Keywords: tropospheric ozone level time series, ozone episodes, the hybrid model, hybrid monte carlo, multilayer perceptron, particle swarm optimization.

To produce reliable and accurate forecasting for tropospheric ozone (O₃) levels is a challenge and significant task related to public health [1]. In this study a multilayer perceptron (MLP) model is trained with the original particle swarm optimization (PSO) algorithm, and named as the MLP-PSO model. It can be used to perform such a task [2,3], but the PSO algorithm tends to suffer from the "curse of dimensionality" problem, when the architecture of the MLP becomes large [4]. Such a difficulty inevitably degrades the model's predictive performance. A proper method for the initialization of the swarm of the PSO can alleviate such a difficulty [5,6,7].

In this study, the hybrid Monte Carlo (HMC) method is employed to sample the weight matrix from the posterior probability distribution of the MLP optimal weight matrix [8,9,10], and the sampled weight matrix is then used to initialize the "weight matrix swarm" in the PSO before the MLP training starts. The MLP-PSO with this new swarm initializing strategy can be considered as a two-staged hybrid model and the selecting of the model parameters are based on the general recommendations given in the literature for the HMC and the PSO, as well as determined by the try and error method [11,12,13,14,15]. Before the predictive experiments, an experiment aiming to compare the initial swarm (particles) (one is sampled by the HMC and the other is randomly distributed) is conducted. The result implies that the swarm sampled by the HMC method has a better convergence rate and reliability for the optimal weight matrix than the one obtained by the random scheme. Within expectation, the visualized experimental results of a 1-day ahead forecast for the daily maximum O₃ level in two selected air monitoring sites, shows that the hybrid model can provide more accurate predictions, especially in episodes [16,17]. Further comparison for the root mean square error (RMSE) of the two models for each season and each site reveals that the level of performance degradation for the MLP-PSO model is obviously larger than that of the hybrid model in episodes. This indicates that the hybrid model is robust to give reasonable predictions for the complex variation patterns of O₃.

1

Yi, J., Prybutok, V.R., "A neural network model forecasting for prediction of daily maximum ozone concentration in an industrialized urban area", Environmental Pollution, 92, 349-357. 1996. doi:10.1016/0269-7491(95)00078-X

2

Gardner, M.W., Dorling, S.R., "Statistical surface ozone models: an improved methodology to account for non-linear behaviour", Atmospheric Environment, 34, 21-34. 2000. doi:10.1016/S1352-2310(99)00359-3

3

Lu, W.Z., Fan, H.Y., Lo, S.M., "Application of evolutionary neural network method in predicting pollutant levels in downtown area of Hong Kong", NeuroComputing, 51(1), 387-400. 2003. doi:10.1016/S0925-2312(02)00623-9

4

Bergh, F.V.D., Engelbrecht, A.P., "A Cooperative approach to particle swarm optimization", Transactions on Evolutionary Computation, Vol. 8, No. 3, JUNE, 2004.

5

Richards, M., Ventura, D., "Choosing a starting configuration for particle swarm optimization", Neural Networks, Proceedings. 2004 IEEE International Joint Conference on, Vol 3, 2309-2312, Vol.3. 2004.

6

Parsopoulos, K.E., Vrahatis, M.N., "Initializing the particle swarm optimizer using the nonlinear simplex method", in Advances in Intelligent Systems, Fuzzy Systems, Evolutionary Computation, A. Grmela and N. E. Mastorakis, Eds. Athens, Greece: WSEAS Press, 216-221. 2002.

7

Wachowiak, M.P., Smolikova, R., Zheng, Y.F., Zurada, J.M., Elmaghraby, A.S., "An approach to multimodal biomedical image registration utilizing particle swarm optimization", Evolutionary Computation, IEEE Transactions on, Vol: 8, 289-301, 2004. doi:10.1109/TEVC.2004.826068

8

Duane, S., Kennedy, A. D., Pendleton, B. J., Roweth, D. Hybrid Monte Carlo. Physics Letters B, 195, 216-222, 1987. doi:10.1016/0370-2693(87)91197-X

9

Neal, R.M., "Bayesian learning for neural networks", Lecture notes in statistics, 118. Berlin: Springer, 1996.

10

Bishop, C.M., "Neural Networks for Pattern Recognition", Clarendon Press, Oxford. 1995.

11

Kennedy, J., Eberhart, R.C., "Particle swarm optimization", in: Proc. IEEE Conference on Neural Networks, IV, Piscataway, NJ, 1942-1948, 1995. doi:10.1109/ICNN.1995.488968

12

Gallad, A.E., Hawary, M. E., Sallam, A., Kalas, A., "Enhancing the particle swarm optimizer via proper parameters selection", Canadian Conference on Electrical and Computer Engineering, 792-797, 2002.

13

Suganthan, P.N., "Particle swarm optimizer with neighborhood operator", in Proc. Evolutionary Computation, Washington, DC, 1958-1962, 1999.

14

Eberhart, R.C., Shi, Y.H., "Particle swarm optimization: Developments, Applications and resources", Evolutionary Computation 1, 81-86. 2001. doi:10.1109/CEC.2001.934374

15

Hu, X.H., Shi,Y.H., Eberhart, R., "Recent advances in particle swarm", Evolutionary Computation, Congress on Vol 1, 90-97, 2004.

16

Chan, L.Y., Chan, C.Y. and Qin, Y., "Surface ozone pattern in Hong Kong", Journal of Applied Meteorology, 37(10), 1153-1165, 1998. doi:10.1175/1520-0450(1998)037<1153:SOPIHK>2.0.CO;2

17

Lee, Y.C., Calori, G., Hills, P., Carmichael, G.R., "Ozone episodes in urban Hong Kong 1994-1999", Atmospheric Environment, 36, 1957-1968, 2002. doi:10.1016/S1352-2310(02)00150-4

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