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Partial convolution for total variation deblurring and denoising by new linearized alternating direction method of multipliers with extension step
Improved particle swarm optimization and neighborhood field optimization by introducing the re-sampling step of particle filter
1. | Research and Development Center, China Academy of Launch Vehicle Technology, Fengtai District, Beijing 100076, China |
2. | Institute of Intelligent Engineering and Mathematics, Liaoning Technical University, Fuxin City, Liaoning Province 123000, China |
3. | Department of Industrial and Systems Engineering, University of Pretoria, Pretoria 0002, South Africa |
A technique of introducing the re-sampling step of particle filter is proposed to improve the particle swarm optimization (PSO) algorithm, a typical global search algorithm. The re-sampling step can decrease particles with low weights and duplicate particles with high weights, given that we define a type of suitable weights for the particles. To prevent the identity of particles, the re-sampling step is followed by the existing method of particle variation. Through this technique, the local search capability is enhanced greatly in the later searching stage of PSO algorithm. More interesting, this technique can also be employed to improve another algorithm of which the philosophy is "learning from neighbors", i.e., the neighborhood field optimization (NFO) algorithm. The improved algorithms (PSO-resample and NFO-resample) are compared with other metaheuristic algorithms through extensive simulations. The experiments show that the improved algorithms are superior in terms of convergence rate, search accuracy and robustness. Our results also suggest that the proposed technique can be general in the sense that it can probably improve other particle-based intelligent algorithms.
References:
[1] |
K. Amin and M. Guerrero-Zapata, A hybrid multiobjective RBF-PSO method for mitigating dos attacks in named data networking, Neurocomputing, 151 (2015), 1262-1282. Google Scholar |
[2] |
K. Amin and M. Guerrero-Zapata, A fuzzy anomaly detection system based on hybrid PSO-Kmeans algorithm in content-centric networks, Neurocomputing, 149 (2015), 1253-1269. Google Scholar |
[3] |
M. S. Arulampalam, S. Maskell, N. Gordon and T. clapp,
A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking, IEEE Transactions on Signal Processing, 50 (2002), 174-188.
doi: 10.1109/78.978374. |
[4] |
T. M. Blackwell and P. Bentley,
Don'T push me! Collision-avoiding swarms, Proceedings of the 2002 Congress on Evolutionary Computation, 2 (2002), 1691-1696.
doi: 10.1109/CEC.2002.1004497. |
[5] |
J. Carpenter, P. Clifford and F. Fearnhead, An improved particle filter for non-linear problems, IEE Proceedings-Radar, Sonar and Navigation, 146 (1999), 2-7. Google Scholar |
[6] |
M. Clerc and J. Kennedy,
The particle swarm-explosion, stability, and convergence in a multidimensional complex space, IEEE Transactions on Evolutionary Computation, 6 (2002), 58-73.
doi: 10.1109/4235.985692. |
[7] |
D. Crisan and A. Doucet,
A survey of convergence result on particle filtering methods for practitioners, IEEE Transactions on Signal Processing, 50 (2002), 736-746.
doi: 10.1109/78.984773. |
[8] |
A. Doucet, S. Godsill and C. Andrieu, On sequential Monte Carlo sampling method for Bayesian filtering, Statistics and Computing, 10 (2000), 197-208. Google Scholar |
[9] | A. Doucet, J. Freitas and N. Gordon, Sequential Monte Carlo Methods in Practice, Springer-Verlag, 2001. Google Scholar |
[10] |
R. C. Eberhart and J. Kennedy,
A new optimizer using particle swarm theory, Proceedings of the 6th International Symposium on Micro machine and Human Science, (1995), 39-43.
doi: 10.1109/MHS.1995.494215. |
[11] |
F. Glover,
Tabu search-part Ⅱ, ORSA Journal on Computing, 2 (1990), 4-32.
doi: 10.1287/ijoc.2.1.4. |
[12] | D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, New York, 1989. Google Scholar |
[13] |
N. J. Gordon, D. J. Salmond and A. F. M. Smith,
Novel approach to nonlinear/non-Gaussian Bayesian state estimation, Radar and Signal Processing, IEE Proceedings F, 140 (1993), 107-113.
doi: 10.1049/ip-f-2.1993.0015. |
[14] |
R. Greiner,
POLO: A probabilistic hill-climbing algorithm, Artificial Intelligence, 84 (1996), 177-208.
doi: 10.1016/0004-3702(95)00040-2. |
[15] |
J. Grobler, A. P. Engelbrecht, G. Kendall and S. Yadavalli, Heuristic space diversity control for improved meta-hyper-heuristic performance, Information Sciences, 300 (2015), 49-62. Google Scholar |
[16] |
J. Grobler and A. P. Engelbrecht, Headless chicken particle swarm optimization algorithms, Tan Y., Shi Y., Niu B. (eds) Advances in Swarm Intelligence. ICSI 2016. Lecture Notes in Computer Science, 9712 (2016), 350-357.
doi: 10.1007/978-3-319-41000-5_35. |
[17] |
J. Grobler and A. P. Engelbrecht,
A scalability analysis of particle swarm optimization roaming behaviour, Advances in Swarm Intelligence. ICSI 2017. Lecture Notes in Computer Science, 10385 (2017), 119-130.
doi: 10.1007/978-3-319-61824-1_13. |
[18] |
J. D. Hol, T. B. Schon and F. Gustafsson,
On resampling algorithms for particle filters, IEEE Nonlinear Statistical Signal Processing Workshop, (2006), 79-82.
doi: 10.1109/NSSPW.2006.4378824. |
[19] |
B. J. Jain, H. Pohlheim and W. Joachim, On termination criteria of evolutionary algorithms, Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation, (2001), 768-775. Google Scholar |
[20] |
J. Kennedy and R. C. Eberhart,
Particle swarm optimization, Proceedings of the IEEE International Conference on Neural Networks, (1995), 1942-1948.
doi: 10.1109/ICNN.1995.488968. |
[21] |
J. Kennedy and R. Mendes,
Population structure and particle swarm performance, Proceedings of the 2002 Congress on Evolutionary Computation, 2 (2002), 1671-1676.
doi: 10.1109/CEC.2002.1004493. |
[22] |
S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi,
Optimization by simulated annealing, Science, 220 (1983), 671-680.
doi: 10.1126/science.220.4598.671. |
[23] |
G. Kitagawa,
Monte Carlo filter and smoother for non-Gaussian nonlinear state space models, Journal of Computational and Graphical Statistics, 5 (1996), 1-25.
|
[24] |
J. Lampinen and R. Storn, Differential evolution, Onwubolu G, Babu BV (eds) New Optimization Techniques in Engineering, (2004), 123-166.
doi: 10.1007/978-3-540-39930-8_6. |
[25] |
J. J. Liang, A. K. Qin, P. N. Suganthan and S. Baskar,
Comprehensive learning particle swarm optimizer for global optimization of multimodal functions, IEEE Transactions on Evolutionary Computation, 10 (2006), 281-295.
doi: 10.1109/TEVC.2005.857610. |
[26] |
J. S. Liu and R. Chen,
Sequential Monte Carlo methods for dynamic systems, Journal of the American Statistical Association, 93 (1998), 1032-1044.
doi: 10.1080/01621459.1998.10473765. |
[27] |
R. Mendes, J. Kennedy and J. Neves,
The fully informed particle swarm: simpler, maybe better, IEEE Transactions on Evolutionary Computation, 8 (2004), 204-210.
doi: 10.1109/TEVC.2004.826074. |
[28] |
K. E. Parsopoulos and M. N. Vrahatis, UPSO-A unified particle swarm optimization scheme, Lecture Series on Computational Sciences, 1 (2004), 868-873. Google Scholar |
[29] |
T. Peram, K. Veeramachaneni and C. K. Mohan,
Fitness-distance-ratio based particle swarm optimization, Proceedings of the 2003 IEEE on Swarm Intelligence Symposium, (2003), 174-181.
doi: 10.1109/SIS.2003.1202264. |
[30] |
Y. Shi and R. C. Eberhart,
A modified particle swarm optimizer, IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence, (1998), 69-73.
doi: 10.1109/ICEC.1998.699146. |
[31] |
R. Storn and K. Price,
Differential evolutional simple and efficient heuristic for global optimization over continuous space, Journal of Global Optimization, 11 (1997), 341-359.
doi: 10.1023/A:1008202821328. |
[32] |
P. N. Suganthan, Particle swarm optimiser with neighborhood operator, Proceedings of the 1999 Congress on Evolutionary Computation, 3 (1999), 1958-1962. Google Scholar |
[33] |
M. D. Vose, Simple Genetic Algorithm: Foundation and Theory, MIT Press, MI, 1999.
![]() |
[34] |
Z. Wu and T. W. S. Chow,
A local multiobjective optimization algorithm using neighborhood field, Structural and Multidisciplinary Optimization, 46 (2012), 853-870.
doi: 10.1007/s00158-012-0800-x. |
[35] |
Z. Wu and T. W. S. Chow,
Neighborhood field for cooperative optimization, Soft Computing, 17 (2013), 819-834.
doi: 10.1007/s00500-012-0955-9. |
[36] |
Z. Wu and T. W. S. Chow, Binary neighborhood field optimization for unit commitment problems, IET Generation Transmission and Distribution, 7 (2013), 299-308. Google Scholar |
[37] |
C. Yang, L. Gu and W. Gui, Particle swarm optimization algorithm with adaptive mutation, Computer Engineering, 34 (2008), 188-190. Google Scholar |
[38] |
X. Yao, Y. Liu and G. M. Lin, Evolutionary programming made faster, IEEE Transactions on Evolutionary Computation, 3 (1999), 82-102. Google Scholar |
[39] |
B. Yao, B. Yu, P. Hu, J. Gao and M. H. Zhang,
An improved particle swarm optimization for carton heterogeneous vehicle routing problem with a collection depot, Annals of Operations Research, 242 (2016), 303-320.
doi: 10.1007/s10479-015-1792-x. |
[40] |
T. T. Zhao, Q. F. Cheng and Z. F. Wang, Nonlinear model predictive control optimization with improved particle swarm algorithm, Liaoning Gongcheng Jishu Daxue Xuebao (Ziran Kexue Ban)/Journal of Liaoning Technical University (Natural Science Edition), 34 (2015), 517-522. Google Scholar |
show all references
References:
[1] |
K. Amin and M. Guerrero-Zapata, A hybrid multiobjective RBF-PSO method for mitigating dos attacks in named data networking, Neurocomputing, 151 (2015), 1262-1282. Google Scholar |
[2] |
K. Amin and M. Guerrero-Zapata, A fuzzy anomaly detection system based on hybrid PSO-Kmeans algorithm in content-centric networks, Neurocomputing, 149 (2015), 1253-1269. Google Scholar |
[3] |
M. S. Arulampalam, S. Maskell, N. Gordon and T. clapp,
A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking, IEEE Transactions on Signal Processing, 50 (2002), 174-188.
doi: 10.1109/78.978374. |
[4] |
T. M. Blackwell and P. Bentley,
Don'T push me! Collision-avoiding swarms, Proceedings of the 2002 Congress on Evolutionary Computation, 2 (2002), 1691-1696.
doi: 10.1109/CEC.2002.1004497. |
[5] |
J. Carpenter, P. Clifford and F. Fearnhead, An improved particle filter for non-linear problems, IEE Proceedings-Radar, Sonar and Navigation, 146 (1999), 2-7. Google Scholar |
[6] |
M. Clerc and J. Kennedy,
The particle swarm-explosion, stability, and convergence in a multidimensional complex space, IEEE Transactions on Evolutionary Computation, 6 (2002), 58-73.
doi: 10.1109/4235.985692. |
[7] |
D. Crisan and A. Doucet,
A survey of convergence result on particle filtering methods for practitioners, IEEE Transactions on Signal Processing, 50 (2002), 736-746.
doi: 10.1109/78.984773. |
[8] |
A. Doucet, S. Godsill and C. Andrieu, On sequential Monte Carlo sampling method for Bayesian filtering, Statistics and Computing, 10 (2000), 197-208. Google Scholar |
[9] | A. Doucet, J. Freitas and N. Gordon, Sequential Monte Carlo Methods in Practice, Springer-Verlag, 2001. Google Scholar |
[10] |
R. C. Eberhart and J. Kennedy,
A new optimizer using particle swarm theory, Proceedings of the 6th International Symposium on Micro machine and Human Science, (1995), 39-43.
doi: 10.1109/MHS.1995.494215. |
[11] |
F. Glover,
Tabu search-part Ⅱ, ORSA Journal on Computing, 2 (1990), 4-32.
doi: 10.1287/ijoc.2.1.4. |
[12] | D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, New York, 1989. Google Scholar |
[13] |
N. J. Gordon, D. J. Salmond and A. F. M. Smith,
Novel approach to nonlinear/non-Gaussian Bayesian state estimation, Radar and Signal Processing, IEE Proceedings F, 140 (1993), 107-113.
doi: 10.1049/ip-f-2.1993.0015. |
[14] |
R. Greiner,
POLO: A probabilistic hill-climbing algorithm, Artificial Intelligence, 84 (1996), 177-208.
doi: 10.1016/0004-3702(95)00040-2. |
[15] |
J. Grobler, A. P. Engelbrecht, G. Kendall and S. Yadavalli, Heuristic space diversity control for improved meta-hyper-heuristic performance, Information Sciences, 300 (2015), 49-62. Google Scholar |
[16] |
J. Grobler and A. P. Engelbrecht, Headless chicken particle swarm optimization algorithms, Tan Y., Shi Y., Niu B. (eds) Advances in Swarm Intelligence. ICSI 2016. Lecture Notes in Computer Science, 9712 (2016), 350-357.
doi: 10.1007/978-3-319-41000-5_35. |
[17] |
J. Grobler and A. P. Engelbrecht,
A scalability analysis of particle swarm optimization roaming behaviour, Advances in Swarm Intelligence. ICSI 2017. Lecture Notes in Computer Science, 10385 (2017), 119-130.
doi: 10.1007/978-3-319-61824-1_13. |
[18] |
J. D. Hol, T. B. Schon and F. Gustafsson,
On resampling algorithms for particle filters, IEEE Nonlinear Statistical Signal Processing Workshop, (2006), 79-82.
doi: 10.1109/NSSPW.2006.4378824. |
[19] |
B. J. Jain, H. Pohlheim and W. Joachim, On termination criteria of evolutionary algorithms, Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation, (2001), 768-775. Google Scholar |
[20] |
J. Kennedy and R. C. Eberhart,
Particle swarm optimization, Proceedings of the IEEE International Conference on Neural Networks, (1995), 1942-1948.
doi: 10.1109/ICNN.1995.488968. |
[21] |
J. Kennedy and R. Mendes,
Population structure and particle swarm performance, Proceedings of the 2002 Congress on Evolutionary Computation, 2 (2002), 1671-1676.
doi: 10.1109/CEC.2002.1004493. |
[22] |
S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi,
Optimization by simulated annealing, Science, 220 (1983), 671-680.
doi: 10.1126/science.220.4598.671. |
[23] |
G. Kitagawa,
Monte Carlo filter and smoother for non-Gaussian nonlinear state space models, Journal of Computational and Graphical Statistics, 5 (1996), 1-25.
|
[24] |
J. Lampinen and R. Storn, Differential evolution, Onwubolu G, Babu BV (eds) New Optimization Techniques in Engineering, (2004), 123-166.
doi: 10.1007/978-3-540-39930-8_6. |
[25] |
J. J. Liang, A. K. Qin, P. N. Suganthan and S. Baskar,
Comprehensive learning particle swarm optimizer for global optimization of multimodal functions, IEEE Transactions on Evolutionary Computation, 10 (2006), 281-295.
doi: 10.1109/TEVC.2005.857610. |
[26] |
J. S. Liu and R. Chen,
Sequential Monte Carlo methods for dynamic systems, Journal of the American Statistical Association, 93 (1998), 1032-1044.
doi: 10.1080/01621459.1998.10473765. |
[27] |
R. Mendes, J. Kennedy and J. Neves,
The fully informed particle swarm: simpler, maybe better, IEEE Transactions on Evolutionary Computation, 8 (2004), 204-210.
doi: 10.1109/TEVC.2004.826074. |
[28] |
K. E. Parsopoulos and M. N. Vrahatis, UPSO-A unified particle swarm optimization scheme, Lecture Series on Computational Sciences, 1 (2004), 868-873. Google Scholar |
[29] |
T. Peram, K. Veeramachaneni and C. K. Mohan,
Fitness-distance-ratio based particle swarm optimization, Proceedings of the 2003 IEEE on Swarm Intelligence Symposium, (2003), 174-181.
doi: 10.1109/SIS.2003.1202264. |
[30] |
Y. Shi and R. C. Eberhart,
A modified particle swarm optimizer, IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence, (1998), 69-73.
doi: 10.1109/ICEC.1998.699146. |
[31] |
R. Storn and K. Price,
Differential evolutional simple and efficient heuristic for global optimization over continuous space, Journal of Global Optimization, 11 (1997), 341-359.
doi: 10.1023/A:1008202821328. |
[32] |
P. N. Suganthan, Particle swarm optimiser with neighborhood operator, Proceedings of the 1999 Congress on Evolutionary Computation, 3 (1999), 1958-1962. Google Scholar |
[33] |
M. D. Vose, Simple Genetic Algorithm: Foundation and Theory, MIT Press, MI, 1999.
![]() |
[34] |
Z. Wu and T. W. S. Chow,
A local multiobjective optimization algorithm using neighborhood field, Structural and Multidisciplinary Optimization, 46 (2012), 853-870.
doi: 10.1007/s00158-012-0800-x. |
[35] |
Z. Wu and T. W. S. Chow,
Neighborhood field for cooperative optimization, Soft Computing, 17 (2013), 819-834.
doi: 10.1007/s00500-012-0955-9. |
[36] |
Z. Wu and T. W. S. Chow, Binary neighborhood field optimization for unit commitment problems, IET Generation Transmission and Distribution, 7 (2013), 299-308. Google Scholar |
[37] |
C. Yang, L. Gu and W. Gui, Particle swarm optimization algorithm with adaptive mutation, Computer Engineering, 34 (2008), 188-190. Google Scholar |
[38] |
X. Yao, Y. Liu and G. M. Lin, Evolutionary programming made faster, IEEE Transactions on Evolutionary Computation, 3 (1999), 82-102. Google Scholar |
[39] |
B. Yao, B. Yu, P. Hu, J. Gao and M. H. Zhang,
An improved particle swarm optimization for carton heterogeneous vehicle routing problem with a collection depot, Annals of Operations Research, 242 (2016), 303-320.
doi: 10.1007/s10479-015-1792-x. |
[40] |
T. T. Zhao, Q. F. Cheng and Z. F. Wang, Nonlinear model predictive control optimization with improved particle swarm algorithm, Liaoning Gongcheng Jishu Daxue Xuebao (Ziran Kexue Ban)/Journal of Liaoning Technical University (Natural Science Edition), 34 (2015), 517-522. Google Scholar |




Algorithm | parameters |
Improved PSO | |
Standard PSO | |
Improved NFO | |
Standard NFO | |
PSO-cf-local | |
UPSO | |
FDRPSO | |
CLPSO | |
LDWPSO | |
DE |
Algorithm | parameters |
Improved PSO | |
Standard PSO | |
Improved NFO | |
Standard NFO | |
PSO-cf-local | |
UPSO | |
FDRPSO | |
CLPSO | |
LDWPSO | |
DE |
| Range of |
Theoretical optimum |
[-100,100] | 0 | |
[-10, 10] | 0 | |
[-100,100] | 0 | |
[-100,100] | 0 | |
[-100,100] | 0 | |
[-100,100] | 0 | |
[-1.28, 1.28] | 0 | |
[-5.12, 5.12] | 0 | |
[-30, 30] | 0 | |
[-600,600] | 0 | |
[-50, 50] | 0 | |
|
[-50, 50] | 0 |
[-65.536, 65.536] | 1 | |
[-5, 5] | 0.0003075 | |
[-5, 5] | -1.03163 | |
0.398 | ||
3 | ||
-3.32 | ||
| Range of |
Theoretical optimum |
[-100,100] | 0 | |
[-10, 10] | 0 | |
[-100,100] | 0 | |
[-100,100] | 0 | |
[-100,100] | 0 | |
[-100,100] | 0 | |
[-1.28, 1.28] | 0 | |
[-5.12, 5.12] | 0 | |
[-30, 30] | 0 | |
[-600,600] | 0 | |
[-50, 50] | 0 | |
|
[-50, 50] | 0 |
[-65.536, 65.536] | 1 | |
[-5, 5] | 0.0003075 | |
[-5, 5] | -1.03163 | |
0.398 | ||
3 | ||
-3.32 | ||
80 | mean | 1.1697e-23 | 1.4034e-22 | 1.3997e-19 | 1.5248e-17 | |
variance | 3.1624e-45 | 1.7331e-43 | 1.9198e-37 | 9.7892e-34 | ||
100 | mean | 1.2345e-24 | 3.4313e-23 | 6.7734e-20 | 1.3077e-17 | |
variance | 1.2889e-47 | 4.0997e-45 | 5.7511e-38 | 1.7539e-33 | ||
150 | mean | 4.8036e-24 | 5.5423e-22 | 4.7328e-19 | 1.5124e-17 | |
variance | 5.3061e-46 | 1.6406e-42 | 1.4786e-36 | 4.8891e-34 | ||
200 | mean | 3.4374e-23 | 2.2118e-21 | 8.3626e-19 | 9.8416e-17 | |
variance | 2.0994e-44 | 1.6926e-41 | 3.6846e-36 | 5.8052e-32 | ||
300 | mean | 3.7652e-23 | 8.6217e-21 | 9.6451e-18 | 1.7330e-16 | |
variance | 1.6413e-44 | 3.3834e-40 | 6.4054e-34 | 8.3178e-32 | ||
80 | mean | 23.0984 | 15.5308 | 15.6512 | 17.5839 | |
variance | 1.3502e+03 | 0.2934 | 0.8921 | 132.7182 | ||
100 | mean | 15.4714 | 15.4349 | 15.4707 | 15.5330 | |
variance | 0.3979 | 0.4585 | 1.4279 | 0.9254 | ||
150 | mean | 15.5411 | 15.5168 | 15.5302 | 15.8413 | |
variance | 0.4272 | 0.9433 | 0.7471 | 1.0840 | ||
200 | mean | 15.7879 | 15.5266 | 15.9301 | 18.0431 | |
variance | 0.4044 | 1.6317 | 1.9228 | 132.4126 | ||
300 | mean | 15.9560 | 15.5901 | 17.9298 | 19.8994 | |
variance | 1.3168 | 0.5490 | 119.4753 | 236.7976 | ||
80 | mean | 14.2808 | 13.4628 | 14.0816 | 15.6759 | |
variance | 18.3861 | 70.4926 | 30.3199 | 46.6280 | ||
100 | mean | 14.1719 | 11.2533 | 12.9326 | 15.5054 | |
variance | 19.8901 | 21.2570 | 36.3528 | 79.5550 | ||
150 | mean | 14.8875 | 12.1143 | 13.0902 | 14.8153 | |
variance | 20.5411 | 29.8877 | 37.4915 | 30.4357 | ||
200 | mean | 15.5786 | 13.5650 | 13.6945 | 15.0470 | |
variance | 37.2106 | 26.6829 | 59.1946 | 39.4785 | ||
300 | mean | 16.3959 | 14.1838 | 15.1895 | 15.7031 | |
variance | 35.1016 | 37.6114 | 42.1339 | 69.3613 | ||
80 | mean | 0.0093 | 0.0089 | 0.0164 | 0.0165 | |
variance | 5.5534e-04 | 3.3844e-04 | 8.0860e-04 | 5.2949e-04 | ||
100 | mean | 0.0092 | 0.0064 | 0.0121 | 0.0156 | |
variance | 4.5978e-04 | 2.2374e-04 | 5.6635e-04 | 5.1330e-04 | ||
150 | mean | 0.0165 | 0.0157 | 0.0153 | 0.0191 | |
variance | 0.0018 | 5.5528e-04 | 4.3368e-04 | 0.0025 | ||
200 | mean | 0.0328 | 0.0179 | 0.0245 | 0.0305 | |
variance | 0.0098 | 5.0790e-04 | 0.0010 | 0.0019 | ||
300 | mean | 0.1185 | 0.0489 | 0.0608 | 0.0676 | |
variance | 0.0615 | 0.0124 | 0.0142 | 0.0109 | ||
80 | mean | 1.1567 | 1.2361 | 1.0774 | 1.2361 | |
variance | 0.2897 | 0.4157 | 0.1512 | 0.4157 | ||
100 | mean | 1.3155 | 1.0774 | 0.1512 | 1.3155 | |
variance | 0.5291 | 0.1512 | 0.4157 | 0.5291 | ||
150 | mean | -1.1567 | 1.4680 | 1.1567 | 1.2361 | |
variance | 0.2897 | 3.7509 | 0.2897 | 0.4157 | ||
200 | mean | 1.0774 | 1.1567 | 1.3155 | 1.0774 | |
variance | 0.1512 | 0.2897 | 0.5291 | 0.1512 | ||
300 | mean | 1.2361 | 1.3948 | 1.2361 | 1.2755 | |
variance | 0.4157 | 0.6299 | 0.4157 | 0.5908 | ||
| 80 | mean | -1.0316 | -1.0316 | -1.0316 | -1.0316 |
variance | 3.6682e-31 | 7.8886e-32 | 1.0847e-31 | 1.2030e-31 | ||
100 | mean | -1.0316 | -1.0316 | -1.0316 | -1.0316 | |
variance | 7.4942e-32 | 1.0255e-31 | 1.0255e-31 | 9.0719e-32 | ||
150 | mean | -1.0316 | -1.0316 | -1.0316 | -1.0316 | |
variance | 5.5220e-32 | 7.2970e-32 | 8.4803e-32 | 1.3805e-31 | ||
200 | mean | -1.0316 | -1.0316 | -1.0316 | -1.0316 | |
variance | 5.3248e-32 | 9.6635e-32 | 9.6635e-32 | 1.1438e-31 | ||
300 | mean | -1.0316 | -1.0316 | -1.0316 | -1.0316 | |
variance | 9.0719e-32 | 1.3213e-31 | 1.4397e-31 | 1.2622e-31 | ||
80 | mean | -3.8628 | -3.8628 | -3.8628 | -3.8628 | |
variance | 6.4394e-21 | 9.9421e-28 | 2.7926e-30 | 3.6524e-30 | ||
100 | mean | -3.8628 | -3.8628 | -3.8628 | -3.8628 | |
variance | 9.0777e-21 | 8.4809e-28 | 3.0844e-30 | 3.5420e-30 | ||
150 | mean | -3.8628 | -3.8628 | -3.8628 | -3.8628 | |
variance | 2.0992e-24 | 4.3654e-28 | 2.8872e-30 | 3.2895e-30 | ||
200 | mean | -3.8628 | -3.8628 | -3.8628 | -3.8628 | |
variance | 8.4359e-28 | 2.8557e-30 | 3.2028e-30 | 3.7944e-30 | ||
300 | mean | -3.8628 | -3.8628 | -3.8628 | -3.8628 | |
variance | 3.2422e-30 | 3.4394e-30 | 3.5814e-30 | 4.2914e-30 | ||
80 | mean | -7.2340 | -7.7273 | -7.2340 | -8.7433 | |
variance | 9.9440 | 7.8747 | 9.9440 | 6.6108 | ||
100 | mean | -8.4358 | -8.4421 | -7.9412 | -7.1354 | |
variance | 6.4802 | 7.9474 | 9.2356 | 10.5886 | ||
150 | mean | -8.6379 | -7.7325 | -8.4424 | -8.0363 | |
variance | 6.1125 | 7.8573 | 7.9354 | 8.4419 | ||
200 | mean | -7.6363 | -6.8345 | -7.5391 | -6.9396 | |
variance | 10.1076 | 10.9456 | 9.3057 | 11.8352 | ||
300 | mean | -7.3312 | -7.9391 | -7.2340 | -7.9373 | |
variance | 9.2654 | 9.2577 | 9.9440 | 9.2681 |
80 | mean | 1.1697e-23 | 1.4034e-22 | 1.3997e-19 | 1.5248e-17 | |
variance | 3.1624e-45 | 1.7331e-43 | 1.9198e-37 | 9.7892e-34 | ||
100 | mean | 1.2345e-24 | 3.4313e-23 | 6.7734e-20 | 1.3077e-17 | |
variance | 1.2889e-47 | 4.0997e-45 | 5.7511e-38 | 1.7539e-33 | ||
150 | mean | 4.8036e-24 | 5.5423e-22 | 4.7328e-19 | 1.5124e-17 | |
variance | 5.3061e-46 | 1.6406e-42 | 1.4786e-36 | 4.8891e-34 | ||
200 | mean | 3.4374e-23 | 2.2118e-21 | 8.3626e-19 | 9.8416e-17 | |
variance | 2.0994e-44 | 1.6926e-41 | 3.6846e-36 | 5.8052e-32 | ||
300 | mean | 3.7652e-23 | 8.6217e-21 | 9.6451e-18 | 1.7330e-16 | |
variance | 1.6413e-44 | 3.3834e-40 | 6.4054e-34 | 8.3178e-32 | ||
80 | mean | 23.0984 | 15.5308 | 15.6512 | 17.5839 | |
variance | 1.3502e+03 | 0.2934 | 0.8921 | 132.7182 | ||
100 | mean | 15.4714 | 15.4349 | 15.4707 | 15.5330 | |
variance | 0.3979 | 0.4585 | 1.4279 | 0.9254 | ||
150 | mean | 15.5411 | 15.5168 | 15.5302 | 15.8413 | |
variance | 0.4272 | 0.9433 | 0.7471 | 1.0840 | ||
200 | mean | 15.7879 | 15.5266 | 15.9301 | 18.0431 | |
variance | 0.4044 | 1.6317 | 1.9228 | 132.4126 | ||
300 | mean | 15.9560 | 15.5901 | 17.9298 | 19.8994 | |
variance | 1.3168 | 0.5490 | 119.4753 | 236.7976 | ||
80 | mean | 14.2808 | 13.4628 | 14.0816 | 15.6759 | |
variance | 18.3861 | 70.4926 | 30.3199 | 46.6280 | ||
100 | mean | 14.1719 | 11.2533 | 12.9326 | 15.5054 | |
variance | 19.8901 | 21.2570 | 36.3528 | 79.5550 | ||
150 | mean | 14.8875 | 12.1143 | 13.0902 | 14.8153 | |
variance | 20.5411 | 29.8877 | 37.4915 | 30.4357 | ||
200 | mean | 15.5786 | 13.5650 | 13.6945 | 15.0470 | |
variance | 37.2106 | 26.6829 | 59.1946 | 39.4785 | ||
300 | mean | 16.3959 | 14.1838 | 15.1895 | 15.7031 | |
variance | 35.1016 | 37.6114 | 42.1339 | 69.3613 | ||
80 | mean | 0.0093 | 0.0089 | 0.0164 | 0.0165 | |
variance | 5.5534e-04 | 3.3844e-04 | 8.0860e-04 | 5.2949e-04 | ||
100 | mean | 0.0092 | 0.0064 | 0.0121 | 0.0156 | |
variance | 4.5978e-04 | 2.2374e-04 | 5.6635e-04 | 5.1330e-04 | ||
150 | mean | 0.0165 | 0.0157 | 0.0153 | 0.0191 | |
variance | 0.0018 | 5.5528e-04 | 4.3368e-04 | 0.0025 | ||
200 | mean | 0.0328 | 0.0179 | 0.0245 | 0.0305 | |
variance | 0.0098 | 5.0790e-04 | 0.0010 | 0.0019 | ||
300 | mean | 0.1185 | 0.0489 | 0.0608 | 0.0676 | |
variance | 0.0615 | 0.0124 | 0.0142 | 0.0109 | ||
80 | mean | 1.1567 | 1.2361 | 1.0774 | 1.2361 | |
variance | 0.2897 | 0.4157 | 0.1512 | 0.4157 | ||
100 | mean | 1.3155 | 1.0774 | 0.1512 | 1.3155 | |
variance | 0.5291 | 0.1512 | 0.4157 | 0.5291 | ||
150 | mean | -1.1567 | 1.4680 | 1.1567 | 1.2361 | |
variance | 0.2897 | 3.7509 | 0.2897 | 0.4157 | ||
200 | mean | 1.0774 | 1.1567 | 1.3155 | 1.0774 | |
variance | 0.1512 | 0.2897 | 0.5291 | 0.1512 | ||
300 | mean | 1.2361 | 1.3948 | 1.2361 | 1.2755 | |
variance | 0.4157 | 0.6299 | 0.4157 | 0.5908 | ||
| 80 | mean | -1.0316 | -1.0316 | -1.0316 | -1.0316 |
variance | 3.6682e-31 | 7.8886e-32 | 1.0847e-31 | 1.2030e-31 | ||
100 | mean | -1.0316 | -1.0316 | -1.0316 | -1.0316 | |
variance | 7.4942e-32 | 1.0255e-31 | 1.0255e-31 | 9.0719e-32 | ||
150 | mean | -1.0316 | -1.0316 | -1.0316 | -1.0316 | |
variance | 5.5220e-32 | 7.2970e-32 | 8.4803e-32 | 1.3805e-31 | ||
200 | mean | -1.0316 | -1.0316 | -1.0316 | -1.0316 | |
variance | 5.3248e-32 | 9.6635e-32 | 9.6635e-32 | 1.1438e-31 | ||
300 | mean | -1.0316 | -1.0316 | -1.0316 | -1.0316 | |
variance | 9.0719e-32 | 1.3213e-31 | 1.4397e-31 | 1.2622e-31 | ||
80 | mean | -3.8628 | -3.8628 | -3.8628 | -3.8628 | |
variance | 6.4394e-21 | 9.9421e-28 | 2.7926e-30 | 3.6524e-30 | ||
100 | mean | -3.8628 | -3.8628 | -3.8628 | -3.8628 | |
variance | 9.0777e-21 | 8.4809e-28 | 3.0844e-30 | 3.5420e-30 | ||
150 | mean | -3.8628 | -3.8628 | -3.8628 | -3.8628 | |
variance | 2.0992e-24 | 4.3654e-28 | 2.8872e-30 | 3.2895e-30 | ||
200 | mean | -3.8628 | -3.8628 | -3.8628 | -3.8628 | |
variance | 8.4359e-28 | 2.8557e-30 | 3.2028e-30 | 3.7944e-30 | ||
300 | mean | -3.8628 | -3.8628 | -3.8628 | -3.8628 | |
variance | 3.2422e-30 | 3.4394e-30 | 3.5814e-30 | 4.2914e-30 | ||
80 | mean | -7.2340 | -7.7273 | -7.2340 | -8.7433 | |
variance | 9.9440 | 7.8747 | 9.9440 | 6.6108 | ||
100 | mean | -8.4358 | -8.4421 | -7.9412 | -7.1354 | |
variance | 6.4802 | 7.9474 | 9.2356 | 10.5886 | ||
150 | mean | -8.6379 | -7.7325 | -8.4424 | -8.0363 | |
variance | 6.1125 | 7.8573 | 7.9354 | 8.4419 | ||
200 | mean | -7.6363 | -6.8345 | -7.5391 | -6.9396 | |
variance | 10.1076 | 10.9456 | 9.3057 | 11.8352 | ||
300 | mean | -7.3312 | -7.9391 | -7.2340 | -7.9373 | |
variance | 9.2654 | 9.2577 | 9.9440 | 9.2681 |
| ||||||||||||||||||||
10 | 348 | 487 | 646 | 78 | - | 253 | 322 | - | 550 | 624 | 1683 | - | 109 | 146 | 46 | 41 | 53 | 87 | 105 | 108 |
20 | 432 | 537 | 794 | 75 | - | 348 | 87 | - | 648 | 746 | - | - | 160 | 149 | 44 | 46 | 55 | 97 | 107 | 93 |
30 | 449 | 549 | 908 | 76 | - | 391 | 255 | - | 1201 | 782 | - | - | 156 | 147 | 44 | 47 | 51 | 77 | 94 | 99 |
40 | 491 | 570 | 1022 | 76 | - | 374 | 282 | - | 780 | 830 | - | - | 81 | 146 | 43 | 49 | 56 | 89 | 86 | 84 |
*-implies the algorithm does not converge. |
| ||||||||||||||||||||
10 | 348 | 487 | 646 | 78 | - | 253 | 322 | - | 550 | 624 | 1683 | - | 109 | 146 | 46 | 41 | 53 | 87 | 105 | 108 |
20 | 432 | 537 | 794 | 75 | - | 348 | 87 | - | 648 | 746 | - | - | 160 | 149 | 44 | 46 | 55 | 97 | 107 | 93 |
30 | 449 | 549 | 908 | 76 | - | 391 | 255 | - | 1201 | 782 | - | - | 156 | 147 | 44 | 47 | 51 | 77 | 94 | 99 |
40 | 491 | 570 | 1022 | 76 | - | 374 | 282 | - | 780 | 830 | - | - | 81 | 146 | 43 | 49 | 56 | 89 | 86 | 84 |
*-implies the algorithm does not converge. |
Function | PSO-resample | Standard PSO | NFO-resample | Standard NFO |
3.4313e-23(4.0997e-45) | 7.5386(24.3743) | 5.0244e-38(6.0588e-74) | 1.0370e-33(2.5810e-65) | |
3.1292e-13(4.2561e-25) | 2.5043(4.7289) | 2.2622e-23(1.2282e-44) | 1.1769e-20(3.3240e-39) | |
4.8851e-11(8.4971e-21) | 49.8877(710.3746) | 1.3053e-07(4.0837e-13) | 5.7124(747.2053) | |
1.5284e-94(5.2777e-187) | 1.5390e-54(2.3745e-107) | 6.3508e-154(9.6797e-306) | 2.8710e-35(1.9782e-68) | |
15.4349(0.4585) | 4.4216e+03(5.1577e+07) | 2.3160(12.4777) | 16.3890(2.6798e+03) | |
0(0) | 68.8400(2.1942e+03) | 0(0) | 0(0) | |
0.5155(0.0432) | 0.6040(0.0987) | 0.1368(0.0049) | 0.2147(0.0059) | |
11.2533(21.2570) | 27.3944(104.6841) | 0(0) | 7.1054e-17(1.2117e-31) | |
1.0509e-11(2.3499e-22) | 4.3043(2.0710) | -6.0396e-16(1.9387e-30) | 1.3465e-14(4.8468e-30) | |
0.0064(3.7421e-04) | 0.8194(0.0562) | 0(0) | 0(0) | |
1.6987(5.8474) | 5.5496(11.4830) | 0.8247(1.1210e-15) | 0.8247(1.9722e-31) | |
-0.2002(0.1663) | 17.6488(186.4889) | -1.1504(3.6713e-12) | -1.1504(1.9722e-31) | |
1.0774(0.1512) | 1.3155(0.5282) | 0.9980(3.5922e-22) | 0.9980(0) | |
0.0035(3.6803e-05) | 0.0041(5.3083e-05) | 9.5850e-04(9.2612e-11) | 0.0044(1.0963e-10) | |
-1.0316(1.0255e-31) | -1.0316(1.9722e-31) | -1.0316(2.0116e-31) | -1.0316(1.9722e-31) | |
0.3979(0) | 0.3979(0) | 0.3979(1.7588e-14) | 0.3979(0) | |
3.0000(8.1600e-29) | 3.0000(2.0905e-30) | 3.0000(1.5108e-09) | 3.0000(3.1554e-30) | |
-3.2789(0.0032) | -3.2694(0.0035) | -3.3215(1.0546e-10) | -3.3215(5.9953e-31) | |
-8.4421(7.9474) | -6.8474(12.3691) | -10.1532(6.5141e-17) | -10.1532(2.9579e-09) | |
-9.8865(3.1789) | -8.2623(11.7828) | -10.4029(2.9297e-12) | -10.4029(1.0758e-11) |
Function | PSO-resample | Standard PSO | NFO-resample | Standard NFO |
3.4313e-23(4.0997e-45) | 7.5386(24.3743) | 5.0244e-38(6.0588e-74) | 1.0370e-33(2.5810e-65) | |
3.1292e-13(4.2561e-25) | 2.5043(4.7289) | 2.2622e-23(1.2282e-44) | 1.1769e-20(3.3240e-39) | |
4.8851e-11(8.4971e-21) | 49.8877(710.3746) | 1.3053e-07(4.0837e-13) | 5.7124(747.2053) | |
1.5284e-94(5.2777e-187) | 1.5390e-54(2.3745e-107) | 6.3508e-154(9.6797e-306) | 2.8710e-35(1.9782e-68) | |
15.4349(0.4585) | 4.4216e+03(5.1577e+07) | 2.3160(12.4777) | 16.3890(2.6798e+03) | |
0(0) | 68.8400(2.1942e+03) | 0(0) | 0(0) | |
0.5155(0.0432) | 0.6040(0.0987) | 0.1368(0.0049) | 0.2147(0.0059) | |
11.2533(21.2570) | 27.3944(104.6841) | 0(0) | 7.1054e-17(1.2117e-31) | |
1.0509e-11(2.3499e-22) | 4.3043(2.0710) | -6.0396e-16(1.9387e-30) | 1.3465e-14(4.8468e-30) | |
0.0064(3.7421e-04) | 0.8194(0.0562) | 0(0) | 0(0) | |
1.6987(5.8474) | 5.5496(11.4830) | 0.8247(1.1210e-15) | 0.8247(1.9722e-31) | |
-0.2002(0.1663) | 17.6488(186.4889) | -1.1504(3.6713e-12) | -1.1504(1.9722e-31) | |
1.0774(0.1512) | 1.3155(0.5282) | 0.9980(3.5922e-22) | 0.9980(0) | |
0.0035(3.6803e-05) | 0.0041(5.3083e-05) | 9.5850e-04(9.2612e-11) | 0.0044(1.0963e-10) | |
-1.0316(1.0255e-31) | -1.0316(1.9722e-31) | -1.0316(2.0116e-31) | -1.0316(1.9722e-31) | |
0.3979(0) | 0.3979(0) | 0.3979(1.7588e-14) | 0.3979(0) | |
3.0000(8.1600e-29) | 3.0000(2.0905e-30) | 3.0000(1.5108e-09) | 3.0000(3.1554e-30) | |
-3.2789(0.0032) | -3.2694(0.0035) | -3.3215(1.0546e-10) | -3.3215(5.9953e-31) | |
-8.4421(7.9474) | -6.8474(12.3691) | -10.1532(6.5141e-17) | -10.1532(2.9579e-09) | |
-9.8865(3.1789) | -8.2623(11.7828) | -10.4029(2.9297e-12) | -10.4029(1.0758e-11) |
Function | PSO-resample | Standard PSO | NFO-resample | Standard NFO |
1.20 | 0.49 | 23.65 | 25.31 | |
1.30 | 0.52 | 25.61 | 25.26 | |
4.35 | 1.77 | 666.50 | 643.08 | |
2.94 | 0.91 | 50.79 | 54.41 | |
1.71 | 0.62 | 31.57 | 31.53 | |
1.49 | 0.51 | 26.43 | 24.78 | |
4.02 | 1.30 | 76.40 | 73.21 | |
1.85 | 0.74 | 33.34 | 35.71 | |
2.46 | 1.05 | 60.64 | 50.17 | |
2.57 | 1.01 | 52.85 | 57.37 | |
6.12 | 2.58 | 158.61 | 149.46 | |
4.42 | 2.22 | 129.69 | 127.31 | |
5.32 | 2.49 | 184.21 | 172.35 | |
1.71 | 0.72 | 42.70 | 42.96 | |
1.27 | 0.54 | 56.11 | 28.77 | |
1.06 | 0.47 | 22.90 | 20.07 | |
1.29 | 0.49 | 28.37 | 25.47 | |
2.09 | 0.84 | 47.97 | 50.29 | |
21.98 | 9.84 | 549.53 | 551.62 | |
2.59 | 1.16 | 133.86 | 120.27 |
Function | PSO-resample | Standard PSO | NFO-resample | Standard NFO |
1.20 | 0.49 | 23.65 | 25.31 | |
1.30 | 0.52 | 25.61 | 25.26 | |
4.35 | 1.77 | 666.50 | 643.08 | |
2.94 | 0.91 | 50.79 | 54.41 | |
1.71 | 0.62 | 31.57 | 31.53 | |
1.49 | 0.51 | 26.43 | 24.78 | |
4.02 | 1.30 | 76.40 | 73.21 | |
1.85 | 0.74 | 33.34 | 35.71 | |
2.46 | 1.05 | 60.64 | 50.17 | |
2.57 | 1.01 | 52.85 | 57.37 | |
6.12 | 2.58 | 158.61 | 149.46 | |
4.42 | 2.22 | 129.69 | 127.31 | |
5.32 | 2.49 | 184.21 | 172.35 | |
1.71 | 0.72 | 42.70 | 42.96 | |
1.27 | 0.54 | 56.11 | 28.77 | |
1.06 | 0.47 | 22.90 | 20.07 | |
1.29 | 0.49 | 28.37 | 25.47 | |
2.09 | 0.84 | 47.97 | 50.29 | |
21.98 | 9.84 | 549.53 | 551.62 | |
2.59 | 1.16 | 133.86 | 120.27 |
Function | PSO-resample | Standard PSO | NFO-resample | Standard NFO |
1.5796e-13(5.5281e-26) | 185.5670(5.1824e+03) | 3.1264e-20(2.3457e-38) | 1.2589e-14(3.8034e-27) | |
6.0313e-09(3.9308e-17) | 15.9041(29.1664) | 1.5768e-13(5.9668e-25) | 4.2327e-10(4.2998e-18) | |
5.7985e-04(4.9215e-07) | 1.7963e+03(4.6628e+05) | 1.0969e-04(1.9506e-07) | 890.1068(7.2077e+06) | |
3.6273e-92(3.1490e-182) | 1.9099e-53(3.6487e-105) | 3.0444e-161(2.2248e-320) | 7.1526e-33(1.2278e-63) | |
36.4677(0.5677) | 8.1082e+05(3.6749e+11) | 22.7611(25.6539) | 27.7804(146.3549) | |
0(0) | 950.9600(7.5934e+04) | 0(0) | 0(0) | |
0.6291(0.0868) | 0.6804(0.1075) | 0.2750(0.0084) | 0.3944(0.0121) | |
53.1581(129.8373) | 85.4913(724.0781) | 5.0148(185.7615) | 80.0579(33.3354) | |
0.0042(4.1661e-04) | 7.3142(2.9770) | 6.6771e-12(1.0702e-21) | 6.6946e-09(1.0756e-15) | |
7.7593e-04(6.0020e-06) | 2.1590(0.6044) | 0(0) | 1.4020e-13(4.7177e-25) | |
5.7450(10.1131) | 16.2519(46.5782) | 0.4123(1.6140e-13) | 0.4123(1.4388e-27) | |
11.0551(421.2096) | 1.9596e+03(3.1327e+07) | -1.1504(1.5460e-12) | -1.1504(3.3189e-27) | |
1.0774(0.1512) | 1.4333(1.2554) | 0.9980(5.3883e-21) | 0.9980(0) | |
0.0038(3.3734e-05) | 0.0052(6.1041e-05) | 9.6003e-04(3.1558e-10) | 0.0044(1.0963e-10) | |
-1.0316(1.0255e-31) | -1.0316(1.9722e-31) | -1.0316(7.2889e-16) | -1.0316(1.6763e-31) | |
0.3979(0) | 0.3979(0) | 0.3979(6.3308e-11) | 0.3979(0) | |
3.0000(9.1551e-28) | 3.0000(2.0984e-30) | 3.0000(6.0843e-19) | 3.0000(3.1554e-30) | |
-3.2741(0.0034) | -3.2647(0.0035) | -3.3215(8.4559e-12) | -3.3215(1.9722e-31) | |
-8.2382(8.2475) | -6.7459(11.4480) | -10.1532(6.6789e-13) | -10.1532(1.2204e-19) | |
-8.6646(9.7556) | -7.2678(12.8782) | -10.4029(5.2199e-09) | -10.4029(3.8379e-15) |
Function | PSO-resample | Standard PSO | NFO-resample | Standard NFO |
1.5796e-13(5.5281e-26) | 185.5670(5.1824e+03) | 3.1264e-20(2.3457e-38) | 1.2589e-14(3.8034e-27) | |
6.0313e-09(3.9308e-17) | 15.9041(29.1664) | 1.5768e-13(5.9668e-25) | 4.2327e-10(4.2998e-18) | |
5.7985e-04(4.9215e-07) | 1.7963e+03(4.6628e+05) | 1.0969e-04(1.9506e-07) | 890.1068(7.2077e+06) | |
3.6273e-92(3.1490e-182) | 1.9099e-53(3.6487e-105) | 3.0444e-161(2.2248e-320) | 7.1526e-33(1.2278e-63) | |
36.4677(0.5677) | 8.1082e+05(3.6749e+11) | 22.7611(25.6539) | 27.7804(146.3549) | |
0(0) | 950.9600(7.5934e+04) | 0(0) | 0(0) | |
0.6291(0.0868) | 0.6804(0.1075) | 0.2750(0.0084) | 0.3944(0.0121) | |
53.1581(129.8373) | 85.4913(724.0781) | 5.0148(185.7615) | 80.0579(33.3354) | |
0.0042(4.1661e-04) | 7.3142(2.9770) | 6.6771e-12(1.0702e-21) | 6.6946e-09(1.0756e-15) | |
7.7593e-04(6.0020e-06) | 2.1590(0.6044) | 0(0) | 1.4020e-13(4.7177e-25) | |
5.7450(10.1131) | 16.2519(46.5782) | 0.4123(1.6140e-13) | 0.4123(1.4388e-27) | |
11.0551(421.2096) | 1.9596e+03(3.1327e+07) | -1.1504(1.5460e-12) | -1.1504(3.3189e-27) | |
1.0774(0.1512) | 1.4333(1.2554) | 0.9980(5.3883e-21) | 0.9980(0) | |
0.0038(3.3734e-05) | 0.0052(6.1041e-05) | 9.6003e-04(3.1558e-10) | 0.0044(1.0963e-10) | |
-1.0316(1.0255e-31) | -1.0316(1.9722e-31) | -1.0316(7.2889e-16) | -1.0316(1.6763e-31) | |
0.3979(0) | 0.3979(0) | 0.3979(6.3308e-11) | 0.3979(0) | |
3.0000(9.1551e-28) | 3.0000(2.0984e-30) | 3.0000(6.0843e-19) | 3.0000(3.1554e-30) | |
-3.2741(0.0034) | -3.2647(0.0035) | -3.3215(8.4559e-12) | -3.3215(1.9722e-31) | |
-8.2382(8.2475) | -6.7459(11.4480) | -10.1532(6.6789e-13) | -10.1532(1.2204e-19) | |
-8.6646(9.7556) | -7.2678(12.8782) | -10.4029(5.2199e-09) | -10.4029(3.8379e-15) |
Function | ||||
PSO-resample | 3.4313e-23(4.0997e-45) | 3.1292e-13(4.2561e-25) | 4.8851e-11(8.4971e-21) | 1.5284e-94(5.2777e-187) |
NFO-resample | 5.0244e-38(6.0588e-74) | 2.2622e-23(1.2282e-44) | 1.3053e-07 (4.0837e-13) | 6.3508e-154(9.6797e-306) |
PSO |
3.1842(5.2344) | 1.5076(0.5649) | 12.8833(67.5186) | 1.7914e-46(3.8620e-91) |
UPSO | 2.0381e-15(8.3665e-30) | 3.7556e-11(2.9156e-20) | 1.7202(2.2547) | 2.8064e-95(1.1021e-188) |
FDRPSO | 3.0682e-09(3.2419e-18) | 8.1237e-06(8.0225e-12) | 1.9837 (5.4554) | 1.4365e-74(4.8423e-147) |
CLPSO | 3.3930e-06(5.9273e-12) | 1.5475e-04(1.8278e-09) | 786.7243(3.3263e+04) | 2.0995e-66(5.6095e-131) |
LDWPSO | 1.2282(0.9361) | 0.5367(0.0501) | 49.3415(1.3333e+03) | 1.0966e-92(2.6342e-183) |
DE | 99.0340(1.0350e+05) | 1.6477(16.3922) | 625.9111(9.9835e+05) | 3.1044e-183(0) |
Function | ||||
PSO-resample | 15.4349(0.4585) | 0(0) | 0.5155( 0.0432) | 11.2533(21.2570) |
NFO-resample | 2.3160(12.4777) | 0(0) | 0.1368(0.0049) | 0(0) |
PSO |
1.2137e+03(1.0794e+06) | 41.7600(706.5824) | 0.4164(0.0697) | 26.6187(95.9579) |
UPSO | 21.4613(478.5440) | 0(0) | 0.5336(0.0577) | 20.7462(41.9989) |
FDRPSO | 47.6522(1.4556e+04) | 0(0) | 0.5480(0.0660) | 31.3348(228.5036) |
CLPSO | 87.8288(1.4948e+03) | 0(0) | 0.6045(0.1044) | 0.5915(0.3101) |
LDWPSO | 1.1821e+03(2.1126e+06) | 14.1200(36.3456) | 0.4455(0.0878) | 29.9535(68.6640) |
DE | 3.3685e+06(1.4229e+14) | 2428(0) | 0.2584(0.0022) | 50.3008(175.7736) |
Function | ||||
PSO-resample | 1.0509e-11(2.3499e-22) | 0.0084(3.7421e-04) | 1.6987( 5.8474) | -0.3243(0.1740) |
NFO-resample | -6.0396e-16(1.9387e-30) | 0(0) | 0.8247(1.1210e-15) | -1.1504(3.6713e-12) |
PSO |
3.8709(0.4796) | 0.8778(0.0276) | 2.0460(1.3128) | 3.2971(20.3606) |
UPSO | 1.1981e-08(7.7256e-17) | 0.0037(4.7966e-05) | 0.8247(1.0699e-31) | -1.1504(6.9108e-29) |
FDRPSO | 1.6932e-05(3.0526e-11) | 0.0398(0.0012) | 0.8247(9.1812e-26) | -1.1500(4.6357e-06) |
CLPSO | 0.0011(1.4550e-07) | 0.0012(1.8683e-06) | 0.8247(7.1869e-16) | -1.1504(3.5925e-12) |
LDWPSO | 2.7815(0.4828) | 0.5950(0.0336) | 3.0484(4.9952) | 0.5622(1.1895) |
DE | 8.4865(0.0087) | 3.9331(29.0800) | 7.6613(0.3984) | 29.9478(384.2202) |
Function | ||||
PSO-resample | 1.0774(0.1512) | 0.0035(3.6803e-05) | -1.0316(1.0255e-31) | 0.3979(0) |
NFO-resample | 0.9980(3.5922e-22) | 9.5850e-04(9.2612e-11) | -1.0316(2.0116e-31) | 0.3979(1.7588e-14) |
PSO |
1.5132(1.1064) | 0.0035(3.6843e-05) | -1.0316(1.9722e-31) | 0.3979(0) |
UPSO | 0.9980(0) | 7.5611e-04(4.6700e-08) | -1.0316(1.9722e-31) | 0.3979(0) |
FDRPSO | 0.9980(1.9722e-33) | 0.0045(3.7597e-05) | -1.0316(1.2735e-18) | 0.3979(2.8926e-14) |
CLPSO | 0.9980(0) | 0.0044(6.1811e-10) | -1.0316( 6.7053e-32) | 0.3979(2.1405e-28) |
LDWPSO | 1.0774(0.1512) | 0.0021(1.5442e-05) | -1.0316(1.9722e-31) | 0.3979(0) |
DE | 0.9980(0) | 0.0044(8.4259e-37) | -1.0316(1.9722e-31) | 0.3979(0) |
Function | ||||
PSO-resample | 3.0000(8.1600e-29) | -3.2789( 0.0032) | -8.4421(7.9474) | -9.8865(3.1789) |
NFO-resample | 3.0000(1.5108e-09) | -3.3215(1.0546e-10) | -10.1532(6.5141e-17) | -10.4029( 2.9297e-12) |
PSO |
3.0000(2.2719e-30) | -3.2836(0.0030) | -8.0573(11.2958) | -9.4854 (6.1741 ) |
UPSO | 3.0000(3.1554e-30) | -3.3215(6.4687e-31) | -9.9511( 0.9802) | -10.4029(4.6701e-30) |
FDRPSO | 3.0000(2.6269e-30) | -3.2931(0.0026) | -7.1588(13.4501) | -10.4029(7.6993e-30) |
CLPSO | 3.0000(6.0537e-29) | -3.3215(9.4155e-15) | -10.1532(5.9021e-17) | -10.4029(4.4227e-09) |
LDWPSO | 3.0000(2.6111e-30) | -3.2741(0.0034) | -8.2319( 6.7778) | -8.1481(11.1390) |
DE | 3.0000(3.1554e-30) | -3.1982(5.4264e-05) | -8.1072(6.0146) | -10.1427(0.7160) |
Function | ||||
PSO-resample | 3.4313e-23(4.0997e-45) | 3.1292e-13(4.2561e-25) | 4.8851e-11(8.4971e-21) | 1.5284e-94(5.2777e-187) |
NFO-resample | 5.0244e-38(6.0588e-74) | 2.2622e-23(1.2282e-44) | 1.3053e-07 (4.0837e-13) | 6.3508e-154(9.6797e-306) |
PSO |
3.1842(5.2344) | 1.5076(0.5649) | 12.8833(67.5186) | 1.7914e-46(3.8620e-91) |
UPSO | 2.0381e-15(8.3665e-30) | 3.7556e-11(2.9156e-20) | 1.7202(2.2547) | 2.8064e-95(1.1021e-188) |
FDRPSO | 3.0682e-09(3.2419e-18) | 8.1237e-06(8.0225e-12) | 1.9837 (5.4554) | 1.4365e-74(4.8423e-147) |
CLPSO | 3.3930e-06(5.9273e-12) | 1.5475e-04(1.8278e-09) | 786.7243(3.3263e+04) | 2.0995e-66(5.6095e-131) |
LDWPSO | 1.2282(0.9361) | 0.5367(0.0501) | 49.3415(1.3333e+03) | 1.0966e-92(2.6342e-183) |
DE | 99.0340(1.0350e+05) | 1.6477(16.3922) | 625.9111(9.9835e+05) | 3.1044e-183(0) |
Function | ||||
PSO-resample | 15.4349(0.4585) | 0(0) | 0.5155( 0.0432) | 11.2533(21.2570) |
NFO-resample | 2.3160(12.4777) | 0(0) | 0.1368(0.0049) | 0(0) |
PSO |
1.2137e+03(1.0794e+06) | 41.7600(706.5824) | 0.4164(0.0697) | 26.6187(95.9579) |
UPSO | 21.4613(478.5440) | 0(0) | 0.5336(0.0577) | 20.7462(41.9989) |
FDRPSO | 47.6522(1.4556e+04) | 0(0) | 0.5480(0.0660) | 31.3348(228.5036) |
CLPSO | 87.8288(1.4948e+03) | 0(0) | 0.6045(0.1044) | 0.5915(0.3101) |
LDWPSO | 1.1821e+03(2.1126e+06) | 14.1200(36.3456) | 0.4455(0.0878) | 29.9535(68.6640) |
DE | 3.3685e+06(1.4229e+14) | 2428(0) | 0.2584(0.0022) | 50.3008(175.7736) |
Function | ||||
PSO-resample | 1.0509e-11(2.3499e-22) | 0.0084(3.7421e-04) | 1.6987( 5.8474) | -0.3243(0.1740) |
NFO-resample | -6.0396e-16(1.9387e-30) | 0(0) | 0.8247(1.1210e-15) | -1.1504(3.6713e-12) |
PSO |
3.8709(0.4796) | 0.8778(0.0276) | 2.0460(1.3128) | 3.2971(20.3606) |
UPSO | 1.1981e-08(7.7256e-17) | 0.0037(4.7966e-05) | 0.8247(1.0699e-31) | -1.1504(6.9108e-29) |
FDRPSO | 1.6932e-05(3.0526e-11) | 0.0398(0.0012) | 0.8247(9.1812e-26) | -1.1500(4.6357e-06) |
CLPSO | 0.0011(1.4550e-07) | 0.0012(1.8683e-06) | 0.8247(7.1869e-16) | -1.1504(3.5925e-12) |
LDWPSO | 2.7815(0.4828) | 0.5950(0.0336) | 3.0484(4.9952) | 0.5622(1.1895) |
DE | 8.4865(0.0087) | 3.9331(29.0800) | 7.6613(0.3984) | 29.9478(384.2202) |
Function | ||||
PSO-resample | 1.0774(0.1512) | 0.0035(3.6803e-05) | -1.0316(1.0255e-31) | 0.3979(0) |
NFO-resample | 0.9980(3.5922e-22) | 9.5850e-04(9.2612e-11) | -1.0316(2.0116e-31) | 0.3979(1.7588e-14) |
PSO |
1.5132(1.1064) | 0.0035(3.6843e-05) | -1.0316(1.9722e-31) | 0.3979(0) |
UPSO | 0.9980(0) | 7.5611e-04(4.6700e-08) | -1.0316(1.9722e-31) | 0.3979(0) |
FDRPSO | 0.9980(1.9722e-33) | 0.0045(3.7597e-05) | -1.0316(1.2735e-18) | 0.3979(2.8926e-14) |
CLPSO | 0.9980(0) | 0.0044(6.1811e-10) | -1.0316( 6.7053e-32) | 0.3979(2.1405e-28) |
LDWPSO | 1.0774(0.1512) | 0.0021(1.5442e-05) | -1.0316(1.9722e-31) | 0.3979(0) |
DE | 0.9980(0) | 0.0044(8.4259e-37) | -1.0316(1.9722e-31) | 0.3979(0) |
Function | ||||
PSO-resample | 3.0000(8.1600e-29) | -3.2789( 0.0032) | -8.4421(7.9474) | -9.8865(3.1789) |
NFO-resample | 3.0000(1.5108e-09) | -3.3215(1.0546e-10) | -10.1532(6.5141e-17) | -10.4029( 2.9297e-12) |
PSO |
3.0000(2.2719e-30) | -3.2836(0.0030) | -8.0573(11.2958) | -9.4854 (6.1741 ) |
UPSO | 3.0000(3.1554e-30) | -3.3215(6.4687e-31) | -9.9511( 0.9802) | -10.4029(4.6701e-30) |
FDRPSO | 3.0000(2.6269e-30) | -3.2931(0.0026) | -7.1588(13.4501) | -10.4029(7.6993e-30) |
CLPSO | 3.0000(6.0537e-29) | -3.3215(9.4155e-15) | -10.1532(5.9021e-17) | -10.4029(4.4227e-09) |
LDWPSO | 3.0000(2.6111e-30) | -3.2741(0.0034) | -8.2319( 6.7778) | -8.1481(11.1390) |
DE | 3.0000(3.1554e-30) | -3.1982(5.4264e-05) | -8.1072(6.0146) | -10.1427(0.7160) |
Function | |
|||||||||||||||||||
PSO-resample | 432 | 537 | 794 | 75 | - | 348 | 87 | - | 648 | 746 | - | - | 160 | 149 | 44 | 46 | 55 | 97 | 107 | 93 |
NFO-resample | 252 | 237 | 54 | 35 | 509 | 182 | 53 | 85 | 257 | 292 | 309 | 249 | 41 | 25 | 17 | 39 | 39 | 73 | 74 | 72 |
PSO |
- | 1026 | - | 76 | - | 357 | 361 | - | 1059 | 1145 | - | 1408 | 86 | 158 | 52 | 53 | 65 | 85 | 105 | 119 |
UPSO | 706 | 745 | - | 63 | - | 519 | 1700 | 1230 | 877 | 877 | 530 | 810 | 204 | 138 | 44 | 52 | 58 | 89 | 122 | 121 |
FDRPSO | 1579 | 1712 | - | 116 | - | 1294 | 735 | 137 | 1737 | - | 1289 | 1550 | 203 | 152 | 106 | 126 | 162 | 182 | 538 | 552 |
CLPSO | 1638 | 1654 | - | 133 | - | 1201 | 820 | - | 1921 | 1888 | 1358 | 1617 | 263 | 351 | 144 | 200 | 348 | 589 | 861 | 737 |
LDWPSO | 1050 | 930 | 1296 | 171 | 1468 | 676 | 1092 | 1068 | 919 | 973 | 1077 | 1072 | 169 | 208 | 82 | 72 | 110 | 179 | 278 | 286 |
DE | 17 | 25 | 38 | 28 | 19 | 27 | 500 | 19 | 41 | 49 | 29 | 18 | 19 | 22 | 17 | 32 | 22 | 25 | 27 | 35 |
Function | |
|||||||||||||||||||
PSO-resample | 432 | 537 | 794 | 75 | - | 348 | 87 | - | 648 | 746 | - | - | 160 | 149 | 44 | 46 | 55 | 97 | 107 | 93 |
NFO-resample | 252 | 237 | 54 | 35 | 509 | 182 | 53 | 85 | 257 | 292 | 309 | 249 | 41 | 25 | 17 | 39 | 39 | 73 | 74 | 72 |
PSO |
- | 1026 | - | 76 | - | 357 | 361 | - | 1059 | 1145 | - | 1408 | 86 | 158 | 52 | 53 | 65 | 85 | 105 | 119 |
UPSO | 706 | 745 | - | 63 | - | 519 | 1700 | 1230 | 877 | 877 | 530 | 810 | 204 | 138 | 44 | 52 | 58 | 89 | 122 | 121 |
FDRPSO | 1579 | 1712 | - | 116 | - | 1294 | 735 | 137 | 1737 | - | 1289 | 1550 | 203 | 152 | 106 | 126 | 162 | 182 | 538 | 552 |
CLPSO | 1638 | 1654 | - | 133 | - | 1201 | 820 | - | 1921 | 1888 | 1358 | 1617 | 263 | 351 | 144 | 200 | 348 | 589 | 861 | 737 |
LDWPSO | 1050 | 930 | 1296 | 171 | 1468 | 676 | 1092 | 1068 | 919 | 973 | 1077 | 1072 | 169 | 208 | 82 | 72 | 110 | 179 | 278 | 286 |
DE | 17 | 25 | 38 | 28 | 19 | 27 | 500 | 19 | 41 | 49 | 29 | 18 | 19 | 22 | 17 | 32 | 22 | 25 | 27 | 35 |
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