Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 184540, 10 pages
http://dx.doi.org/10.1155/2014/184540
Research Article

Geometric Generalisation of Surrogate Model-Based Optimisation to Combinatorial and Program Spaces

1Department of Computer Science and Engineering, Kwangwoon University, Nowon-gu, Seoul 139-701, Republic of Korea
2Department of Computer Science, Streatham Campus, University of Exeter, Exeter EX4 4QF, UK
3Computer Science Department, Umm Al-Qura University, Makkah 21955, Saudi Arabia
4Department of Computer Engineering, Gachon University, Seongnam-si, Gyeonggi-do 461-701, Republic of Korea

Received 14 March 2014; Accepted 31 March 2014; Published 29 April 2014

Academic Editor: Ker-Wei Yu

Copyright © 2014 Yong-Hyuk Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. M. Pardalos and M. G. C. Resende, Handbook of Applied Optimization, Oxford University Press, 2002.
  2. P. M. Pardalos and E. Romeijn, Eds., Handbook of Global Optimization. Volume 2, vol. 62, Kluwer Academic Publishers, 2002. View at MathSciNet
  3. J.-H. Seo, Y.-H. Kim, H.-B. Ryou, S.-H. Cha, and M. Jo, “Optimal sensor deployment for wireless surveillance sensor networks by a hybrid steady-state genetic algorithm,” IEICE Transactions on Communications, vol. E91-B, no. 11, pp. 3534–3543, 2008. View at Publisher · View at Google Scholar · View at Scopus
  4. S. S. Tong and B. A. Gregory, “Turbine preliminary design using artificial intelligence and numerical optimization techniques,” Journal of Turbomachinery, vol. 114, no. 1, pp. 1–10, 1992. View at Google Scholar · View at Scopus
  5. H.-M. Gutmann, “A radial basis function method for global optimization,” Journal of Global Optimization, vol. 19, no. 3, pp. 201–227, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. D. R. Jones, M. Schonlau, and W. J. Welch, “Efficient global optimization of expensive black-box functions,” Journal of Global Optimization, vol. 13, no. 4, pp. 455–492, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. R. G. Regis and C. A. Shoemaker, “Constrained global optimization of expensive black box functions using radial basis functions,” Journal of Global Optimization, vol. 31, no. 1, pp. 153–171, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. D. R. Jones, “A taxonomy of global optimization methods based on response surfaces,” Journal of Global Optimization, vol. 21, no. 4, pp. 345–383, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. N. A. C. Cressie, Statistics for Spatial Data, John Wiley & Sons, New York, NY, USA, 1993. View at MathSciNet
  10. T. Mitchell, Machine Learning, McGraw Hill, 1997.
  11. J.-H. Seo, Y.-H. Lee, and Y.-H. Kim, “Feature selection for very short-term heavy rainfall prediction using evolutionary computation,” Advances in Meteorology, vol. 2014, Article ID 203545, 15 pages, 2014. View at Publisher · View at Google Scholar
  12. G.-M. Yoon, J. Kim, Y.-H. Kim, and B.-R. Moon, “Performance improvement by genetic feature selection and adjusting ratings’mid-point value in the neural network-based recommendation models,” Advances in Information Sciences and Service Sciences, vol. 4, no. 11, pp. 37–43, 2012. View at Google Scholar
  13. A. Moraglio, R. Poli, and R. Seehuus, “Geometric crossover for biological sequences,” in Proceedings of the European Conference on Genetic Programming, pp. 121–132, 2006.
  14. R. Poli, W. B. Langdon, and N. F. McPhee, A Field Guide to Genetic Programming, Lulu Enterprises, 2008.
  15. K. Seo, S. Hyun, and E. D. Goodman, “Genetic programming-based automatic gait generation in joint space for a quadruped robot,” Advanced Robotics, vol. 24, no. 15, pp. 2199–2214, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. Y. Jin, “A comprehensive survey of fitness approximation in evolutionary computation,” Soft Computing Journal, vol. 9, no. 1, pp. 3–12, 2005. View at Google Scholar
  17. L. Bajer and M. Holena, “Surrogate model for continuous and discrete genetic optimization based on RBF networks,” in Proceedings of the International Conference on Intelligent Data Engineering and Automated Learning, pp. 251–258, 2010.
  18. I. Voutchkov, A. J. Keane, A. Bhaskar, and T. M. Olsen, “Weld sequence optimization: the use of surrogate models for solving sequential combinatorial problems,” Computer Methods in Applied Mechanics and Engineering, vol. 194, no. 30–33, pp. 3535–3551, 2005. View at Publisher · View at Google Scholar · View at Scopus
  19. T. L. Lew, A. B. Spencer, F. Scarpa, K. Worden, A. Rutherford, and F. Hemez, “Identification of response surface models using genetic programming,” Mechanical Systems and Signal Processing, vol. 20, no. 8, pp. 1819–1831, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. A. Moraglio and A. Kattan, “Geometric generalisation of surrogate model based optimisation to combinatorial spaces,” in Proceedings of the 11th European Conference on Evolutionary Computation in Combinatorial Optimization, pp. 142–154, 2011.
  21. A. Moraglio, Y.-H. Kim, and Y. Yoon, “Geometric surrogate-based optimisation for permutation-based problems,” in Proceedings of the 13th Annual Genetic and Evolutionary Computation Conference (GECCO '11), pp. 133–134, July 2011. View at Publisher · View at Google Scholar · View at Scopus
  22. C. M. Bishop, Pattern Recognition and Machine Learning, Springer, New York, NY, USA, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  23. L. C. Jain, Radial Basis Function Networks, Springer, 2001.
  24. A. Moraglio, Towards a Geometric Unification of Evolutionary Algorithms [Ph.D. thesis], University of Essex, 2007.
  25. A. Moraglio, Y.-H. Kim, Y. Yoon, and B.-R. Moon, “Geometric crossovers for multiway graph partitioning,” Evolutionary Computation, vol. 15, no. 4, pp. 445–474, 2007. View at Publisher · View at Google Scholar · View at Scopus
  26. Y. Yoon and Y.-H. Kim, “Geometricity of genetic operators for real-coded representation,” Applied Mathematics and Computation, vol. 219, no. 23, pp. 10915–10927, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. Y. Yoon, Y.-H. Kim, A. Moraglio, and B.-R. Moon, “Quotient geometric crossovers and redundant encodings,” Theoretical Computer Science, vol. 425, pp. 4–16, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. S. Kauffman, Origins of Order: Self-Organization and Selection in Evolution, Oxford University Press, 1993.
  29. Y.-H. Kim and Y. Yoon, “A new Kernighan-Lin-type local search for the quadratic assignment problem,” in Proceedings of the International Conference on Scientific Computing, pp. 185–189, 2009.
  30. C. E. Rasmussen, Gaussian Processes for Machine Learning, MIT Press, 2006.
  31. Y.-H. Kim and B.-R. Moon, “New topologies for genetic search space,” in Genetic and Evolutionary Computation Conference (GECCO '05), pp. 1393–1399, June 2005. View at Publisher · View at Google Scholar · View at Scopus
  32. Y. Yoon and Y.-H. Kim, “A Mathematical Design of Genetic Operators on GLn(Z2),” Mathematical Problems in Engineering, vol. 2014, Article ID 540936, 8 pages, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. J. D. Schaffer and L. J. Eshelman, “On crossover as an evolutionary viable strategy,” in Proceedings of the 4th International Conference on Genetic Algorithms, pp. 61–68, 1991.
  34. T. Jones and S. Forrest, “Fitness distance correlation as a measure of problem difficulty for genetic algorithms,” in Proceedings of the 6th International Conference on Genetic Algorithms, pp. 184–192, 1995.
  35. A. Moraglio and R. Poli, “Geometric landscape of homologous crossover for syntactic trees,” in Proceedings of the IEEE Congress on Evolutionary Computation (IEEE CEC '05), pp. 427–434, September 2005. View at Scopus
  36. A. Ekart and S. Z. Nemeth, “A metric for genetic programs and fitness sharing,” in Proceedings of the European Conference on Genetic Programming, pp. 259–270, 2000.
  37. A. Moraglio, K. Krawiec, and C. G. Johnson, “Geometric semantic genetic programming,” in Proceedings of the 12th International Conference on Parallel Problem Solving from Nature, pp. 21–31, 2012.