A Comparison Between GA and PSO Algorithms in Training ANN to Predict the Refractive Index of Binary Liquid Solutions

Document Type : Research Paper


Faculty of Chemical Engineering, Babol Noshirvani University of Technology, Babol, Iran


A total of 1099 data points consisting of alcohol-alcohol, alcohol-alkane, alkane-alkane, alcohol-amine and acid-acid binary solutions were collected from scientific literature to develop an appropriate artificial neural network (ANN) model. Temperature, molecular weight of the pure components, mole fraction of one component and the structural groups of the components were used as input parameters of the network while the refractive index was selected as its output. The ANN was optimized once by genetic algorithm (GA) and once again by particle swarm optimization algorithm (PSO) in order to predict the refractive index of binary solutions. The optimal topology of the ANN-GA consisted of 13 neurons in the hidden layer and the optimal topology of the ANN-PSO consisted of 16 neurons in the hidden layer. The results revealed that the ANN optimized by PSO had a better accuracy (MSE=0.003441 for test data) compared to the ANN optimized with GA (MSE=0.005117 for test data).


[1] Riazi, M. R. and Roomi, Y. A. (2001). “Use of the Refractive Index in the Estimation of Thermophysical Properties of Hydrocarbons and Petroleum Mixtures.” Industrial & Engineering Chemistry Research, Vol. 40, No. 8, pp. 1975-1984.
[2] Ali, A. and Tariq, T. (2008). “Deviations in refractive index parameters and applicability of mixing rules in binary mixtures of benzene +1, 2-dicholoroethane at different temperatures.” Chemical Engineering Communications, Vol. 195, No.1, pp. 43–56.
[3] Lorentz, A. H. (1881). “Ueber die Anwendung des Satzes vom Virial in der kinetischen Theorie der Gase.” Wiedemanns Annalen (Annalen der Physik), Vol. 248, No. 1, pp. 127–136.
[4] Tropf., W. J., Thomas, M. E. and Harris, T. J. (1995). Handbook of Optics. 2nd ed. Vol. 2, Chapter 33, McGraw-Hill, New York.
[5] Koohyar F. J. (2013). “Refractive Index and Its Applications.” Journal of Thermodynamics & Catalysis, Vol.4, No.2.
[6] Lipkin, M. R. and Martin, C. C. (1946), “Equation Relating Density, Refractive index, and Molecular Weight for Paraffins and Naphthenes.” Industrial and Engineering Chemistry, vol. 18, No. 6. pp. 380-382.
[7] Deetlefs, M., Seddon, K.R. and Shara, M. (2006). “Predicting of Physical Properties of Ionic Liquids.” Physical Chemistry Chemical Physics, Vol.8, No. 5, pp. 642-649.
[8] Sattari, M., Kamari, A., Mohammadi, A.H. and Ramjugernath, D. (2014). “A group contribution method for estimating the refractive indices of ionic liquids.” Molecular Liquids, Vol. 200, Part B, pp. 410-415.
[9] Moosavi, M. and Soltani, N. (2013). “Prediction of hydrocarbon densities using an artificial neural network–group contribution method up to high temperatures and pressures.” Thermochimica Acta, Vol. 556, pp. 89-96.
[10] Lashkarblooki, M., Hezave, A. Z., Al-Ajmi, A. M. and Ayatollahi, S. (2012). “Viscosity prediction of ternary mixtures containing ILs using multi-layer perceptron artificial neural network.” Fluid Phase Equilibria Vol. 326, pp.15-20.
[11] Ozerdem, M. S. (2008). “Artificial neural network approach to predict the electrical conductivity and density of Ag–Ni binary alloys.” Journal of Materials Processing Technology, Vol. 208, No. 1-3, pp. 470-476.
[12] Griffin, W. O. and Darsey, J. A. (2013). “Artificial neural network prediction indicators of density functional theory metal hydride models.” International Journal of Hydrogen Energy, Vol. 38, No. 27, pp. 11920-11929.
[13] Hassan, A. M., Alrashdan, A., Hayajneh, M.T. and Mayyas, A.T. (2009). “Prediction of density, porosity and hardness in aluminum–copper-based composite materials using artificial neural network.” Journal of Materials Processing Technology, Vol. 209, No. 2, pp. 894-899.
[14] Torkar, D., Novak, S. and Novak, F. (2008). “Apparent viscosity prediction of alumina–paraffin suspensions using artificial neural networks”, Journal of Materials Processing Technology, Vol. 203, No. 1-3, pp. 208-215.
[15] Ghaderi, F., Ghaderi, A. H., Najafi, B. and Gha-deri, N. (2013). “Viscosity prediction by computational method and artificial neural network approach: The case of six refrigerants.” The Journal of Supercritical Fluids, Vol. 81, pp. 67-78.
[16] Deosarkar, M. P. and Sathe, V. S. (2012). “Predicting effective viscosity of magnetite ore slurries by using artificial neural network.” Powder Technology, Vol. 219, pp. 264-270.
[17] Salam, M., Al-Alawi, S. and Maqrashi, A. (2008). “Prediction of equivalent salt deposit density of contaminated glass plates using artificial neural networks.” Journal of Electrostatics, Vol. 66, pp. 526-530.
[18] Ahmadi, S. H., Sepaskhah, A. R., Andersen, M.N., Plauborg, F., Jensen, C. R. and Hansen, S. (2014). “Modeling root length density of field grown potatoes under different irrigation strategies and soil textures using artificial neural networks.” Field Crops Research. Vol. 162, pp. 99-107.
[19] Ghaedi, A. (2015). “Simultaneous prediction of the thermodynamic properties of aqueous solution of ethylene glycol monoethyl ether using artificial neural network.” Journal of Molecular Liquids, Vol. 207, pp.327-333.
[20] Soriano, A. N., Ornedo-Ramos, K. F. P., Muriel, C. A. M., Adornado, A. P., Bungay, V. C., & Li, M. H. (2016). “Prediction of refractive index of binary solutions consisting of ionic liquids and alcohols (methanol or ethanol or 1-propanol) using artificial neural network”, Journal of the Taiwan Institute of Chemical Engineers, Vol.65, pp. 83-90.
[21] Sexton, R. S., Dorsey, R. E. and Sikander, N.A. (2002). “Simultaneous optimization of neural network function and architecture algorithm.” Decision Support Systems, pp. 1034-1047.
[22] Braik M., Sheta A. and Arieqat A. (2008). "A comparison between GAs and PSO in training ANN to model the TE chemical process reactor." In AISB 2008 Convention communication, interaction and social intelligence, Vol. 11, p. 24-30
[23] Fogel, D. B. (1994). “An introduction to simulated evolutionary optimization.” IEEE Transactions on Neural Networks. Vol. 5, No. 1, pp. 3-14.
[24] Huang, Y. (2009). “Advances in Artificial Neural Networks – Methodological Development and Application”, Algorithms. Vol. 2, No. 3, pp.973-1007.
[25] Abbass, H. A., Sarker, R. and Newton, C. (2001). “PDE: A Pareto-frontier Differential Evolution Approach for Multi-objective Optimization Problems.” in Proceedings of the Congress on Evolutionary Computation 2001 (CEC’2001), Vol. 2, pp. 971–978, Piscataway, New Jersey, IEEE Service Center.
[26] Kiran, R., Jetti, S. R. and Venayagamoorthy, G. K. (2006). ‘Online training of generalized neuron with particle swarm optimization’, in International Joint Conference on Neural Networks, IJCNN 06, Vancouver, BC, Canada, pp. 5088– 5095. IEEE, (2006).
[27] Choenauer, M. and Michalewicz, Z. (1997). “Evolutionary computation control and cybernetics.” Proceedings of the IEEE, Vol. 26, No. 3, pp. 307–338.
[28] Sit, C. W. (2005). “Application of Artificial Neural Network-Genetic Algorithm in Inferential Estimation and Control of a Distillation Column”, ME thesis, Faculty of Chemical and Natural Resources Engineering, Universiti Teknologi Malaysia.
[29] Sheta, A. and Turabieh, H. (2006). “A comparison between genetic algorithms and sequential quadratic programming in solving constrained optimization problems”, ICGST International Journal on Artificial Intelligence and Machine Learning, Vol. 6, No. 1, pp. 67–74.
[30] Gen, M. and Cheng, R. (1997). Genetic Algorithms and Engineering Design, John Wiley & Son, Inc., Hoboken.
[31] Sheta, A., Turabieh, H. and Vasant, P. (2007). “Hybrid optimization genetic algorithms (HOGA) with interactive evolution to solve constraint optimization problems.” International Journal of Computational Science, Vol.1, No. 4, pp. 395–406.
[32] Sheta A. and Eghneem, K. (2007). “Training artificial neural networks using genetic algorithms to predict the price of the general index for Amman stock exchange”, in Midwest Artificial Intelligence and Cognitive Science Conference, DePaul University, Chicago, IL, USA, Vol. 92, pp. 7–13.
[33] Kennedy, J. and Eberhart, R. C. (1995). “Particle swarm optimization’, Proceedings of IEEE International Conference on Neural Networks (Perth, Australia), IEEE Service Center, Piscataway, NJ, Vol. 5, No. 3, pp. 1942–1948.
[34] Kennedy, J., Eberhart, R. C. and Shi, Y. (2001). Swarm Intelligence, Morgan Kaufmann Publishers, San Francisco.
[35] Kiran, R., Jetti, S. R. and Venayagamoorthy G. K. (2006). “Online training of generalized neuron with particle swarm optimization”, in International Joint Conference on Neural Networks, IJCNN 06, Vancouver, BC, Canada, pp. 5088– 5095. IEEE.
[36] Richer, T.J. and Blackwell, T.M. (2006). “When is a swarm necessary?”, in Proceedings of the 2006 IEEE Congress on Evolutionary Computation, eds., Gary G. Yen, Simon M. Lucas, Gary Fogel, Graham Kendall, Ralf Salomon, Byoung-Tak Zhang, Carlos A. Coello, and Thomas Philip Runarsson, pp. 1469–1476, Vancouver, BC, Cana-da, IEEE Press.
[37] Kwok, N., Liu, D. and Tan, K. (2006). “An empirical study on the setting of control coefficient in particle swarm optimization”, in Proceedings of IEEE Congress on Evolutionary Computation (CEC 2006), Vancouver, BC, Canada, pp. 3165–3172, Vancouver, BC, Canada, IEEE Press.
[38] Orge, B., Iglesias, M., Rodriguez, A., Canosa, J. M. and Tojo. J. (1997) “Mixing properties of (methanol, ethanol, or 1-propanol) with (n-pentane, n-hexane, n-heptane and n-octane) at 298.15 K.” Fluid Phase Equilibria, Vol. 133, No. 1-2, pp. 213-227.
[39] Segade., L., de Liano, J. J., Domınguez-Prez, M., Oscar, C., Cabanas, M. and Jimenez. E. (2003). “Density, Surface Tension, and Refractive Index of Octane + 1-Alkanol Mixtures at T = 298.15 K.” Journal of Chemical & Engineering Data, Vol. 48, No. 5, pp.1251-1255.
[40] Aucejo, A., Burguet, A. C., Munoz, R. and Marques, J.L. (1995). “Densities, Viscosities, and Refractive Indices of Some n-Alkane Binary Liquid Systems at 298.15 K.” Journal of Chemical and Engineering Data, Vol. 40, No. 1, pp. 141-147.
[41] Mehra, R. (2003). “Application of refractive index mixing rules in binary systems of hexade-cane and heptadecane with n-alkanols at different temperatures.” Journal of Chemical Sciences. Vol. 115, No. 2, pp. 147–154.
[42] Resa, J. M., Gonzalez, C. and Goenaga, J. M. (2005). “Density, Refractive Index, Speed of Sound at 298.15 K, and Vapor-Liquid Equilibria at 101.3 kPa for Binary Mixtures of Methanol + 2-Methyl-1-butanol and Ethanol + 2-Methyl-1-butanol.” Journal of Chemical & Engineering Data, Vol. 50, No. 5, pp.1570-1575.
[43] Resa, J.M., Gonzalez, C. and Goenaga, J. M. (2006). “Density, Refractive Index, Speed of Sound at 298.15 K, and Vapor-Liquid Equilibria at 101.3 kPa for Binary Mixtures of Propanol + 2-Methyl-1-butanol and Propanol + 3-Methyl-1-butanol.” Journal of Chemical & Engineering Data, Vol. 51, Vol. 1, pp. 73-78.
[44] Bahadur, I., Naidoo, P., Singh, S., Ramjuger-nath, D. and Deenadayalu, N. (2014). “Effect of temperature on density, sound velocity, refractive index and their derived properties for the binary systems (heptanoic acid + propanoic or butanoic acids)”, The Journal of Chemical Thermodynamics, Vol. 78 pp. 7–15.
[45] Kijevcanin, M. L., Radovic, I. R., Djordjevic, B. D., Tasic, A.Z. and Serbanovic, S. P. (2011). “Experimental determination and modeling of densities and refractive indices of the binary systems alcohol + dicyclohexylamine at T = (288.15–323.15) K.” Themochimica Acta Vol. 525, No. 1, pp.114– 128.
[46] Poling, B. E., Prausnitz, J. M. and O’Connell, J. (2001). The Properties of Gases and Liquids, 5th edition. Mcgraw-hill. New York. pp. 723-73.