Abstract
Grammar-based Immune Programming (GIP) is a method for evolving programs in an arbitrary language using an immunological inspiration. GIP is applied here to solve the relevant modeling problem of finding a system of differential equations –in analytical form– which better explains a given set of data obtained from a certain phenomenon. Computational experiments are performed to evaluate the approach, showing that GIP is an efficient technique for symbolic modeling.
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Bernardino, H.S., Barbosa, H.J.C.: Grammar-based immune programming for symbolic regression. In: Andrews, P.S., Timmis, J., Owens, N.D.L., Aickelin, U., Hart, E., Hone, A., Tyrrell, A.M. (eds.) ICARIS 2009. LNCS, vol. 5666, pp. 274–287. Springer, Heidelberg (2009)
Bernardino, H.S., Barbosa, H.J.C.: Artificial Immune Systems for Optimization. In: Chiong, R. (ed.) Nature-Inspired Algorithms for Optimisation. vol. 193, pp. 389–411. Springer, Heidelberg (2009)
Bernardino, H.S., Barbosa, H.J.C.: Comparing two ways of inferring a differential equation model via grammar-based immune programming. In: Proc. of the Iberian-Latin-American Congress on Computational Methods in Engineering (2010)
Bernardino, H.S., Barbosa, H.J.C.: Grammar-based immune programming. Natural Computing 10, 209–241 (2011)
Cao, H., Kang, L., Chen, Y.: Evolutionary modelling of systems of ordinary differential equations with genetic programming. Genetic Programming and Evolvable Machines (1), 309–337 (2000)
Ciccazzo, A., Conca, P., Nicosia, G., Stracquadanio, G.: An advanced clonal selection algorithm with ad-hoc network-based hypermutation operators for synthesis of topology and sizing of analog electrical circuits. In: Bentley, P.J., Lee, D., Jung, S. (eds.) ICARIS 2008. LNCS, vol. 5132, pp. 60–70. Springer, Heidelberg (2008)
de Castro, L.N., von Zuben, F.J.: Learning and optimization using the clonal selection principle. IEEE Trans. Evo. Comp. 6(3), 239–251 (2002)
Gan, Z., Chow, T.W., Chau, W.: Clone selection programming and its application to symbolic regression. Expert Systems with Appl. 36(2), 3996–4005 (2009)
Gan, Z., Zhao, M.-B., Chow, T.W.: Induction machine fault detection using clone selection programming. Expert Systems with Appl. 36(4), 8000–8012 (2009)
Hofbauer, J., Sigmund, K.: The Theory of Evolution and Dynamical Systems. Cambridge University Press, Cambridge (1988)
Iba, H.: Inference of differential equation models by genetic programming. Information Sciences 178(23), 4453–4468 (2008)
Johnson, C.G.: Artificial immune system programming for symbolic regression. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 345–353. Springer, Heidelberg (2003)
Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection (Complex Adaptive Systems). MIT Press, Cambridge (1992)
Koza, J.R., Bennett III, F.H., Andre, D., Keane, M.A.: Synthesis of topology and sizing of analog electrical circuits by means of genetic programming. Computer Methods in Applied Mechanics and Engineering 186(2-4), 459–482 (2000)
Lau, A., Musilek, P.: Immune programming models of cryptosporidium parvum inactivation by ozone and chlorine dioxide. Information Sciences 179(10), 1469–1482 (2009)
McKinney, B., Tian, D.: Grammatical immune system evolution for reverse engineering nonlinear dynamic bayesian models. Cancer Informatics 6, 433–447 (2008)
Musilek, P., Lau, A., Reformat, M., Wyard-Scott, L.: Immune programming. Information Sciences 176(8), 972–1002 (2006)
O’Neill, M., Brabazon, A.: Grammatical differential evolution. In: Proceedings of the 2006 International Conference on Artificial Intelligence - ICAI 2006, pp. 231–236. CSREA Press, Las Vegas (2006)
O’Neill, M., Brabazon, A., Adley, C.: The automatic generation of programs for classification problems with grammatical swarm. In: Rauterberg, M. (ed.) ICEC 2004. LNCS, vol. 3166, pp. 57–67. Springer, Heidelberg (2004)
O’Neill, M., Ryan, C.: Grammatical evolution. IEEE Transactions on Evolutionary Computation 5(4), 349–358 (2001)
Ryan, C., Collins, J., Neill, M.O.: Grammatical evolution: Evolving programs for an arbitrary language. In: Banzhaf, W., Poli, R., Schoenauer, M., Fogarty, T.C. (eds.) EuroGP 1998. LNCS, vol. 1391, pp. 83–95. Springer, Heidelberg (1998)
Sakamoto, E., Iba, H.: Inferring a system of differential equations for a gene regulatory network by using genetic programming. In: Proceedings of the Congress on Evolutionary Computation, pp. 720–726 (2001)
Schmidt, M.D., Lipson, H.: Data-mining dynamical systems: Automated symbolic system identification for exploratory analysis. In: Proc. of the Biennial ASME Conf. on Engineering Systems Design and Analysis, Haifa, Israel (2008)
Tominaga, D., Koga, N., Okamoto, M.: Efficient numerical optimization algorithm based on genetic algorithm for inverse problem. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 251–258 (2000)
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Bernardino, H.S., Barbosa, H.J.C. (2011). Inferring Systems of Ordinary Differential Equations via Grammar-Based Immune Programming. In: Liò, P., Nicosia, G., Stibor, T. (eds) Artificial Immune Systems. ICARIS 2011. Lecture Notes in Computer Science, vol 6825. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22371-6_19
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DOI: https://doi.org/10.1007/978-3-642-22371-6_19
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