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Optimizing constrained problems through a T-Cell artificial immune system
Keywords:
artificial immune system, constrained optimization problemAbstract
In this paper, we present a new model of an artificial immune system (AIS), based on the process that suffers the T-Cell, it is called T-Cell Model. It is used for solving constrained (numerical) optimization problems. The model operates on three populations: Virgins, Effectors and Memory. Each of them has a different role. Also, the model dynamically adapts the tolerance factor in order to improve the exploration capabilities of the algorithm. We also develop a new mutation operator which incorporates knowledge of the problem. We validate our proposed approach with a set of test functions taken from the specialized literature and we compare our results with respect to Stochastic Ranking (which is an approach representative of the state-of-theart in the area), with respect to an AIS previously proposed and a self-organizing migrating genetic algorithm for constrained optimization (C-SOMGA).
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References
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[3] P. Chootinan and A. Chen. Constraint handling in genetic algorithms using a gradient-based repair method. Computers and Operations Research 33, pp. 22632281, 2006.
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[6] Carlos A. Coello Coello and Nareli Cruz-Cortés. Hybridizing a genetic algorithm with an artificial immune system for global optimization. Engineering Optimization, 36(5):607–634, October 2004.
[7] Nareli Cruz Cort ́es, Daniel Trejo-Pérez, and Carlos A. Coello Coello. Handling constrained in global optimization using artificial immune system. In Christian Jacob, Marcin L. Pilat, Peter J. Bentley, and Jonathan Timmis, editors, Artificial Immune Systems. 4th International Conference, ICARIS 2005, pages 234–247. Springer. Lecture Notes in Computer Science Vol. 3627, Banff, Canada, August 2005.
[8] K. Deep. A self-organizing migrating genetic algorithm for constrained optimization. Applied Mathematics and Computation 198, pp. 237250, 2008.
[9] Bernabe Dorronsoro. An ́alisis de varianza (ANOVA) con MATLAB MINI-HOWTO.
[10] H. Chueh G. C. Luh and W. W. Liu. MOIA: Multi Objective Immune Algorithm. Engineering Optimization, 35(2):143–164, 2003.
[11] Simon M. Garrett. How do we evaluate artificial immune systems? Evol. Comput., 13(2):145–177, 2005.
[12] R. Hess. A heuristic search for estimating a global solution of non convex programming problems. Operations Research 21, pp.12671280, 1973.
[13] D.M. Himmelblau. Applied nonlinear programming. McGraw-Hill: New York, 1972.
[14] J. E. Hunt and D. E. Cooke. An adaptative, distributed learning system based on the immune system. In Procceding of the IEEE International Conference on System, Man and Cybernatics, pages 2494-2499, 1995.
[15] N. K. Jerne. The imune system. Scientific American, 229(1):52-60, 1973.
[16] Johnny Kelsey and Jon Timmis. Immune inspired somatic contiguous hypermutation for function optimisation. In Erick Cant ́u-Paz, James A. Foster, Kalyanmoy Deb, Lawrence Davis, Rajkumar Roy, Una-May O’Reilly, Hans-Georg Beyer, Russell K. Standish, Graham Kendall, Stewart W. Wilson, Mark Harman, Joachim Wegener, Dipankar Dasgupta, Mitchell A. Potter, Alan C. Schultz, Kathryn A. Dowsland, Natasa Jonoska, and Julian F. Miller, editors, GECCO, volume 2723 of Lecture Notes in Computer Science, pages 207–218. Springer, 2003.
[17] Slawomir Koziel and Zbigniew Michalewicz. Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization. Evolutionary Computation, 7(1):19–44, 1999.
[18] S. Esquivel L. Cagnina and C. Coello Coello. A bi-population pso with a shake-mechanism for solving numerical optimization. In Proceedings of the Congress on Evolutionary Computation 2007.
[19] G. C. Luh and H. Chueh. Multi-objective optimal designof truss structure with immune algorithm. Computers and Structures, 82:829–844, 2004.
[20] L. Nunes de Castro and J. Timmis. An artificial immune network for multimodal function optimization. In Proccedings of the 2002 Congress on Evolutionary Computation (CEC’2002), volume 1, pages 669–674, Honolulu, Hawaii, May 2002.
[21] L. Nunes de Castro and F.J. Von Zuben. Learning and optimization using the clonal selection principle. IEEE Transactions on Evolutionary Computation, 6(3):239–251, 2002.
[22] Thomas P. Runarsson and Xin Yao. Stochastic Ranking for Constrained Evolutionary Optimization. IEEE Transactions on Evolutionary Computation, 4(3):284–294, September 2000.
[23] L. Allen S. Forrest, A. Perelson and R. Cherukuri. Self-nonself discrimination in a computer. IEEE Symposium on Research in Security and Privacy, pages 202–212, May 1994.
[2] Jerzy Balicki. Multi-criterion Evolutionary Algorithm with Model of the Immune System to Handle Constraints for Task Assignments. In Leszek Rutkowski, J ̈org H. Siekmann, Ryszard Tadeusiewicz, and Lotfi A. Zadeh, editors, Artificial Intelligence and Soft Computing - ICAISC 2004, 7th International Conference. Proceedings, pages 394–399, Zakopane, Poland, June 2004. Springer. Lecture Notes in Computer Science. Volume 3070.
[3] P. Chootinan and A. Chen. Constraint handling in genetic algorithms using a gradient-based repair method. Computers and Operations Research 33, pp. 22632281, 2006.
[4] Carlos A. Coello Coello. Theoretical and Numerical Constraint Handling Techniques used with Evolutionary Algorithms: A Survey of the State of the Art. Computer Methods in Applied Mechanics and Engineering, 191(11-12):1245–1287, January 2002.
[5] J. Liang T. Runarsson E. Mezura-Montes M. Clere P. Suganthan C. Coello Coello and K. Deb. Problem definitions and evaluation criteria for the cec 2006 special session on constrained real-parameter optimization. Technical Report, Nanyang Technological University, 2006.
[6] Carlos A. Coello Coello and Nareli Cruz-Cortés. Hybridizing a genetic algorithm with an artificial immune system for global optimization. Engineering Optimization, 36(5):607–634, October 2004.
[7] Nareli Cruz Cort ́es, Daniel Trejo-Pérez, and Carlos A. Coello Coello. Handling constrained in global optimization using artificial immune system. In Christian Jacob, Marcin L. Pilat, Peter J. Bentley, and Jonathan Timmis, editors, Artificial Immune Systems. 4th International Conference, ICARIS 2005, pages 234–247. Springer. Lecture Notes in Computer Science Vol. 3627, Banff, Canada, August 2005.
[8] K. Deep. A self-organizing migrating genetic algorithm for constrained optimization. Applied Mathematics and Computation 198, pp. 237250, 2008.
[9] Bernabe Dorronsoro. An ́alisis de varianza (ANOVA) con MATLAB MINI-HOWTO.
[10] H. Chueh G. C. Luh and W. W. Liu. MOIA: Multi Objective Immune Algorithm. Engineering Optimization, 35(2):143–164, 2003.
[11] Simon M. Garrett. How do we evaluate artificial immune systems? Evol. Comput., 13(2):145–177, 2005.
[12] R. Hess. A heuristic search for estimating a global solution of non convex programming problems. Operations Research 21, pp.12671280, 1973.
[13] D.M. Himmelblau. Applied nonlinear programming. McGraw-Hill: New York, 1972.
[14] J. E. Hunt and D. E. Cooke. An adaptative, distributed learning system based on the immune system. In Procceding of the IEEE International Conference on System, Man and Cybernatics, pages 2494-2499, 1995.
[15] N. K. Jerne. The imune system. Scientific American, 229(1):52-60, 1973.
[16] Johnny Kelsey and Jon Timmis. Immune inspired somatic contiguous hypermutation for function optimisation. In Erick Cant ́u-Paz, James A. Foster, Kalyanmoy Deb, Lawrence Davis, Rajkumar Roy, Una-May O’Reilly, Hans-Georg Beyer, Russell K. Standish, Graham Kendall, Stewart W. Wilson, Mark Harman, Joachim Wegener, Dipankar Dasgupta, Mitchell A. Potter, Alan C. Schultz, Kathryn A. Dowsland, Natasa Jonoska, and Julian F. Miller, editors, GECCO, volume 2723 of Lecture Notes in Computer Science, pages 207–218. Springer, 2003.
[17] Slawomir Koziel and Zbigniew Michalewicz. Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization. Evolutionary Computation, 7(1):19–44, 1999.
[18] S. Esquivel L. Cagnina and C. Coello Coello. A bi-population pso with a shake-mechanism for solving numerical optimization. In Proceedings of the Congress on Evolutionary Computation 2007.
[19] G. C. Luh and H. Chueh. Multi-objective optimal designof truss structure with immune algorithm. Computers and Structures, 82:829–844, 2004.
[20] L. Nunes de Castro and J. Timmis. An artificial immune network for multimodal function optimization. In Proccedings of the 2002 Congress on Evolutionary Computation (CEC’2002), volume 1, pages 669–674, Honolulu, Hawaii, May 2002.
[21] L. Nunes de Castro and F.J. Von Zuben. Learning and optimization using the clonal selection principle. IEEE Transactions on Evolutionary Computation, 6(3):239–251, 2002.
[22] Thomas P. Runarsson and Xin Yao. Stochastic Ranking for Constrained Evolutionary Optimization. IEEE Transactions on Evolutionary Computation, 4(3):284–294, September 2000.
[23] L. Allen S. Forrest, A. Perelson and R. Cherukuri. Self-nonself discrimination in a computer. IEEE Symposium on Research in Security and Privacy, pages 202–212, May 1994.
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Published
2008-10-01
How to Cite
Aragón, V. S., Esquivel, S. C., & Coello Coello, C. (2008). Optimizing constrained problems through a T-Cell artificial immune system. Journal of Computer Science and Technology, 8(03), p. 158–165. Retrieved from https://journal.info.unlp.edu.ar/JCST/article/view/758
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