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An enhanced differential evolution algorithmwith adaptive weight bounds for efficient training ofneural networks

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Warianty tytułu
PL
Ulepszony algorytm ewolucji różnicowej z adaptacyjnymi granicami wag dla efektywnego szkolenia sieci neuronowych
Języki publikacji
EN
Abstrakty
EN
Artificial neural networks are essential intelligent tools for various learning tasks. Training them is challenging due to the nature of the data set, many training weights, and their dependency, which gives rise to a complicated high-dimensional error function for minimization. Thus, global optimization methods have become an alternative approach. Many variants of differential evolution (DE) have been applied as training methods to approximate the weights of a neural network. However, empirical studies show that they suffer from generally fixed weight bounds. In this research, we propose an enhanced differential evolution algorithm with adaptive weight bound adjustment (DEAW) for the efficient training of neural networks. The DEAW algorithm uses small initial weight bounds and adaptive adjustment in the mutation process. It gradually extends the bounds when a component of a mutant vector reaches its limits. We also experiment with using several scales of an activation function with the DEAW algorithm. Then, we apply the proposed method with its suitable setting to solve function approximation problems. DEAW can achieve satisfactory results compared to exact solutions.
PL
Sztuczne sieci neuronowe są niezbędnymi inteligentnymi narzędziami do realizacji różnych zadań uczenia się. Ich szkolenie stanowi wyzwanie ze względu na charakter zbioru danych, wiele wag treningowych i ich zależności, co powoduje powstanie skomplikowanej, wielowymiarowej funkcji błędu do minimalizacji. Dlatego alternatywnym podejściem stały się metody optymalizacji globalnej. Wiele wariantów ewolucji różnicowej (DE) zostało zastosowanych jako metody treningowe do aproksymacji wag sieci neuronowej. Jednak badania empiryczne pokazują, że cierpią one z powodu ogólnie ustalonych granic wag. W tym badaniu proponujemy ulepszony algorytm ewolucji różnicowej z adaptacyjnym dopasowaniem granic wag (DEAW) dla efektywnego szkolenia sieci neuronowych. Algorytm DEAW wykorzystuje małe początkowe granice wag i adaptacyjne dostosowanie w procesie mutacji. Stopniowo rozszerza on granice, gdy składowa wektora mutacji osiąga swoje granice. Eksperymentujemy również z wykorzystaniem kilku skal funkcji aktywacji z algorytmem DEAW. Następnie, stosujemy proponowaną metodę z jej odpowiednim ustawieniem do rozwiązywania problemów aproksymacji funkcji. DEAW może osiągnąć zadowalające rezultaty w porównaniu z rozwiązaniami dokładnymi.
Rocznik
Strony
4--13
Opis fizyczny
Bibliogr. 31 poz., tab., wykr.
Twórcy
  • Khon Kaen University, Faculty of Science, Department of Mathematics, Khon Kaen, Thailand
  • Khon Kaen University, Faculty of Science, Department of Mathematics, Khon Kaen, Thailand
Bibliografia
  • [1] Baioletti M., Di Bari G., Milani A., Poggioni V.: Differential Evolution for Neural Networks Optimization. Mathematics 8(1), 2020, 69 [http://doi.org/10.3390/math8010069].
  • [2] Bartlett P. L.: For Valid Generalization, the Size of the Weights is More Important than the Size of the Network. Proceedings of the 9th International Conference on Neural Information Processing Systems, 1996, 134–140.
  • [3] Bartlett P. L.: The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network. IEEE Transactions on Information Theory 44, 1998, 525–536 [http://doi.org/10.1109/18.661502].
  • [4] Chen L.: A global optimization algorithm for neural network training. Proceedings of International Conference on Neural Networks 1993, 443–446 [http://doi.org/10.1109/IJCNN.1993.713950].
  • [5] Chihaoui M., Bellil W., Amar C. B.: Multi Mother Wavelet Neural Network based on Genetic Algorithm for 1D and 2D Functions Approximation. Proceedings of the International Conference on Fuzzy Computation and International Conference on Neural Computation 2010, 429–434 [http://doi.org/10.5220/0003083704290434].
  • [6] Cong H., Nguyen N., Huy V. N., Bùi T.: The Influence of Initial Weights on Neural Network Training. Journal of Science and Technology 95, 2013, 18–25.
  • [7] Das S., Suganthan P. N.: Differential Evolution: A Survey of the State-of-the-Art. IEEE Transactions on Evolutionary Computation 15, 2011, 4–31 [http://doi.org/10.1109/TEVC.2010.2059031].
  • [8] Das S., Mullick S. S., Suganthan P. N.: Recent advances in differential evolution –An updated survey. Swarm and Evolutionary Computation 17, 2016, 1–30 [http://doi.org/10.1016/j.swevo.2016.01.004].
  • [9] Dhar V. K., Tickoo A. K., Koul R., Dubey B. P.: Comparative performance of some popular artificial neural network algorithms on benchmark and function approximation problems. Pramana 74, 2010, 307–324 [http://doi.org/10.1007/s12043-010-0029-4].
  • [10] Gao Y., Liu J.: A modified differential evolution algorithm and its application in the training of BP neural network. IEEE/ASME International Conference on Advanced Intelligent Mechatronics 2008, 1373–1377.
  • [11] Garro B. A., Sossa H., Vázquez R. A.: Evolving Neural Networks: A Comparison between Differential Evolution and Particle Swarm Optimization. Advances in Swarm Intelligence 2011, 447–454 [http://doi.org/10.1007/978-3-642-21515-5_53].
  • [12] Hahm N., Hong B. I.: An approximation by neural networkswith a fixed weight. Computers and Mathematics with Applications 47, 2004, 1897–1903 [http://doi.org/10.1016/j.camwa.2003.06.008].
  • [13] Ismailov V. E.: Approximation by neural networks with weights varying on a finite set of directions. Journal of Mathematical Analysis and Applications 389, 2012, 72–83 [http://doi.org/10.1016/j.jmaa.2011.11.037].
  • [14] Jesus R. J., Antunes M. L., da Costa R. A., Dorogovtsev S. N., Mendes J. F., Aguiar R. L.: Effect of the initial configuration of weights on the training and function of artificial neural networks. Mathematics 9, 2021, 1–16 [http://doi.org/10.3390/math9182246].
  • [15] Mendes R., Cortez P., Rocha M., Neves J.: Particle swarms for feedforward neural network training. Proceedings of the International Joint Conference on Neural Networks – IJCNN'02 2002, 1895–1899 [http://doi.org/10.1109/IJCNN.2002.1007808].
  • [16] Mezura M. E., Velázquez R. J., Coello C.: A comparative study of differential evolution variants for global optimization. GECCO 2006 – Genetic and Evolutionary Computation Conference 1, 2006, 485–492 [http://doi.org/10.1145/1143997.1144086].
  • [17] Migdady H.: Boundness of a Neural Network Weights Using the Notion of a Limit of a Sequence. International Journal of Data Mining and Knowledge Management Process 4, 2014, 1–8 [http://doi.org/10.5121/ijdkp.2014.4301].
  • [18] Mirjalili S. A., Hashim S. Z. M., Sardroudi H. M. Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm. Applied Mathematics and Computation 218, 2012, 11125–11137 [http://doi.org/10.1016/j.amc.2012.04.069].
  • [19] Morse G., Stanley K. O.: Simple Evolutionary Optimization Can Rival Stochastic Gradient Descent in Neural Networks. Proceedings of the Genetic and Evolutionary Computation Conference 2016, 477–484 [http://doi.org/10.1145/2908812.2908916].
  • [20] Mohamad F. A., Nor A. M. I., Wei H. L., Koon M. A.: Differential evolution: A recent review based on state-of-the-art works. Alexandria Engineering Journal 61(5), 2022, 3831–3872 [http://doi.org/10.1016/j.aej.2021.09.013].
  • [21] Piotrowski A. P.: Differential Evolution algorithms applied to Neural Network training suffer from stagnation. Applied Soft Computing 21, 2014, 382–406 [http://doi.org/10.1016/j.asoc.2014.03.039].
  • [22] Prechelt L.: A quantitative study of experimental evaluations of neural network learning algorithms: Current research practice. Neural Networks 9, 1996, 457–462 [http://doi.org/10.1016/0893-6080(95)00123-9].
  • [23] Prieto A., Prieto B., Ortigosa E. M., Ros E.: Neural networks: An overview of early research, current frameworks and new challenges. Neurocomputing 214, 2016, 242–268 [http://doi.org/10.1016/j.neucom.2016.06.014].
  • [24] Rumelhart D. E., Hinton G. E., Williams R. J.: Learning representations by back-propagating errors. Nature 323, 1986, 533–536 [http://doi.org/10.1038/323533a0].
  • [25] Si T., Hazra S., Jana N. D.: Artificial Neural Network Training Using Differential Evolutionary Algorithm for Classification. Advances in Intelligent and Soft Computing 232, 2012, 769–778 [http://doi.org/10.1007/978-3-642-27443-5-88].
  • [26] Storn R., Price K.: Differential Evolution A Simple and Efficient Heuristic for global Optimization over Continuous Spaces. Journal of Global Optimization 11, 1997, 341–359 [http://doi.org/10.1023/A:1008202821328].
  • [27] Subudhi B., Jena D.: An improved differential evolution trained neural network scheme for nonlinear system identification. International Journal of Automation and Computing 6, 2009, 137–144 [http://doi.org/10.1007/s11633-009-0137-0].
  • [28] Yang S., Ting T. O., Man K. L., Guan S. U.: Investigation of Neural Networks for Function Approximation. Procedia Computer Science 17, 2013, 586–594 [http://doi.org/10.1016/j.procs.2013.05.076].
  • [29] Zainuddin Z., Pauline O.: Function Approximation Using Artificial Neural Networks. International Journal of Systems Applications, Engineering and Development 1, 2007, 173–178 [http://doi.org/10.5555/1466915.1466916].
  • [30] Zhang J. R., Lok T. M., Lyu M. R.: A hybrid particle swarm optimization–back-propagation algorithm for feedforward neural network training. Applied Mathematics and Computation 185, 2007, 1026–1037 [http://doi.org/10.1016/j.amc.2006.07.025].
  • [31] UCI machine learning benchmark repository. the UC Irvine Machine Learning Repository, 2019 [http://archive.ics.uci.edu/ml/datasets.php].
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6cbf061f-6858-4e4b-9d67-0c6dcc9c0f31
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