Introduction
Related work
Black hole algorithm
Related work of prolonging the lifetime of WSN
Energy consumption and application models
Energy consumption model
Application model
Improvement of black hole algorithm
Levy flight strategy
Edge regeneration strategy
The pseudo-code of LEBH
Simulation experiment
The performance test of LEBH
Name | Parameters |
---|---|
LEBH | D = 50; N = 60; Levy flight rate = 0.7; selection rate = 0.65 |
BH | D = 50; N = 60 |
PSO | D = 50; N = 60; w = 0.2; c1 = \(-\)0.07; c2 = 3.74 |
GA | D = 50; N = 60; crossover rate = 0.01; mutation rate = 0.9 |
BA | D = 50; N = 60; pulse rate = 0.5; loudness = 0.6; fmin = 0; fmax = 1 |
WOA | D = 50; N = 60; Probability switch = 0.5 |
SCA | D = 50; N = 60; Probability switch = 0.5 |
BH | WOA | GA | PSO | SCA | BA | LEBH | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
f1 | –1.40E+03 | \(=\) | –1.36E+03 | > | 1.61E+05 | > | –1.22E+03 | > | 2.70E+04 | > | –1.39E+03 | > | –1.40E+03 |
f2 | 2.78E+07 | > | 8.10E+07 | > | 5.34E+09 | > | 5.97E+06 | > | 5.07E+08 | > | 5.19E+06 | > | 4.76E+06 |
f3 | 7.94E+09 | > | 4.11E+10 | > | 7.38E+19 | > | 2.45E+10 | > | 1.09E+11 | > | 5.10E+08 | < | 1.19E+09 |
f4 | 3.18E+04 | > | 6.18E+04 | > | 6.55E+05 | > | 5.83E+03 | < | 6.37E+04 | > | 1.98E+04 | < | 2.28E+04 |
f5 | –9.01E+02 | > | –8.07E+02 | > | 8.99E+04 | > | –9.38E+02 | > | 2.44E+03 | > | –9.96E+02 | > | –1.00E+03 |
f6 | –7.96E+02 | > | –6.66E+02 | > | 2.88E+04 | > | –8.04E+02 | > | 1.21E+03 | > | –8.40E+02 | < | –8.14E+02 |
f7 | –6.19E+02 | > | –3.18E+02 | > | 6.09E+06 | > | –2.39E+02 | > | –6.06E+02 | > | 9.86E+02 | > | –6.33E+02 |
f8 | –6.79E+02 | \(=\) | –6.79E+02 | \(=\) | –6.79E+02 | \(=\) | –6.79E+02 | \(=\) | –6.79E+02 | \(=\) | –6.79E+02 | \(=\) | –6.79E+02 |
f9 | –5.31E+02 | > | –5.29E+02 | > | –5.19E+02 | > | –5.30E+02 | > | –5.26E+02 | > | –5.33E+02 | > | –5.34E+02 |
f10 | –4.67E+02 | > | –2.17E+02 | > | 2.18E+04 | > | –4.64E+02 | > | 3.42E+03 | > | –4.96E+02 | > | –4.99E+02 |
f11 | 4.33E+02 | > | 4.02E+02 | > | 2.11E+03 | > | 1.74E+02 | > | 3.09E+02 | > | 7.61E+02 | > | –3.42E+02 |
f12 | 5.53E+02 | > | 6.50E+02 | > | 1.96E+03 | > | 3.37E+02 | < | 4.56E+02 | < | 8.98E+02 | > | 4.59E+02 |
f13 | 6.43E+02 | > | 8.43E+02 | > | 2.03E+03 | > | 6.86E+02 | > | 5.53E+02 | < | 1.16E+03 | > | 5.63E+02 |
f14 | 8.57E+03 | > | 8.92E+03 | > | 1.64E+04 | > | 8.11E+03 | > | 1.36E+04 | > | 8.93E+03 | > | 1.83E+03 |
f15 | 8.89E+03 | > | 1.15E+04 | > | 1.61E+04 | > | 1.03E+04 | > | 1.44E+04 | > | 8.81E+03 | > | 8.79E+03 |
f16 | 2.02E+02 | > | 2.03E+02 | > | 2.05E+02 | > | 2.03E+02 | > | 2.03E+02 | > | 2.02E+02 | > | 2.02E+02 |
f17 | 1.35E+03 | > | 1.47E+03 | > | 5.26E+03 | > | 1.18E+03 | > | 1.31E+03 | > | 2.65E+03 | > | 6.51E+02 |
f18 | 1.45E+03 | > | 1.51E+03 | > | 5.29E+03 | > | 1.28E+03 | < | 1.40E+03 | > | 2.94E+03 | > | 1.36E+03 |
f19 | 6.14E+02 | > | 6.74E+02 | > | 2.59E+07 | > | 7.75E+02 | > | 4.29E+04 | > | 5.68E+02 | > | 5.36E+02 |
f20 | 6.24E+02 | < | 6.25E+02 | > | 6.25E+02 | > | 6.25E+02 | > | 6.24E+02 | < | 6.25E+02 | > | 6.25E+02 |
f21 | 1.68E+03 | < | 1.86E+03 | > | 1.26E+04 | > | 1.59E+03 | < | 4.67E+03 | > | 1.53E+03 | < | 1.69E+03 |
f22 | 1.27E+04 | > | 1.28E+04 | > | 1.86E+04 | > | 1.20E+04 | > | 1.54E+04 | > | 1.27E+04 | > | 3.02E+03 |
f23 | 1.28E+04 | > | 1.39E+04 | > | 1.81E+04 | > | 1.36E+04 | > | 1.61E+04 | > | 1.22E+04 | < | 1.25E+04 |
f24 | 1.43E+03 | > | 1.41E+03 | > | 2.08E+03 | > | 1.47E+03 | > | 1.43E+03 | > | 1.45E+03 | > | 1.39E+03 |
f25 | 1.54E+03 | < | 1.53E+03 | < | 1.76E+03 | > | 1.68E+03 | > | 1.55E+03 | > | 1.47E+03 | < | 1.54E+03 |
f26 | 1.61E+03 | < | 1.65E+03 | < | 1.79E+03 | > | 1.70E+03 | > | 1.59E+03 | < | 1.69E+03 | > | 1.66E+03 |
f27 | 3.56E+03 | > | 3.54E+03 | > | 4.68E+03 | > | 3.91E+03 | > | 3.66E+03 | > | 3.50E+03 | > | 3.44E+03 |
f28 | 7.50E+03 | > | 8.79E+03 | > | 1.72E+04 | > | 7.92E+03 | > | 6.84E+03 | > | 1.08E+04 | > | 5.63E+03 |
\(>/=/<\) | 22/2/4 | 25/1/2 | 27/1/0 | 23/1/4 | 23/1/4 | 21/1/6 |
Clustering experiments
Dataset | Kmeans | PSO | GA | BA | WOA | SCA | BH | LEBH |
---|---|---|---|---|---|---|---|---|
Iris | 10.93% | 10.00% | 20.93% | 13.20% | 9.40% | 21.80% | 9.67% | 8.73% |
Cmc | 60.27% | 60.07% | 59.58% | 60.41% | 60.11% | 60.07% | 59.84% | 59.06% |
Wine | 29.78% | 28.26% | 29.38% | 28.60% | 28.26% | 28.71% | 28.31% | 28.09% |
Seeds | 10.71% | 10.57% | 22.29% | 10.43% | 10.81% | 14.29% | 10.48% | 10.48% |
Experimental parameters of prolong the lifetime of the WSN
Parameters | Values |
---|---|
Bound | \(100 m \times 100 m\) |
Number of nodes | 100 |
Initial energy | 0.2 J |
\(E_{elec}\) | \(50 pJ/bit\) |
\(E_{mp}\) | \(0.0013 pJ/bit/m^4\) |
\(E_{fs}\) | \(10 pJ/bit/m^2\) |
Data message b | \(500 bytes/message\) |
q | 1000 |
\(\alpha \) | 0.75 |
a | \(5 nJ/number\) |
Simulation experiment of LEBH-BS, Random-BS and Static-BS
Algorithm | First node die | Last node die |
---|---|---|
LEBH-BS | 1.56E+03 | 4.32E+03 |
Random-BS | 9.25E+02 | 2.67E+03 |
Static-BS | 7.17E+02 | 2.23E+03 |
Simulation experiment of LEBH-BS and other heuristic algorithms
Algorithm | First node die | Last node die |
---|---|---|
LEBH-BS | 1.56E+03 | 4.32E+03 |
PSO-BS | 1.53E+03 | 4.23E+03 |
WOA-BS | 1.52E+03 | 4.24E+03 |
BH-BS | 1.51E+03 | 4.25E+03 |
GA-BS | 1.51E+03 | 4.27E+03 |
GWO-BS | 1.53E+03 | 4.27E+03 |
SCA-BS | 1.52E+03 | 4.27E+03 |
Algorithm | p value of First node die | p value of last node die |
---|---|---|
PSO-BS | 3.13E-03 | 1.03E-03 |
WOA-BS | 3.29E-03 | 3.54E-03 |
BH-BS | 2.83E-04 | 1.40E-02 |
GA-BS | 2.74E-03 | 4.98E-023 |
GWO-BS | 5.33E-033 | 6.50E-02 |
SCA-BS | 1.48E-04 | 9.10E-02 |