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2017 | OriginalPaper | Chapter

General Meta-Model Framework for Surrogate-Based Numerical Optimization

Authors : Žiga Lukšič, Jovan Tanevski, Sašo Džeroski, Ljupčo Todorovski

Published in: Discovery Science

Publisher: Springer International Publishing

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Abstract

We present a novel, general framework for surrogate-based numerical optimization. We introduce the concept of a modular meta model that can be easily coupled with any optimization method. It incorporates a dynamically constructed surrogate that efficiently approximates the objective function. We consider two surrogate management strategies for deciding when to evaluate the surrogate and when to evaluate the true objective. We address the task of estimating parameters of non-linear models of dynamical biological systems from observations. We show that the meta model significantly improves the efficiency of optimization, achieving up to 50% reduction of the time needed for optimization and substituting up to 63% of the total number of evaluations of the objective function. The improvement is a result of the use of an adaptive management strategy learned from the history of objective evaluations.

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Footnotes
1
The implementation of the framework, the two meta-model variants, the models and data are available at http://​source.​ijs.​si/​zluksic/​metamodel/​.
 
Literature
1.
go back to reference Arkin, A., Ross, J.: Statistical construction of chemical reaction mechanisms from measured time-series. J. Phys. Chem. 99(3), 970–979 (1995)CrossRef Arkin, A., Ross, J.: Statistical construction of chemical reaction mechanisms from measured time-series. J. Phys. Chem. 99(3), 970–979 (1995)CrossRef
2.
go back to reference Ashyraliyev, M., Fomekong-Nanfack, Y., Kaandorp, J.A., Blom, J.G.: Systems biology: parameter estimation for biochemical models. FEBS J. 276(4), 886–902 (2009)CrossRef Ashyraliyev, M., Fomekong-Nanfack, Y., Kaandorp, J.A., Blom, J.G.: Systems biology: parameter estimation for biochemical models. FEBS J. 276(4), 886–902 (2009)CrossRef
3.
go back to reference Bagheria, S., Konena, W., Emmerich, M., Bäck, T.: Solving the G-problems in less than 500 iterations: improved efficient constrained optimization by surrogate modeling and adaptive parameter control. arXiv https://arxiv.org/abs/1512.09251 (2015) Bagheria, S., Konena, W., Emmerich, M., Bäck, T.: Solving the G-problems in less than 500 iterations: improved efficient constrained optimization by surrogate modeling and adaptive parameter control. arXiv https://​arxiv.​org/​abs/​1512.​09251 (2015)
6.
go back to reference Buse, O., Pérez, R., Kuznetsov, A.: Dynamical properties of the repressilator model. Phys. Rev. E 81, 066206 (2010)MathSciNetCrossRef Buse, O., Pérez, R., Kuznetsov, A.: Dynamical properties of the repressilator model. Phys. Rev. E 81, 066206 (2010)MathSciNetCrossRef
7.
go back to reference Chou, I.C., Voit, E.O.: Recent developments in parameter estimation and structure identification of biochemical and genomic systems. Math. Biosci. 219(2), 57–83 (2009)MathSciNetCrossRefMATH Chou, I.C., Voit, E.O.: Recent developments in parameter estimation and structure identification of biochemical and genomic systems. Math. Biosci. 219(2), 57–83 (2009)MathSciNetCrossRefMATH
8.
go back to reference Das, S., Mullick, S.S., Suganthan, P.N.: Recent advances in differential evolution - an updated survey. Swarm Evol. Comput. 27, 1–30 (2016)CrossRef Das, S., Mullick, S.S., Suganthan, P.N.: Recent advances in differential evolution - an updated survey. Swarm Evol. Comput. 27, 1–30 (2016)CrossRef
9.
go back to reference Elowitz, M., Leibler, S.: A synthetic oscillatory network of transcriptional regulators. Nature 403, 335–338 (2000)CrossRef Elowitz, M., Leibler, S.: A synthetic oscillatory network of transcriptional regulators. Nature 403, 335–338 (2000)CrossRef
10.
go back to reference Gennemark, P., Wedelin, D.: Efficient algorithms for ordinary differential equation model identification of biological systems. IET Syst. Biol. 1(2), 120–129 (2007)CrossRef Gennemark, P., Wedelin, D.: Efficient algorithms for ordinary differential equation model identification of biological systems. IET Syst. Biol. 1(2), 120–129 (2007)CrossRef
11.
go back to reference Hutter, F., Hoos, H.H., Leyton-Brown, K.: Sequential model-based optimization for general algorithm configuration. In: Coello, C.A.C. (ed.) LION 2011. LNCS, vol. 6683, pp. 507–523. Springer, Heidelberg (2011). doi:10.1007/978-3-642-25566-3_40 CrossRef Hutter, F., Hoos, H.H., Leyton-Brown, K.: Sequential model-based optimization for general algorithm configuration. In: Coello, C.A.C. (ed.) LION 2011. LNCS, vol. 6683, pp. 507–523. Springer, Heidelberg (2011). doi:10.​1007/​978-3-642-25566-3_​40 CrossRef
12.
go back to reference Jaqaman, K., Danuser, G.: Linking data to models: data regression. Nat. Rev. Mol. Cell Biol. 7(11), 813–819 (2006)CrossRef Jaqaman, K., Danuser, G.: Linking data to models: data regression. Nat. Rev. Mol. Cell Biol. 7(11), 813–819 (2006)CrossRef
13.
go back to reference Jin, Y.: Surrogate-assisted evolutionary computation: recent advances and future challenges. Swarm Evol. Comput. 1(2), 61–70 (2011)CrossRef Jin, Y.: Surrogate-assisted evolutionary computation: recent advances and future challenges. Swarm Evol. Comput. 1(2), 61–70 (2011)CrossRef
14.
15.
go back to reference Kikuchi, S., Tominaga, D., Arita, M., Takahashi, K., Tomita, M.: Dynamic modeling of genetic networks using genetic algorithm and S-system. Bioinformatics 19(5), 643–650 (2003)CrossRef Kikuchi, S., Tominaga, D., Arita, M., Takahashi, K., Tomita, M.: Dynamic modeling of genetic networks using genetic algorithm and S-system. Bioinformatics 19(5), 643–650 (2003)CrossRef
16.
go back to reference Kirk, P., Silk, D., Stumpf, M.P.H.: Reverse engineering under uncertainty. Uncertainty in Biology: A Computational Modeling Approach. SMTEB, vol. 17, pp. 15–32. Springer, Cham (2016)CrossRef Kirk, P., Silk, D., Stumpf, M.P.H.: Reverse engineering under uncertainty. Uncertainty in Biology: A Computational Modeling Approach. SMTEB, vol. 17, pp. 15–32. Springer, Cham (2016)CrossRef
17.
go back to reference Mallipeddi, R., Lee, M.: An evolving surrogate model-based differential evolution algorithm. Appl. Soft Comput. 34, 770–787 (2015)CrossRef Mallipeddi, R., Lee, M.: An evolving surrogate model-based differential evolution algorithm. Appl. Soft Comput. 34, 770–787 (2015)CrossRef
19.
go back to reference Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, Heidelberg (2006)MATH Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, Heidelberg (2006)MATH
20.
go back to reference Pintér, J.: Global Optimization in Action: Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications. Springer, Heidelberg (1995) Pintér, J.: Global Optimization in Action: Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications. Springer, Heidelberg (1995)
21.
go back to reference Regis, R.G.: Constrained optimization by radial basis function interpolation for high-dimensional expensive black-box problems with infeasible initial points. Eng. Optim. 46(2), 218–243 (2013)MathSciNetCrossRef Regis, R.G.: Constrained optimization by radial basis function interpolation for high-dimensional expensive black-box problems with infeasible initial points. Eng. Optim. 46(2), 218–243 (2013)MathSciNetCrossRef
22.
go back to reference Storn, R., Price, K.: Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)MathSciNetCrossRefMATH Storn, R., Price, K.: Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)MathSciNetCrossRefMATH
23.
go back to reference Su, G.: Gaussian process assisted differential evolution algorithm for computationally expensive optimization problems. In: Proceedings of the IEEE Pacific-Asia Workshop on Computational Intelligence and Industrial Application, pp. 272–276 (2008) Su, G.: Gaussian process assisted differential evolution algorithm for computationally expensive optimization problems. In: Proceedings of the IEEE Pacific-Asia Workshop on Computational Intelligence and Industrial Application, pp. 272–276 (2008)
24.
go back to reference Sun, J., Garibaldi, J., Hodgman, C.: Parameter estimation using metaheuristics in systems biology: a comprehensive review. IEEE/ACM Trans. Comput. Biol. Bioinform. 9(1), 185–202 (2012)CrossRef Sun, J., Garibaldi, J., Hodgman, C.: Parameter estimation using metaheuristics in systems biology: a comprehensive review. IEEE/ACM Trans. Comput. Biol. Bioinform. 9(1), 185–202 (2012)CrossRef
25.
26.
go back to reference Tashkova, K., Korošec, P., Šilc, J., Todorovski, L., Džeroski, S.: Parameter estimation with bio-inspired meta-heuristic optimization: modeling the dynamics of endocytosis. BMC Syst. Biol. 5(1), 1–26 (2011)CrossRef Tashkova, K., Korošec, P., Šilc, J., Todorovski, L., Džeroski, S.: Parameter estimation with bio-inspired meta-heuristic optimization: modeling the dynamics of endocytosis. BMC Syst. Biol. 5(1), 1–26 (2011)CrossRef
Metadata
Title
General Meta-Model Framework for Surrogate-Based Numerical Optimization
Authors
Žiga Lukšič
Jovan Tanevski
Sašo Džeroski
Ljupčo Todorovski
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-67786-6_4

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