An Immune Self-adaptive Differential Evolution Algorithm with Application to Estimate Kinetic Parameters for Homogeneous Mercury Oxidation

Abstract

Abstract: A new version of differential evolution(DE) algorithm,in which immune concepts and methods are applied to determine the parameter setting,named immune self-adaptive differential evolution(ISDE),is proposed to improve the performance of the DE algorithm.During the actual operation,ISDE seeks the optimal parameters arising from the evolutionary process,which enable ISDE to alter the algorithm for different optimization problems and improve the performance of ISDE by the control parameters' self-adaptation.The performance of the proposed method is studied with the use of nine benchmark problems and compared with original DE algorithm and other well-known self-adaptive DE algorithms.The experiments conducted show that the ISDE clearly outperforms the other DE algorithms in all benchmark functions.Furthermore,ISDE is applied to develop the kinetic model for homogeneous mercury(Hg) oxidation in flue gas,and satisfactory results are obtained.

Key words: differential evolution, immune system, evolutionary computation, parameter estimation

摘要： A new version of differential evolution(DE) algorithm,in which immune concepts and methods are applied to determine the parameter setting,named immune self-adaptive differential evolution(ISDE),is proposed to improve the performance of the DE algorithm.During the actual operation,ISDE seeks the optimal parameters arising from the evolutionary process,which enable ISDE to alter the algorithm for different optimization problems and improve the performance of ISDE by the control parameters' self-adaptation.The performance of the proposed method is studied with the use of nine benchmark problems and compared with original DE algorithm and other well-known self-adaptive DE algorithms.The experiments conducted show that the ISDE clearly outperforms the other DE algorithms in all benchmark functions.Furthermore,ISDE is applied to develop the kinetic model for homogeneous mercury(Hg) oxidation in flue gas,and satisfactory results are obtained.

关键词: differential evolution, immune system, evolutionary computation, parameter estimation

HU Chunping, YAN Xuefeng. An Immune Self-adaptive Differential Evolution Algorithm with Application to Estimate Kinetic Parameters for Homogeneous Mercury Oxidation[J]. , 2009, 17(2): 232-240.

胡春平, 颜学峰. An Immune Self-adaptive Differential Evolution Algorithm with Application to Estimate Kinetic Parameters for Homogeneous Mercury Oxidation[J]. , 2009, 17(2): 232-240.

References

1 Storn, R., Price, K., “Differential evolution-A simple and efficient heuristic for global optimization over continuous spaces”, Technical Report TR-95-012, International Computer Science Institute, Berkeley, CA, USA (1995).
2 Ingber, L., “Simulated annealing:Practice versus theory”, Math. Comput. Model., 18, 29-57 (1993).
3 Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., Numerical Recipes in C, Cambridge University Press, UK (1992).
4 Muehlenbein, H., Schlierkamp, V., “Predictive models for the breeder genetic algorithm (I) Continuous parameter optimizations”, Evolut. Comput., 1, 25-49 (1993).
5 Voigt, H.M., “Soft genetic operators in evolutionary algorithms”, Lecture Notes in Computer Science, 899, 123-141 (1995).
6 Aluffi-Pentini, F., Parisi, V., Zirilli, F., “Global optimization and stochastic differential equations”, J. Optimiz. Theory Appl., 47, 1–16 (1985).
7 Vesterstrom, J., Thomsen, R., “A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems”, In:Proceedings of the Sixth Congress on Evolutionary Computation, IEEE Press, USA, 332-339 (2004).
8 Eberhart, R., Kennedy, J., “A new optimizer using particle swarm theory”, In:Proceedings of the Sixth International Symposium on Micromachine and Human Science, IEEE Press, Nagoya, Japan, 39-43 (1995).
9 Krink, T., Paterlini, S., Resti, A., “Using differential evolution to improve the accuracy of bank rating systems”, Comput. Stat. Data An., 52, 68-87 (2007).
10 Holland, J.H., Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Harbor (1975).
11 Brest, J., Bo kovi , B., Greiner, S., umer, V., Mau ec., M., “Performance comparison of self-adaptive and adaptive differential evolution algorithms”, Soft Comput., 11, 617-629 (2007).
12 Liu, J., Lampinen., J., “A fuzzy adaptive differential revolution algorithm”, In:Proceedings of the IEEE International Region 10 Conference on Computers, Communications, Control and Power Engineering, IEEE Press, Beijing, China, 606-611(2002).
13 Storn, R., “On the usage of differential evolution for function optimization”, In:Biennial Conference of North American Fuzzy Information Processing Society, IEEE Press, Berkeley, USA, 519–523 (1996).
14 Babu, B., Jehan, M., “Differential evolution for multi-objective optimization”, In:Proceedings of the IEEE Congress on Evolutionary Computation, IEEE Press, Canberra, Australia, 2696-2703 (2003).
15 Abbass., H., “The self-adaptive pareto differential evolution algorithm”, In:Proceedings of the IEEE Congress on Evolutionary Computation, IEEE Press, Hawaii, USA, 831-836 (2002).
16 Omran, M., Salman, A., Engelbrecht, A., “Self-adaptive differential evolution”, In:Proceedings of the International Conference on Computational Intelligence and Security, IEEE Press, Xi'an, China, 192-199 (2005).
17 Yuan, X.H., Zhang, Y., Wang, L., Yuan, Y.B., “An enhanced differential evolution algorithm for daily optimal hydro generation scheduling”, Comput. Math. Appl., 55, 2458-2468 (2008).
18 Nobakhti, A., Wang, H., “A simple self-adaptive differential evolution algorithm with application on the ALSTOM gasifier”, Appl. Soft Comput., 8, 350–370 (2008).
19 Eiben, A., Hinterding, R., Michalewicz, Z., “Parameter control in evolutionary algorithms”, IEEE T. Evolut. Comput., 3, 124-141 (1999).
20 Carlos, A.C.C., “Use of a self-adaptive penalty approach for engineering optimization problems”, Comput. Ind., 41, 113-127 (2000).
21 He, Q., Wang, L., “An effective co-evolutionary particle swarm optimization for constrained engineering design problems”, Eng. Appl. Artif. Intel., 20, 89-99 (2007).
22 Hu, F.Z., Wang, L., He, Q., “An effective co-evolutionary differential evolution for constrained optimization”, Appl. Math. Comput., 186, 340-356 (2007).
23 Storn, R., Price, K., “Differential evolution-A simple and efficient heuristic for global optimization over continuous spaces”, J. Global Optim., 11, 341-359 (1997).
24 Agarwal, H., Stenger, H.G., Wu, S., Fan, Z., “Effects of H₂O, SO₂ and NO on homogeneous Hg oxidation by Cl₂ ”, Energ. Fuel., 20, 1068-1075 (2006).
25 Agarwal, H., Romero, C.E., Stenger, H.G., “Comparing and interpreting laboratory results of Hg oxidation by a chlorine species”, Fuel Process. Technol., 88, 723-730 (2007).
26 Farmer, J.D., Packard, N.H., Perelson, A.S., “The immune system, adaptation, and machine learning”, Phys. D, 2, 187-204 (1986).
27 Wu, X.L., Lu, J.G., Sun, Y.X., “An improved differential evolution for optimization of chemical process”, Chin. J. Chem. Eng., 16, 228-234 (2008).
28 Jiao, L.C., Wang, L., “A novel genetic algorithm based on immunity”, IEEE T. Syst. Man Cy. A, 30, 552-561 (2000).
29 Zeng, C.W., Gu, T.L., “A novel immunity-growth genetic algorithm for traveling salesman problem”, In:Proceedings of IEEE Conference on Natural Computation, IEEE Press, Haikou, China, 394-398 (2007).
30 Xin, Y., Liu, Y., Lin, G.M., “Evolutionary programming made faster”, IEEE T. Evolut. Comput., 3, 82-102 (1999).
31 Krink, T., Filipi , B., Fogel, B., “Noisy optimization problems-A particular challenge for differential evolution?”, In:Proceedings of the IEEE Congress on Evolutionary Computation, IEEE Press, Portland, USA, 332-339 (2004).
32 Salman, A., Engelbrecht, A., Omran, M., “Empirical analysis of self-adaptive differential evolution”, Eur. J. Oper. Res., 83, 785–804 (2007).
33 Niksa, S., Helble, J.J., Fujiwara, N., “Kinetic modeling of homogeneous mercury oxidation:The importance of NO and H₂O in predicting oxidation in coal-derived systems”, Environ. Sci. Technol., 35, 3701-3706 (2001).
34 Agarwal, H., Stenger, H.G., “Development of a predictive kinetic model for homogeneous Hg oxidation data”, Math. Comput. Model., 45, 109-125 (2007).

[1]	Zhansheng Li, Jiayu Song, Shouhai Zhang, Jinyan Wang, Xigao Jian. Measurement and correlation of liquid-liquid equilibrium for the ternary system (water + 1,2-dichloroethane + sulfolane) at 288.15, 298.15, and 308.15 K [J]. Chinese Journal of Chemical Engineering, 2022, 51(11): 109-114.
[2]	Markus Enekvist, Xiaodong Liang, Xiangping Zhang, Kim Dam-Johansen, Georgios M. Kontogeorgis. Estimating Hansen solubility parameters of organic pigments by group contribution methods [J]. Chinese Journal of Chemical Engineering, 2021, 29(3): 186-197.
[3]	Kamel Hendaoui, Malika Trabelsi-Ayadi, Fadhila Ayari. Optimization and mechanisms analysis of indigo dye removal using continuous electrocoagulation [J]. Chinese Journal of Chemical Engineering, 2021, 29(1): 242-252.
[4]	Feiran Sun, Tao Liu, Yi Cao, Xiongwei Ni, Zoltan Kalman Nagy. Kinetic parameter estimation for cooling crystallization process based on cell average technique and automatic differentiation [J]. Chinese Journal of Chemical Engineering, 2020, 28(6): 1637-1651.
[5]	Peixian Zang, Guoming Sun, Yongming Zhao, Yiqing Luo, Xigang Yuan. Stochastic optimization based on a novel scenario generation method for midstream and downstream petrochemical supply chain [J]. Chinese Journal of Chemical Engineering, 2020, 28(3): 815-823.
[6]	Liang Ming, Jinsong Zhao. Feature selection for chemical process fault diagnosis by artificial immune systems [J]. Chin.J.Chem.Eng., 2018, 26(8): 1599-1604.
[7]	Denglong Ma, Wei Tan, Zaoxiao Zhang, Jun Hu. Gas emission source term estimation with 1-step nonlinear partial swarm optimization-Tikhonov regularization hybrid method [J]. Chin.J.Chem.Eng., 2018, 26(2): 356-363.
[8]	Lili Tao, Bin Xu, Zhihua Hu, Weimin Zhong. Multi-objective optimization of p-xylene oxidation process using an improved self-adaptive differential evolution algorithm [J]. , 2017, 25(8): 983-991.
[9]	Yong Li, Jizheng Chu, Jiarui Zhang. A new generic reaction for modeling fluid catalytic cracking risers [J]. , 2017, 25(10): 1449-1460.
[10]	Yong Li, Jizheng Chu, Jiarui Zhang. A new generic reaction for modeling fluid catalytic cracking risers [J]. , 2017, 25(10): 1449-1460.
[11]	Felix Gebauer, Mark W. Hlawitschka, Hans-Jörg Bart. CFD aided investigation of single droplet coalescence [J]. , 2016, 24(2): 249-252.
[12]	Xu Chen, Wenli Du, Feng Qian. Solving chemical dynamic optimization problems with ranking-based differential evolution algorithms [J]. Chin.J.Chem.Eng., 2016, 24(11): 1600-1608.
[13]	Chong Su, Hongguang Li. A novel interactive preferential evolutionary method for controller tuning in chemical processes [J]. , 2015, 23(2): 398-411.
[14]	NIAN Xiaoyu, WANG Zhenlei, QIAN Feng. A Hybrid Algorithm Based on Differential Evolution and Group Search Optimization and Its Application on Ethylene Cracking Furnace [J]. Chin.J.Chem.Eng., 2013, 21(5): 537-543.
[15]	ZHAO Chao, XU Qiaoling, LIN Siming, LI Xuelai. Hybrid Differential Evolution for Estimation of Kinetic Parameters for Biochemical Systems [J]. Chin.J.Chem.Eng., 2013, 21(2): 155-162.