Surrogate based Evolutionary Algorithm for Design Optimization
Optimization is often a critical issue for most system
design problems. Evolutionary Algorithms are population-based,
stochastic search techniques, widely used as efficient global
optimizers. However, finding optimal solution to complex high
dimensional, multimodal problems often require highly
computationally expensive function evaluations and hence are
practically prohibitive. The Dynamic Approximate Fitness based
Hybrid EA (DAFHEA) model presented in our earlier work [14]
reduced computation time by controlled use of meta-models to
partially replace the actual function evaluation by approximate
function evaluation. However, the underlying assumption in
DAFHEA is that the training samples for the meta-model are
generated from a single uniform model. Situations like model
formation involving variable input dimensions and noisy data
certainly can not be covered by this assumption. In this paper we
present an enhanced version of DAFHEA that incorporates a
multiple-model based learning approach for the SVM approximator.
DAFHEA-II (the enhanced version of the DAFHEA framework) also
overcomes the high computational expense involved with additional
clustering requirements of the original DAFHEA framework. The
proposed framework has been tested on several benchmark functions
and the empirical results illustrate the advantages of the proposed
technique.
[1] A. Ratle.., "Accelerating the convergence of evolutionary algorithms by
fitness landscape approximation", Parallel Problem Solving from
Nature-PPSN V, Springer-Verlag, pp. 87-96, 1998.
[2] A. Smola and B. Schölkopf, "A Tutorial on Support Vector Regression",
NeuroCOLT Technical Report NC-TR-98-030, Royal Holloway
College, University of London, UK, 1998.
[3] B. Dunham, D. Fridshal., R. Fridshal and J. North, "Design by natural
selection", Synthese, 15, pp. 254-259, 1963.
[4] B. Schölkopf , J. Burges and A. Smola, ed., "Advances in Kernel
Methods: Support Vector Machines", MIT Press, 1999.
[5] C. Bishop, "Neural Networks for Pattern Recognition", Oxford Press,
1995.
[6] D. B├╝che., N. Schraudolph, and P. Koumoutsakos, "Accelerating
Evolutionary Algorithms Using Fitness Function Models", Proc.
Workshops Genetic and Evolutionary Computation Conference,
Chicago, 2003.
[7] H. D. Vekeria and i. C. Parmee, "The use of a co-operative multi-level
CHC GA for structural shape optimization", Fourth European Congress
on Intelligent Techniques and Soft Computing - EUFIT-96, 1996.
[8] H. S. Kim and S. B. Cho, " An efficient genetic algorithm with less
fitness evaluation by clustering", Proceedings of IEEE Congress on
Evolutionary Computation, pp. 887-894, 2001.
[9] J. Sacks, W. Welch, T. Mitchell and H. Wynn, "Design and analysis of
computer experiments", Statistical Science, 4(4), 1989.
[10] K. Rasheed, "An Incremental-Approximate-Clustering Approach for
Developing Dynamic Reduced Models for Design Optimization",
Proceedings of IEEE Congress on Evolutionary Computation, 2000.
[11] K. Rasheed, S. Vattam and X. Ni., "Comparison of Methods for Using
Reduced Models to Speed Up Design Optimization", The Genetic and
Evolutionary Computation Conference (GECCO'2002), 2002.
[12] K. Won, T. Roy and K. Tai, "A Framework for Optimization Using
Approximate Functions", Proceedings of the IEEE Congress on
Evolutionary Computation- 2003, Vol.3, IEEE Catalogue No.
03TH8674C, ISBN 0-7803-7805-9.
[13] M. A. El-Beltagy and A. J. Keane, "Evolutionary optimization for
computationally expensive problems using Gaussian processes", Proc.
Int. Conf. on Artificial Intelligence (IC-AI'2001), CSREA Press, Las
Vegas, pp. 708-714, 2001.
[14] M. Bhattacharya and G. Lu, "DAFHEA: A Dynamic Approximate
Fitness based Hybrid Evolutionary Algorithm", Proceedings of the IEEE
Congress on Evolutionary Computation- 2003, Vol.3, IEEE Catalogue
No. 03TH8674C, ISBN 0-7803-7805-9, pp. 1879-1886.
[15] P. Hajela and A. Lee., "Topological optimization of rotorcraft subfloor
structures for crashworthiness considerations", Computers and
Structures, vol.64, pp. 65-76, 1997.
[16] R. Myers and D. Montgomery, "Response Surface Methodology", John
Wiley & Sons, 1985.
[17] S. Pierret, "Three-dimensional blade design by means of an artificial
neural network and Navier-Stokes solver", Proceedings of Fifth
Conference on Parallel Problem Solving from Nature, Amsterdam, 1999.
[18] S. R. Gunn, "Support Vector Machines for Classification and
Regression", Technical Report, School of Electronics and Computer
Science, University of Southampton, (Southampton, U.K.), 1998.
[19] T. Hastie, R. Tibshirani, J. Friedman, "The Elements of Statistical
Learning: Data Mining, Inference, and Prediction", Springer Series in
Statistics, ISBN 0-387-95284-5.
[20] V. Cherkassky and Y. Ma, "Multiple Model Estimation: A New
Formulation for Predictive Learning", under review in IEE Transaction
on Neural Network.
[21] V. Torczon and M. W. Trosset, "Using approximations to accelerate
engineering design optimisation", ICASE Report No. 98-33. Technical
report, NASA Langley Research Center Hampton, VA 23681-2199,
1998.
[22] V. V. Toropov, a. A. Filatov and A. A. Polykin, "Multiparameter
structural optimization using FEM and multipoint explicit
approximations", Structural Optimization, vol. 6, pp. 7-14, 1993.
[23] V. Vapnik, "The Nature of Statistical Learning Theory", Springer-
Verlag, NY, USA, 1999.
[24] Y. Jin, M. Olhofer and B. Sendhoff, "A Framework for Evolutionary
Optimization with Approximate Fitness Functions", IEEE Transactions
on Evolutionary Computation, 6(5), pp. 481-494, (ISSN: 1089-778X).
2002.
[25] Y. Jin, M. Olhofer and B. Sendhoff., "On Evolutionary Optimisation
with Approximate Fitness Functions", Proceedings of the Genetic and
Evolutionary Computation Conference GECCO, Las Vegas, Nevada,
USA. pp. 786- 793, July 10-12, 2000.
[26] Y. Jin., "A comprehensive survey of fitness approximation in
evolutionary computation", Soft Computing Journal, 2003 (in press).
[1] A. Ratle.., "Accelerating the convergence of evolutionary algorithms by
fitness landscape approximation", Parallel Problem Solving from
Nature-PPSN V, Springer-Verlag, pp. 87-96, 1998.
[2] A. Smola and B. Schölkopf, "A Tutorial on Support Vector Regression",
NeuroCOLT Technical Report NC-TR-98-030, Royal Holloway
College, University of London, UK, 1998.
[3] B. Dunham, D. Fridshal., R. Fridshal and J. North, "Design by natural
selection", Synthese, 15, pp. 254-259, 1963.
[4] B. Schölkopf , J. Burges and A. Smola, ed., "Advances in Kernel
Methods: Support Vector Machines", MIT Press, 1999.
[5] C. Bishop, "Neural Networks for Pattern Recognition", Oxford Press,
1995.
[6] D. B├╝che., N. Schraudolph, and P. Koumoutsakos, "Accelerating
Evolutionary Algorithms Using Fitness Function Models", Proc.
Workshops Genetic and Evolutionary Computation Conference,
Chicago, 2003.
[7] H. D. Vekeria and i. C. Parmee, "The use of a co-operative multi-level
CHC GA for structural shape optimization", Fourth European Congress
on Intelligent Techniques and Soft Computing - EUFIT-96, 1996.
[8] H. S. Kim and S. B. Cho, " An efficient genetic algorithm with less
fitness evaluation by clustering", Proceedings of IEEE Congress on
Evolutionary Computation, pp. 887-894, 2001.
[9] J. Sacks, W. Welch, T. Mitchell and H. Wynn, "Design and analysis of
computer experiments", Statistical Science, 4(4), 1989.
[10] K. Rasheed, "An Incremental-Approximate-Clustering Approach for
Developing Dynamic Reduced Models for Design Optimization",
Proceedings of IEEE Congress on Evolutionary Computation, 2000.
[11] K. Rasheed, S. Vattam and X. Ni., "Comparison of Methods for Using
Reduced Models to Speed Up Design Optimization", The Genetic and
Evolutionary Computation Conference (GECCO'2002), 2002.
[12] K. Won, T. Roy and K. Tai, "A Framework for Optimization Using
Approximate Functions", Proceedings of the IEEE Congress on
Evolutionary Computation- 2003, Vol.3, IEEE Catalogue No.
03TH8674C, ISBN 0-7803-7805-9.
[13] M. A. El-Beltagy and A. J. Keane, "Evolutionary optimization for
computationally expensive problems using Gaussian processes", Proc.
Int. Conf. on Artificial Intelligence (IC-AI'2001), CSREA Press, Las
Vegas, pp. 708-714, 2001.
[14] M. Bhattacharya and G. Lu, "DAFHEA: A Dynamic Approximate
Fitness based Hybrid Evolutionary Algorithm", Proceedings of the IEEE
Congress on Evolutionary Computation- 2003, Vol.3, IEEE Catalogue
No. 03TH8674C, ISBN 0-7803-7805-9, pp. 1879-1886.
[15] P. Hajela and A. Lee., "Topological optimization of rotorcraft subfloor
structures for crashworthiness considerations", Computers and
Structures, vol.64, pp. 65-76, 1997.
[16] R. Myers and D. Montgomery, "Response Surface Methodology", John
Wiley & Sons, 1985.
[17] S. Pierret, "Three-dimensional blade design by means of an artificial
neural network and Navier-Stokes solver", Proceedings of Fifth
Conference on Parallel Problem Solving from Nature, Amsterdam, 1999.
[18] S. R. Gunn, "Support Vector Machines for Classification and
Regression", Technical Report, School of Electronics and Computer
Science, University of Southampton, (Southampton, U.K.), 1998.
[19] T. Hastie, R. Tibshirani, J. Friedman, "The Elements of Statistical
Learning: Data Mining, Inference, and Prediction", Springer Series in
Statistics, ISBN 0-387-95284-5.
[20] V. Cherkassky and Y. Ma, "Multiple Model Estimation: A New
Formulation for Predictive Learning", under review in IEE Transaction
on Neural Network.
[21] V. Torczon and M. W. Trosset, "Using approximations to accelerate
engineering design optimisation", ICASE Report No. 98-33. Technical
report, NASA Langley Research Center Hampton, VA 23681-2199,
1998.
[22] V. V. Toropov, a. A. Filatov and A. A. Polykin, "Multiparameter
structural optimization using FEM and multipoint explicit
approximations", Structural Optimization, vol. 6, pp. 7-14, 1993.
[23] V. Vapnik, "The Nature of Statistical Learning Theory", Springer-
Verlag, NY, USA, 1999.
[24] Y. Jin, M. Olhofer and B. Sendhoff, "A Framework for Evolutionary
Optimization with Approximate Fitness Functions", IEEE Transactions
on Evolutionary Computation, 6(5), pp. 481-494, (ISSN: 1089-778X).
2002.
[25] Y. Jin, M. Olhofer and B. Sendhoff., "On Evolutionary Optimisation
with Approximate Fitness Functions", Proceedings of the Genetic and
Evolutionary Computation Conference GECCO, Las Vegas, Nevada,
USA. pp. 786- 793, July 10-12, 2000.
[26] Y. Jin., "A comprehensive survey of fitness approximation in
evolutionary computation", Soft Computing Journal, 2003 (in press).
@article{"International Journal of Information, Control and Computer Sciences:54655", author = "Maumita Bhattacharya", title = "Surrogate based Evolutionary Algorithm for Design Optimization", abstract = "Optimization is often a critical issue for most system
design problems. Evolutionary Algorithms are population-based,
stochastic search techniques, widely used as efficient global
optimizers. However, finding optimal solution to complex high
dimensional, multimodal problems often require highly
computationally expensive function evaluations and hence are
practically prohibitive. The Dynamic Approximate Fitness based
Hybrid EA (DAFHEA) model presented in our earlier work [14]
reduced computation time by controlled use of meta-models to
partially replace the actual function evaluation by approximate
function evaluation. However, the underlying assumption in
DAFHEA is that the training samples for the meta-model are
generated from a single uniform model. Situations like model
formation involving variable input dimensions and noisy data
certainly can not be covered by this assumption. In this paper we
present an enhanced version of DAFHEA that incorporates a
multiple-model based learning approach for the SVM approximator.
DAFHEA-II (the enhanced version of the DAFHEA framework) also
overcomes the high computational expense involved with additional
clustering requirements of the original DAFHEA framework. The
proposed framework has been tested on several benchmark functions
and the empirical results illustrate the advantages of the proposed
technique.", keywords = "Evolutionary algorithm, Fitness function,Optimization, Meta-model, Stochastic method.", volume = "1", number = "10", pages = "3079-6", }