ||
Least | 2.33E+00 | 3.12E+00 | 7.93E+00 | 9.78E+01 | 0.2759 | 0.2759 | 0.2759 | 1.4837 | ||
Time(s) | 1.52 | 4.29 | 0.75 | 1.01 | 7.73 | 5.67 | 1.72 | 3.56 | ||
\({{{F}}_{3}}(x)\) | Best | 1.59E+01 | 2.62E+03 | 3.79E+03 | 3.94E+06 | \({{{F}}_{15}}(x)\) | 0.0004 | 0.0007 | 0.0003 | 0.0018 |
Ave | 3.24E+02 | 1.11E+04 | 6.58E+04 | 5.53E+06 | 0.0006 | 0.0009 | 0.0008 | 0.0188 | ||
Std | 2.79E+02 | 7.86E+03 | 8.01E+04 | 9.44E+05 | 0.0001 | 0.0002 | 0.0004 | 0.0144 | ||
Least | 8.84E+02 | 2.82E+04 | 2.44E+05 | 7.35E+06 | 0.0007 | 0.0012 | 0.0012 | 0.0414 | ||
Time(s) | 1.62 | 4.56 | 0.67 | 1.03 | 0.69 | 4.07 | 0.51 | 1.11 | ||
\({{{F}}_{4}}(x)\) | Best | 7.82E+00 | 1.16E+01 | 4.26E+00 | 2.75E+01 | \({{{F}}_{16}}(x)\) | −1.0316 | −1.0316 | −1.0316 | −1.0316 |
Ave | 1.10E+01 | 1.39E+01 | 8.87E+00 | 3.80E+01 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | ||
Std | 1.75E+00 | 1.71E+00 | 3.18E+00 | 6.02E+00 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | ||
Least | 1.38E+01 | 1.76E+01 | 1.37E+01 | 4.56E+01 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | ||
Time(s) | 1.65 | 4.44 | 0.71 | 0.99 | 0.69 | 4.02 | 0.48 | 1.03 | ||
\({{{F}}_{5}}(x)\) | Best | 2.18E+01 | 1.23E+05 | 2.35E+04 | 2.84E+07 | \({{{F}}_{17}}(x)\) | 0.3979 | 0.3979 | 0.3979 | 0.3979 |
Ave | 3.53E+03 | 2.60E+05 | 1.85E+05 | 2.17E+08 | 0.3979 | 0.3979 | 0.3979 | 0.4050 | ||
Std | 6.17E+03 | 1.68E+05 | 1.43E+05 | 1.64E+08 | 0.0000 | 0.0000 | 0.0000 | 0.0181 | ||
Least | 1.97E+04 | 7.39E+05 | 5.26E+05 | 6.26E+08 | 0.3979 | 0.3979 | 0.3979 | 0.4585 | ||
Time(s) | 1.68 | 4.22 | 0.71 | 0.99 | 0.55 | 3.96 | 0.48 | 0.96 | ||
\({{{F}}_{6}}(x)\) | Best | 1.18E−06 | 1.69E+01 | 1.23E+01 | 5.58E+03 | \({{{F}}_{18}}(x)\) | 3.0000 | 3.0000 | 3.0000 | 3.0000 |
Ave | 1.97E−06 | 4.23E+01 | 7.04E+01 | 9.79E+03 | 3.0000 | 3.0000 | 3.0000 | 3.1902 | ||
Std | 4.82E−07 | 1.52E+01 | 6.88E+01 | 2.77E+03 | 0.0000 | 0.0000 | 0.0000 | 0.4335 | ||
Least | 2.68E−06 | 7.19E+01 | 2.21E+02 | 1.54E+04 | 3.0000 | 3.0000 | 3.0000 | 4.4262 | ||
Time(s) | 1.49 | 4.11 | 0.68 | 1.01 | 0.56 | 3.92 | 0.47 | 1.01 | ||
\({{{F}}_{7}}(x)\) | Best | 1.32E−03 | 4.58E−02 | 3.86E−02 | 1.06E+00 | \({{{F}}_{19}}(x)\) | −3.8628 | −3.8628 | −3.8628 | −3.8610 |
Ave | 3.22E−03 | 9.98E−02 | 9.96E−02 | 2.67E+00 | −3.8628 | −3.8628 | −3.8628 | −3.8338 | ||
Std | 1.44E−03 | 3.59E−02 | 4.13E−02 | 1.06E+00 | 0.0000 | 0.0000 | 0.0000 | 0.0286 | ||
Least | 5.92E−03 | 1.47E−01 | 1.70E−01 | 4.34E+00 | −3.8627 | −3.8628 | −3.8628 | −3.7728 | ||
Time(s) | 2.65 | 4.55 | 1.02 | 1.58 | 0.87 | 3.98 | 0.51 | 1.07 | ||
\({{{F}}_{8}}(x)\) | Best | −1.12E+04 | −7.15E+03 | −9.50E+03 | −4.36E+03 | \({{{F}}_{20}}(x)\) | −3.3220 | −3.3220 | −3.3220 | −3.2371 |
Ave | −9.87E+03 | −6.64E+03 | −8.69E+03 | −3.59E+03 | −3.3098 | −3.2975 | −3.2863 | −2.8282 | ||
Std | 6.81E+02 | 2.48E+02 | 6.03E+02 | 4.29E+02 | 0.0363 | 0.0472 | 0.0545 | 0.2925 | ||
Least | −8.66E+03 | −6.37E+03 | −7.35E+03 | −3.01E+03 | −3.2010 | −3.2031 | −3.2031 | −2.4106 | ||
Time(s) | 2.11 | 4.16 | 0.82 | 1.15 | 0.90 | 4.01 | 0.54 | 1.09 | ||
\({{{F}}_{9}}(x)\) | Best | 5.00E+00 | 9.30E+01 | 3.30E+01 | 1.86E+02 | \({{{F}}_{21}}(x)\) | −10.1532 | −10.1532 | −10.1532 | −10.1343 |
Ave | 1.05E+01 | 1.14E+02 | 4.54E+01 | 2.16E+02 | −10.1528 | −9.5991 | −6.1441 | −5.6314 | ||
Std | 3.50E+00 | 1.50E+01 | 8.64E+00 | 1.99E+01 | 0.0005 | 1.4688 | 3.3929 | 2.8659 | ||
Least | 1.80E+01 | 1.46E+02 | 5.80E+01 | 2.48E+02 | −10.1516 | −5.2009 | −2.6305 | −2.3410 | ||
Time(s) | 1.96 | 4.18 | 0.77 | 1.09 | 1.06 | 4.18 | 0.57 | 1.09 | ||
\({{{F}}_{10}}(x)\) | Best | 3.36E+00 | 1.98E+01 | 2.05E+00 | 1.40E+01 | \({{{F}}_{22}}(x)\) | −10.4028 | −10.4029 | −10.4029 | −10.3995 |
Ave | 4.08E+00 | 1.99E+01 | 3.17E+00 | 1.55E+01 | −10.4025 | −10.4014 | −8.3432 | −5.9089 | ||
Std | 6.37E−01 | 3.23E−02 | 6.57E−01 | 8.27E−01 | 0.0003 | 0.0040 | 3.1944 | 3.5255 | ||
Least | 5.23E+00 | 1.99E+01 | 4.39E+00 | 1.68E+01 | −10.4020 | −10.3895 | −2.7659 | −2.6599 | ||
Time(s) | 2.00 | 4.17 | 0.75 | 1.12 | 1.26 | 4.18 | 0.62 | 1.24 | ||
\({{{F}}_{11}}(x)\) | Best | 1.20E−03 | 1.04E−01 | 2.73E−02 | 5.69E+01 | \({{{F}}_{23}}(x)\) | −10.5363 | −10.5364 | −10.5364 | −10.5204 |
Ave | 5.45E−03 | 3.41E−01 | 5.35E−02 | 9.12E+01 | −10.5361 | −10.5364 | −9.4642 | −6.1392 | ||
Std | 2.70E−03 | 1.95E−01 | 2.39E−02 | 2.66E+01 | 0.0002 | 0.0000 | 2.1445 | 3.7675 | ||
Least | 9.75E−03 | 7.90E−01 | 9.22E−02 | 1.44E+02 | −10.5358 | −10.5363 | −5.1747 | −2.2335 | ||
Time(s) | 1.85 | 4.26 | 0.79 | 1.28 | 1.52 | 4.29 | 0.72 | 1.18 | ||
\({{{F}}_{12}}(x)\) | Best | 6.71E+01 | 7.41E+01 | 7.91E+01 | 6.73E+03 | |||||
Ave | 1.16E+02 | 1.34E+02 | 1.11E+02 | 4.81E+05 | ||||||
Std | 3.09E+01 | 4.54E+01 | 3.00E+01 | 6.36E+05 | ||||||
Least | 1.61E+02 | 2.32E+02 | 1.89E+02 | 1.95E+06 | ||||||
Time(s) | 2.17 | 4.42 | 0.84 | 1.34 |
