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Issue No.01 - January/February (2012 vol.9)
pp: 185-202
Jianyong Sun , Centre for Plant Integrative Biol. (CPIB), Univ. of Nottingham, Nottingham, UK
J. M. Garibaldi , Intell. Modelling & Anal. Res. Group (IMA), Univ. of Nottingham, Nottingham, UK
C. Hodgman , Centre for Plant Integrative Biol. (CPIB), Univ. of Nottingham, Nottingham, UK
This paper gives a comprehensive review of the application of metaheuristics to optimization problems in systems biology, mainly focusing on the parameter estimation problem (also called the inverse problem or model calibration). It is intended for either the system biologist who wishes to learn more about the various optimization techniques available and/or the metaheuristic optimizer who is interested in applying such techniques to problems in systems biology. First, the parameter estimation problems emerging from different areas of systems biology are described from the point of view of machine learning. Brief descriptions of various metaheuristics developed for these problems follow, along with outlines of their advantages and disadvantages. Several important issues in applying metaheuristics to the systems biology modeling problem are addressed, including the reliability and identifiability of model parameters, optimal design of experiments, and so on. Finally, we highlight some possible future research directions in this field.
Biological system modeling, Mathematical model, Computational modeling, Systems biology, Optimization, Biochemistry, Parameter estimation,evolutionary algorithms., Systems biology, parameter estimation problem, model calibration, heuristic, metaheuristic
Jianyong Sun, J. M. Garibaldi, C. Hodgman, "Parameter Estimation Using Metaheuristics in Systems Biology: A Comprehensive Review", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.9, no. 1, pp. 185-202, January/February 2012, doi:10.1109/TCBB.2011.63
[1] A. Abraham, C. Grosan, and H. Ishibuchi, Hybrid Evolutionary Algorithms. Springer, 2007.
[2] M.A. Abramson, C. Audet, and J.E. Dennis, “Generalized Pattern Searches with Derivative Information,” Math. Programming, vol. 100, no. 1, pp. 3-25, 2004.
[3] B.S. Adiwijaya, P.I. Barton, and B. Tidor, “Biological Network Design Strategies: Discovery through Dynamic Optimization,” Molecular Biosystems, vol. 2, no. 12, pp. 650-659, 2006.
[4] C.M. Alexandre and L. Hennig, “FLC or Not FLC: The Other Side of Vernalisation,” J. Experimental Botany, vol. 52, pp. 1127-1135, 2008.
[5] R. Alfieri, E. Mosca, I. Merelli, and L. Milanesi, “Parameter Estimation for Cell Cycle Ordinary Differential Equation (ODE) Models Using a Grid Approach,” Proc. HealthGrid 2007, Studies in Health Technology and Informatics, vol. 126, pp. 93-102, 2007.
[6] J.S. Almeida and E.O. Voit, “Neural-Network-Based Parameter Estimation in S-System Models of Biological Networks,” Genome Informatics, vol. 14, pp. 114-123, 2003.
[7] U. Alon, An Introduction to Systems Biology. Chapman and Hall, 2006.
[8] S. Ando, E. Sakamoto, and H. Iba, “Evolutionary Modeling and Inference of Gene Network,” Information Science, vol. 145, pp. 237-259, 2002.
[9] I. Arisi, A. Cattaneo, and V. Rosato, “Parameter Estimate of Signal Transduction Pathways,” BMC Neuroscience, vol. 7, 2006, doi:10.1186/1471-2202-7-S1-S6.
[10] N. Arora and L.T. Biegler, “A Trust Region SQP Algorithm for Equality Constrained Parameter Estimation with Simple Parameter Bounds,” Computational Optimization and Applications, vol. 28, pp. 51-86, 2004.
[11] M. Ashyraliyev, J. Jaeger, and J.G. Blom, “Parameter Estimation and Determinability Analysis Applied to drosophila Gap Gene Circuits,” BMC Systems Biology, vol. 2, article 83, 2008.
[12] S. Audoly, G. Bellu, L. D'Angiò, M.P. Saccomani, and C. Cobelli, “Global Identifiability of Nonlinear Models of Biological Systems,” IEEE Trans. Biomedical Eng., vol. 48, no. 1, pp. 55-65, Jan. 2001.
[13] C. Auliac, V. Frouin, X. Gidrol, and F. D'Alche-Buc, “Evolutionary Approaches for the Reverse-Engineering of Gene Regulatory Networks: A Study on a Biologically Realistic Dataset,” BMC Bioinformatics, vol. 9, article 91, 2008.
[14] C.T.H. Baker, G.A. Bocharov, J.M. Ford, P.M. Lumb, S.J. Norton, C.A.H. Paul, T. Junt, P. Krebs, and B. Ludewig, “Computational Approaches to Parameter Estimation and Model Selection in Immunology,” J. Computational and Applied Math., vol. 184, pp. 50-76, 2005.
[15] E. Balsa-Canto, A.A. Alonso, and J.R. Banga, “Computational Procedures for Optimal Experimental Design in Biological Systems,” IET Systems Biology, vol. 2, no. 4, pp. 163-172, July 2008.
[16] E. Balsa-Canto, M. Peifer, J.R. Banga, J. Timmer, and C. Fleck, “Hybrid Optimization Method with General Switching Strategy for Parameter Estimation,” BMC System Biology, vol. 2, no. 26, pp. 1-9, 2008.
[17] E. Balsa-Canto, V. Vassiliadis, and J. Banga, “Dynamic Optimization of Single- and Multi-Stage Systems Using a Hybrid Stochastic-Deterministic Method,” Industrial and Eng. Chemistry Research, vol. 44, no. 5, pp. 1514-1523, 2005.
[18] J.R. Banga, “Optimization in Computational Systems Biology,” BMC Systems Biology, vol. 2, article 47, 2008.
[19] J.R. Banga and J.J. Casares, “Integrated Controlled Random Search: Application to a Wastewater Treatment Plant Model,” Proc. IChemE Symp. Ser. 100, pp. 183-192, 1987.
[20] J.R. Banga, K.J. Versyck, and J.F. Van Impe, “Computation of Optimal Identification Experiments for Nonlinear Dynamic Process Models: A Stochastic Global Optimization Approach,” Industrial and Eng. Chemistry Research, vol. 41, no. 10, pp. 2452-2430, 2002.
[21] H.T. Banks, H.T. Tran, and D. Gulick, Mathematical and Experimental Modeling of Physical and Biological Processes. Chapman and Hall, 2009.
[22] W. Banzhaf, P. Nordin, R.E. Keller, and F.D. Francone, Genetic Programming: An Introduction: On the Automatic Evolution of Computer Programs and Its Applications. Morgan Kaufmann, 1998.
[23] P. Berman, B. DasGupta, and E. Sontag, “Computational Complexities of Combinatorial Problems With Applications to Reverse Eng. of Biological Networks,” Advances in Computational Intelligence: Theory & Applications, pp. 303-316, World Scientific, 2006.
[24] D. Braun, S. Basu, and R. Weiss, “Parameter Estimation for Two Synthetic Gene Networks: A Case Study,” Proc. IEEE Int'l Conf. Acoustics, Speech, and Signal Processing, vol. 5, pp. 769-772, 2005.
[25] M. Brown, F. He, and L.F. Yeung, “Robust Measurement Selection for Biochemical Pathway Experimental Design,” Proc. The First Int'l Symp. Optimization and Systems Biology, pp. 259-266, Aug. 2007.
[26] C.G. Broyden, “The Convergence of a Class of Double-Rank Minimization Algorithms,” J. Inst. of Math. and Its Applications, vol. 6, pp. 76-90, 1970.
[27] M. Brusco and S. Stahl, “Branch-and-Bound Applications in Combinatorial Data Analysis,” Ser. Statistics and Computing, Springer, 2005.
[28] D. Buche, N.N. Schraudolph, and P. Koumoutsakos, “Accelerating Evolutionary Algorithms with Gaussian Process Fitness Function Models,” IEEE Trans. Systems, Man and Cybernetics, Part C: Applications and Rev., vol. 35, no. 2, pp. 183-194, May 2005.
[29] A.P. Burgard, P. Pharkya, and C.D. Maranas, “OptKnock: A Bilevel Programming Framework fo Identifying Gene Knockout Strategies for Microbial Strain Optimization,” Biotechnology and Bioeng., vol. 84, no. 6, pp. 647-657, 2003.
[30] G.C. Cawley and N.L.C. Talbot, “Preventing Over-Fitting during Model Selection via Bayesian Regularisation of the Hyper-Parameters,” J. Machine Learning Research, vol. 8, pp. 841-861, 2007.
[31] Y.J. Chang and N.V. Sahinidis, “Optimization of Metabolic Pathways under Stability Considerations,” Computers and Chemical Eng., vol. 29, no. 3, pp. 467-479, 2005.
[32] C. Chaouiya, “Petri Net Modelling of Biological Networks,” Briefings in Bioinformatics, vol. 8, pp. 210-219, 2007.
[33] J.P. Chiou and F.S. Wang, “Hybrid Method of Evolution Algorithms for Static and Dynamic Optimization Problems with Application to a Fedbatch Fermentation Process,” Computers and Chemical Eng., vol. 23, pp. 1277-1291, 1999.
[34] I-C. Chou, H. Martens, and E.O. Voit, “Parameter Estimation in Biochemical Systems Models with Alternating Regression,” Theoretical Biology and Medical Modelling, vol. 3, no. 25, pp. 1-11, 2006.
[35] A.R. Conn, N. Gould, and P.L. Toint, “A Globally Convergent Augmented Lagrangian Algortithm for Optimization with General Constraints and Simple Bounds,” SIAM J. Numerical Analysis, vol. 28, no. 2, pp. 545-572, 1991.
[36] A.R. Conn, N. Gould, and P.L. Toint, “A Globally Congergent Lagrangian Barrier Algorithm for Optimization with General Inequality Constraints and Simple Bounds,” Math. of Computation, vol. 66, no. 217, pp. 261-288, 1997.
[37] M. Dasika, A. Gupta, and C. Maranas, “A Mixed Integer Linear Programing (milp) Framework for Inferring Time Delay in Gene Regulatory Networks,” Proc. Pacific Symp. Biocomputing, pp. 474-486, 2004.
[38] M.S. Dasika and C.D. Maranas, “Optcircuit: An Optimization Based Method for Computational Design of Genetic Circuits,” BMC Systems Biology, vol. 2, article 24, 2008.
[39] M.J. Dunlop, E. Franco, and R.M. Murray, “A Multi-Model Approach to Identification of Biosynthetic Pathways,” Proc. Am. Control Conf., pp. 1600-1605, July 2007.
[40] J.A. Egea, M. Rodriguez-Fernandez, J.R. Banga, and R. Marti, “Scatter Search for Chemical and Bio-Process Optimization,” J. Global Optimization, vol. 37, pp. 481-503, 2007.
[41] M. Laguna, F. Glover, and R. Martí, Advances in Evolutionary Computation: Theory and Applications, pp. 519-537. Springer-Verlag, 2003.
[42] H.-Y. Fan and J. Lampinen, “A Trigonometric Mutation Operation to Differential Evolution,” J. Global Optimization, vol. 27, no. 1, pp. 105-129, 2003.
[43] D. Fell, Understanding the Control of Metabolism. Portland Press, 1997.
[44] J. Fisher and T.A. Henzinger, “Executable Cell Biology,” Nature Biotechnology, vol. 25, no. 11, pp. 1239-1249, 2007.
[45] R. Fletcher, Practicle Methods of Optimization. Wiley, 2000.
[46] K.G. Gadkar, F.J. Doyle, and J.S. Edward, “Estimating Optimal Profiles of Genetic Alterations Using Constraint-Based Models,” Biotechnology and Bioeng., vol. 89, no. 2, pp. 243-251, 2005.
[47] E. Gill, W. Murray, and M.A. Saunders, “SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization,” SIAM J. Optimization, vol. 12, no. 4, pp. 979-1006, 2002.
[48] A. Gilman and J. Ross, “Genetic-Algorithm Selection of a Regulatory Structure that Directs Flux in a Simple Metabolic Model,” Biophysical J., vol. 69, pp. 1321-1333, 1995.
[49] L. Glass and S.A. Kauffman, “The Logical Analysis of Continuous, Non-Linear Biochemical Control Networks,” J. Theoretical Biology, vol. 39, pp. 103-129, 1973.
[50] O.R. Gonzalez, C. Kuper, K. JungJr., P.C. Naval, and E. Mendoza, “Parameter Estimation Using Simulated Annealing for S-System Models of Biochemical Networks,” Bioinformatics, vol. 23, no. 4, pp. 480-486, 2007.
[51] X. Gu, “Systems Biology Approaches to the Computational Modelling of Tryanothione Metabolism in Trypanosoma Brucei,” PhD thesis, Univ. of Glasgow, 2010.
[52] S. Han, Y. Yoon, and K.H. Cho, “Inferring Biomolecular Interaction Networks Based on Convex Optimization,” Computational Biology and Chemistry, vol. 31, nos. 5/6, pp. 347-354, 2007.
[53] J. Handl, D.B. Kell, and J. Knowles, “Multiobjective Optimization in Bioinformatics and Computational Biology,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 4, no. 2, pp. 279-292, Apr.-June 2007.
[54] N. Hansen, S.D. Muller, and P. Koumoutsakos, “Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adoption (CMA-ES),” Evolutionary Computation, vol. 11, no. 1, pp. 1-18, 2003.
[55] Recent Advances in Memetic Algorithms, W.E. Hart, N. Krasnogor, and J.E. Smith, eds., vol. 166. Springer, 2005.
[56] T. Higuchi, S. Tsutsui, and M. yamamura, “Theoretical Analysis of Simplex Crossover for Real-Coded Genetic Algorithms,” Proc. Int'l Conf. Parallel Problem Solving from Nature, pp. 365-374, 2000.
[57] S.-Y. Ho, C.-H. Hsieh, and F.-C. Yu, “Inference of S-system Models for Large-Scale Genetic Networks,” Proc. 21st Int'l Conf. Data Eng. (ICDE '05), p. 1155, 2005.
[58] S.-Y. Ho, C.-H. Hsieh, F.-C. Yu, and H.-L. Huang, “An Intelligent Two-Stage Evolutionary Algorithm for Dynamic Pathway Identification from Gene Expression Profiles,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 4, no. 4, pp. 648-704, Oct.-Dec. 2007.
[59] T. Hohm and E. Zitzler, “Multiobjectivization for Parameter Estimation: A Case-Study on the Segment Polarity Network of Drosophila,” Proc. 11th Ann. Conf. Genetic and Evolutionary Computation, pp. 209-216, 2009.
[60] R. Hooke and T.A. Jeeves, “‘Direct Search’ Solution of Numerical and Statistical Problems,” J. the ACM, vol. 8, no. 2, pp. 212-229, 1961.
[61] S. Hoops, S. Sahle, R. Gauges, C. Lee, J. Pahle, N. Simus, M. Singhai, L. Xu, P. Mendes, and U. Kummer, “COPASI—A Complex Pathway Simulator,” Systems Biology, vol. 22, no. 24, pp. 3067-3074, 2006.
[62] B. Ibrahim, S. Diekmann, E. Schmitt, and P. Dittrich, In-Silico “Modeling of the Mitotic Spindle Assembly Checkpoint,” PLoS One, vol. 3, no. 2:e1555 2008, doi: 10.1371/journal.pone.0001555.
[63] C. Igel, N. Hansen, and S. Roth, “Covariance Matrix Adaptation for Multi-Objective Optimization,” Evolutionary Computation J., vol. 15, no. 1, pp. 1-28, 2007.
[64] F.J. DoyleIII and J. Stelling, “Systems Interface Biology,” J. Royal Soc. Interface, vol. 3, pp. 603-616, 2006.
[65] L. Ingber, “Very Fast Simulated Rea-Annealing,” Math. and Computer Modelling, vol. 12, no. 8, pp. 967-973, 1989.
[66] J.E. DennisJr., D.M. Gay, and R.E. Welsch, “An Adaptive Nonlinear Least-Squares Algorithm,” ACM Trans. Math. Software, vol. 7, no. 3, pp. 348-368, 1981.
[67] Fuzzy Systems in Bioinformatics and Computational Biology, vol. 242 of Studies in Fuzziness and Soft Computing, Y. Jin and L. Wang, eds. Springer, 2009.
[68] Knowledge Incorporation in Evolutionary Computation, ser. Studies in Fuzziness and Soft Computing, Y.C. Jin, ed., vol. 167, Springer, 2005.
[69] K.A. De Jong, “An Analysis of Behavior of a Class of Genetic Adaptive Systems,” PhD thesis, The Univ. of Michigan, 1975.
[70] B.H. Junker and F. Schreiber, Analysis of Biological Networks. Wiley, 2008.
[71] K.J. Kauffman, P. Prakash, and J.S. Edward, “Advances in Flux Balance Analysis,” Current Opinion in Biotechnology, vol. 14, no. 5, pp. 491-496, 2003.
[72] S.A. Kauffman, “Metabolic Stability and Epigenesis in Randomly Constructed Genetic Nets,” J. Theoretical Biology, vol. 22, pp. 437-467, 1969.
[73] D.B. Kell, “Metabolomics and System Biology: Making Sense of the Soup,” Current Opinion in Microbiology, vol. 7, pp. 296-307, 2004.
[74] J. Kennedy and R.C. Eberhart, Swarm Intelligence. Morgan Kaufmann, 2001.
[75] Biological Networks, ser. Complex Systems and Interdisciplinary Science, F. Képès, ed., vol. 3, World Scientific, 2007.
[76] S. Kikuchi, D. Tominaga, M. Arita, K. Takahashi, and M. Tomita, “Dynamical Modeling of Genetic Networks Using Genetic Algorithm and S-system,” Bioinformatics, vol. 19, no. 5, pp. 643-650, 2003.
[77] K-Y. Kim, D-Y. Cho, and B-T. Zhang, “Multi-Stage Evolutionary Algorithms for Efficient Identification of Gene Regulatory Networks,” Proc. EvoWorkshops, pp. 45-56, 2006.
[78] S. Kim, J. Kim, and K.H. Cho, “Inferring Gene Regulatory Networks from Temporal Expression Profiles Under Time-Delay and Noise,” Computational Biology and Chemistry, vol. 31, no. 4, pp. 239-245, 2007.
[79] S. Kimura, M. Hatakeyama, and A. Konagaya, “Inference of S-System Models of Genetic Networks from Noisy Time-Series Data,” Chem-Bio Informatics J., vol. 4, no. 1, pp. 1-14, 2004.
[80] S. Kimura, K. Ide, A. Kashihara, M. Kano, M. Hatakeyama, R. Masui, N. Nakagawa, S. Yokoyama, S. Kuramitsu, and A. Konagaya, “Inference of S-System Models of Genetic Networks Using a Cooperative Coevolutionary Algorithm,” Bioinformatics, vol. 21, no. 7, pp. 1154-1163, 2005.
[81] J. Kitagawa and H. Iba, “Identifying Metabolic Pathways and Gene Regulation Networks with Evolutionary Algorithms,” Evolutionary Computation in Bioinformatics, G.B. Fogel and D.W. Corne, eds., pp. 255-278, Morgan Kaufmann Publishers, 2003.
[82] H. Kitano, “Computational Systems Biology,” Nature, vol. 420, no. 14, pp. 206-210, 2002.
[83] H. Kitano, “System Biology: A Brief Overview,” Science, vol. 295, pp. 1662-1664, 2002.
[84] S.H. Kleinstein, D. Bottino, and G.S. Lett, “Nonuniform Sampling for Global Optimization of Kinetic Rate Constants in Biological Pathways,” Proc. Winter Simulation Conf., L.F. Perrone, F.P. Wieland, J. Liu, B.G. Lawson, D.M. Nicol, and R.M. Fujimoto, eds., pp. 1611-1616, 2006.
[85] J.R. Koza, W. Mydlowec, G. Lanza, J. Yu, and M.A. Keane, “Reverse Engineering of Metabolic Pathways from Observed Data Using Genetic Programming,” Proc. Pacific Symp. Biocomputing, vol. 6, pp. 434-445, 2000.
[86] A. Kremling and J. Saez-Rodriguez, “Systems Biology—An Engineering Perspective,” J. Biotechnology, vol. 129, pp. 329-351, 2007.
[87] L. Kuepfer, U. Sauer, and P.A. Parrilo, “Efficient Classification of Complete Parameter Regions Based On Semidefinite Programming,” BMC Bioinformatics, vol. 8, article 12, 2007.
[88] Z. Kutalik, W. Tucker, and V. Moulton, “S-System Parameter Estimation for Noisy Metabolic Profiles Using Newton-Flow Analysis,” IET Systms Biology, vol. 1, no. 3, pp. 174-180, May 2007.
[89] R. Lall and E.O. Voit, “Parameter Estimation in Modulated, Unbranched Reaction Chains with Biochemical Systems,” Computational Biology and Chemistry, vol. 29, pp. 309-318, 2005.
[90] T. Lenser, T. Hinze, B. Ibrahim, and P. Dittrich, “Towards Evolutionary Network Reconstruction Tools for Systems Biology,” Proc. Fifth European Conf. Evolutionary Computation, Machine Learning and Data Mining in Bioinformatics (EvoBIO), pp. 132-142, 2007.
[91] K. Levenberg, “A Method For the Solution of Certain Non-Linear Problems in Least Squares,” The Quarterly of Applied Math., vol. 2, pp. 164-168, 1944.
[92] W. Liebermeister and E. Klipp, “Bringing Metabolic Networks to Life: Integration of Kinetic, Metabolic, and Proteomic Data,” Theoretical Biology and Medical Modelling, vol. 3, article 42, 2006.
[93] G. Liliacci and M. Khammash, “Parameter Estimation and Model Selection in Computational Biology,” PLoS Computational Biology, vol. 6, no. 3:e1000696, Mar. 2010., doi:10.1371/journal.pcbi.1000696.
[94] P.-K. Liu and F.-S. Wang, “Inference of Biochemical Network Models in S-System Using Multiobjective Optimization Approach,” Bioinformatics, vol. 24, no. 8, pp. 1085-1092, 2008.
[95] P.-K. Liu and F.-S. Wang, “Inverse Problems of Biological Systems Using Multi-Objective Optimization,” J. the Chinese Inst. of Chemical Eng., vol. 39, no. 5, pp. 399-406, 2008.
[96] P.-K. Liu and F.-S. Wang, “Hybrid Differential Evolution with Geometric Mean Mutation in Parameter Estimation of Bioreaction Systems with Large Parameter Search Space,” J. Computers and Chemical Eng., vol. 33, pp. 1851-1860, 2009.
[97] P.-K. Liu and F.-S. Wang, “Hybrid Differential Evolution Including Geometric Mean Mutation for Optimization of Biochemical Systems,” J. Taiwan Inst. of Chemical Eng., vol. 41, pp. 65-72, 2010.
[98] P.-K. Liu, C.-H. Yuh, and F.-S. Wang, “Inference of Genetic Regulatory Networks Using S-System and Hybrid Differential Evolution,” Proc. IEEE Congress Evolutionary Computation, pp. 1736-1743, 2008.
[99] R. Mahadevan, J.S. Edwards, and F.J. DoyleIII, “Dynamic Flux Balance Analysis of Diauxic Growth in Escherichia Coli,” Biophysical J., vol. 83, pp. 1331-1340, Sept. 2002.
[100] R. Manner, S.W. Mahfoud, and S.W. Mahfoud, “Crowding and Preselection Revisited,” Parallel Problem Solving from Nature, pp. 27-36, 1992.
[101] D. Marbach, C. Mattiussi, and D. Floreano, “Bio-Mimetic Evolutionary Reverse Engineering of Genetic Regulatory Networks,” Proc. Fifth European Conf. Evolutionary Computation, Machine Learning and Data Mining in Bioinformatics, E. Marchiori, J.H. Moore, and J.C. Rajapakse, eds., pp. 155-165, 2007.
[102] Y. Matsubara, S. Kikuchi adn, M. Sugimoto, and M. Tomita, “Parameter Estimation for Stiff Equations of Biosystems Using Radial Basis Function Networks,” BMC Bioinformatics, vol. 7, article 230, 2006.
[103] N. Matsumaru, F. Centler, K.-P. Zauner, and P. Dittrich, “Self-Adaptive Scouting—Autonomous Experimentation for Systems Biology,” Lecture Notes in Artificial Intelligence, LNCS, vol. 3005, pp. 52-62, Springer, 2004.
[104] K. Matsumura, H. Oida, and S. Kimura, “Inference of S-System Models of Genetic Networks by Function Optimization Using Genetic Programming,” Trans. Information Processing Soc. Japan, vol. 46, no. 11, pp. 2814-2830, 2005.
[105] C. Mattiussi and D. Floreano, “Analog Genetic Encoding for the Evolution of Circuits and Networks,” IEEE Trans. Evolutionary Computation, vol. 11, no. 5, pp. 596-607, Oct. 2007.
[106] P. Mendes and D.B. Kell, “Non-Linear Optimization of Biochemical Pathways: Applications to Metabolic Engineering and Parameter Estimation,” Bioinformatics, vol. 14, no. 1, pp. 869-883, 1998.
[107] C. Modchang, W. Triampo, and Y. Lenbury, “Mathematical Modeling and Application of Genetic Algorithm to Parameter Estimation in Signal Transduction: Trafficking and Promiscuous Coupling of G-Protein Coupled Receptors,” Computers in Biology and Medicine, vol. 38, pp. 574-582, 2008.
[108] C.G. Moles, P. Mendes, and J.R. Banga, “Parameter Estimation in Biochemical Pathways: A Comparison of Global Optimization Methods,” Genome Research, vol. 13, nos. 2467-2474, 2003.
[109] J.H. Moore and L.W. Hahn, “Grammatical Evolution for the Discovery of Petri Net Models of Complex Genetic Systems” Proc. Int'l Conf. Genetic and Evolutionary Computation, Cantu-Paz et al., eds., pp. 2412-2413, 2003.
[110] J.H. Moore and L.W. Hahn, “Petri Net Modeling of High-Order Genetic Systems Using Grammatical Evolution,” BioSystems, vol. 72, pp. 177-186, 2003.
[111] J.H. Moore and L.W. Hahn, “Systems Biology Modeling in Huamn Genetics Using Petri Nets and Grammatical Evolution,” Proc. Genetic and Evolutionary Computation (GECCO '04) Conf., pp. 392-401, 2004.
[112] R. Morishita, H. Imade, I. Ono, N. Ono, and M. Okamoto, “Finding Multiple Solutions Based on an Evolutionary Algorithm for Inference of Genetic Networks by S-System,” Proc. Congress Evolutionary Computation (CEC '03), vol. 1, pp. 615-622, 2003.
[113] M. Motta Jafelice, B.F.Z. Bechara, L.C. Barros, R.C. Bassanezi, and F. Gomide, “Cellular Automata with Fuzzy Parameters in Microscopic Study of Positive HIV Individuals,” Math. and Computer Modelling, vol. 50, nos. 1/2, pp. 32-44, 2009.
[114] J.A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” Computer J., vol. 7, pp. 308-313, 1965.
[115] J. Nielsen, “Principles of Optimal Metabolic Network Operation,” Molecular Systems Biology, vol. 3, article 126, 2007.
[116] D. Noble, “Systems Biology and the Heart,” BioSystems, vol. 83, pp. 75-80, 2006.
[117] N. Noman and H. Iba, “Inference of Gene Regulatory Networks Using S-System and Differential Evolution,” Proc. Conf. Genetic and Evolutionary Computation, pp. 439-446, 2005.
[118] N. Noman and H. Iba, “Reverse Engineering Genetic Networks Using Evolutionary Computation,” Genome Informatics, vol. 16, no. 2, pp. 205-214, 2005.
[119] N. Noman and H. Iba, “Inferring Gene Regulatory Networks Using Differential Evolution with Local Search Heuristics,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 4, no. 4, pp. 634-647, Oct.-Dec. 2007.
[120] J. Nummela and B.A. Julstrom, “Evolving Petri Nets to Represent Metabolic Pathways,” Genetic and Evolutionary Computation Conf., Hans-Georg Beyer and Una-May O'Reilly, eds., pp. 2133-2139, 2005.
[121] M. O'Neill and C. Ryan, “Grammatical Evolution,” IEEE Trans. Evolutionary Computation, vol. 5, no. 4, pp. 349-358, Aug. 2001.
[122] M. Patan and B. Bogacka, “Optimum Experimental Designs for Dynamic Systems in the Presence of Correlated Errors,” Computational Statistics & Data Analysis, vol. 51, pp. 5644-5661, 2007.
[123] K.R. Patil, I. Rocha, J. Forster, and J. Nielsen, “Evolutionary Programming as A Platform for in Silico Metabolic Engineering,” BMC Bioinformatics, vol. 6, no. 1, p. 308, 2005.
[124] M. Peifer and J. Timmer, “Parameter Estimation in Ordinary Differential Equations for Biochemical Processes Using the Method of Multiple Shooting,” IET System Biology, vol. 1, no. 2, pp. 78-88, Mar. 2007.
[125] A. Pettinen, O. Yli-Harja, and M-L. Linne, “Comparison of Automated Parameter Estimation Methods for Neuronal Signalling Networks,” Neurocomputing, vol. 69, pp. 1371-1374, 2006.
[126] J.W. Pinney, D.R. Westhead, and G.A. McConkey, “Petri Net Representations in Systems Biology,” Biochemical Soc. Trans., vol. 31, no. 6, pp. 1513-1515, 2003.
[127] P.K. Polisetty, E.O. Voit, and E.P. Gatzke, “Identification of Metabolic System Parameters Using Global Optimization Methods,” Theoretical Biology and Medical Modelling, vol. 3, no. 4, pp. 1-15, 2006.
[128] M.J.D. Powell, “The NEWUOA Software for Unconstrained Optimisation without Derivatives,” Technical Report NA2004/08, Dept. of Applied Math. and Theoretical Physics, Univ. of Cambridge, 2004.
[129] A.A. Poyton, M.S. Varziri, K.B. McAuley, P.J. Mclellan, and J.O. Ramsay, “Parameter Estimation In Continuous-Time Dynamic Models Using Principal Differential Analysis,” Computers and Chemical Eng., vol. 30, pp. 698-708, 2006.
[130] K. Praveen, D. Sanjoy, and W. Stephen, “LRJ: A Multi-Objective GA-Simplex Hybrid Approach for Gene Regulatory Network Models,” Proc. IEEE Congress Evolutionary Computation, pp. 2084-2090, 2004.
[131] J.O. Ramsay, G. Hooker, D. Campbell, and J. Cao, “Parameter Estimation for Differential Equations: A Generalized Smoothing Approach,” J. the Royal Statistical Soc.: Series B (Statistical Methodology), vol. 69, no. 5, pp. 741-796, 2007.
[132] M. Rodriguez-Fernandez, J.A. Egea, and J.R. Banga, “Novel Metaheuristic for Parameter Estimation in Nonlinear Dynamic Biological Systems,” BMC Bioinformatics, vol. 7, pp. 483-501, 2006.
[133] M. Rodriguez-Fernandez, P. Mendes, and J.R. Banga, “A Hybrid Approach for Efficient and Robust Parameter Estimation in Biochemical Pathways,” BioSystems, vol. 83, pp. 248-265, 2006.
[134] T. Rudge and N. Geard, “Evolving Gene Regulatory Networks for Cellular Morphogenesis,” Proc. The Second Australian Conf. Artificial Life, Dec. 2005.
[135] T.P. Runarsson and X. Yao, “Stochastic Ranking for Constrained Evolutionary Optimization,” IEEE Trans. Evolutionary Computation, vol. 4, no. 3, pp. 284-294, Sept. 2000.
[136] Handbook of Fuzzy Computation, E. Ruspini, P. Bonissone, and W. Pedrycz , eds. IOP Publishing, Ltd., 1998.
[137] H. Salis and Y. Kaznessis, “Accurate Hybrid Stochastic Simulation of a System of Coupled Chemical or Biochemical Reactions,” J. Chemical Physics, vol. 122, no. 5: 54103, 2005.
[138] H. Salis, V. Sotiropoulos, and Y.N. Kaznessis, “Multiscale Hy3S: Hybrid Stochastic Simulation for Supercomputers,” BMC Bioinformatics, vol. 7, article 93, 2006.
[139] M.A. Savageau, “Biochemical Systems Analysis I: Some Mathematical Properties of the Rate Law for the Component Enzymatic Reactions,” J. Theoretical Biology, vol. 25, no. 3, pp. 365-369, 1969.
[140] M.A. Savageau, “Biochemical Systems Analysis II: The Steady State Solutions for an N-Pool System Using a Power-Law Approximation,” J. Theoretical Biology, vol. 25, no. 3, pp. 370-379, 1969.
[141] M.A. Savageau, “Biochemical Systems Analysis III: Dynamic Solutions Using a Power-Law Approximation,” J. Theoretical Biology, vol. 26, no. 2, pp. 215-226, 1970.
[142] R. Schuetz, L. Kuepfer, and U. Sauer, “Systematic Evaluation of Objective Functions for Predicting Intracellular Fluxes in Escherichia Coli,” Molecular Systems Biology, vol. 3, article 119, 2007.
[143] D. Segre, D. Vitkup, and G.M. Church, “Analysis of Optimality in Natural and Perturbed Metabolic Networks,” Proc. Nat'l Academy of Sciences of USA, vol. 99, no. 23, pp. 15112-15117, 2002.
[144] S. Sheikh-Bahaei and C.A. Hunt, “Prediction of in vitro Heapatic Biliary Excretion Using Stochastic Agent-Based Modeling and Fuzzy Clustering,” Proc. Winter Simulation Conf., L.F. Perrone, F.P. Wieland, J. Liu, B.G. Lawson, D.M. Nicol, and R.M. Fujimoto, eds., pp. 1617-1624, 2006.
[145] Advances in Metaheuristics for Hard Optimization, Natural Computing Series, P. Siarry, and Z. Michalewicz, eds. Springer, 2008.
[146] A. Sirbu, H.J. Ruskin, and M. Crane, “Comparison of Evolutionary Algorithms in Gene Regulatory Network Model Inference,” BMC Bioinformatics, vol. 11, no. 1, p. 59, 2010.
[147] C. Spieth, F. Streichert, N. Speer, and A. Zell, “Optimizing Topology and Parameters of Gene Regulatory Network Models from Time-Series Experiments,” Proc. Genetic and Evolutionary Computation Conf., K. Deb et al., eds., pp. 461-470, 2004.
[148] C. Spieth, R. Worzischek, and F. Streichert, “Comparing Evolutionary Algorithms on the Problem of Network Inference,” Proc. Eighth Ann. Conf. Genetic and Evolutionary Computation, pp. 305-306, 2006.
[149] J. Srividhya, E.J. Crampin, and P.E. McSharry, “Reconstructing Biochemical Pathways from Time Course Data,” Proteomics, vol. 7, pp. 828-838, 2007.
[150] R. Storn and K. Price, “Differential Evolution—A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces,” J. Global Optimization, vol. 11, pp. 341-359, 1997.
[151] F. Streichert, H. Planatscher, C. Spieth, H. Ulmer, and A. Zell, “Comparing Genetic Programming and Evolution Strategies on Inferring Gene Regulatory Networks,” Proc. Genetic and Evolutionary Computation Conf., pp. 471-480, 2004.
[152] D. Tominaga, N. Koga, and M. Okamoto, “Efficient Numerical Optimization Algorithm Based on Genetic Algorithm for Inverse Problem: System for the Inference of Genetic Networks,” Proc. Genetic and Evolutionary Computation Conf., pp. 251-258, 2000.
[153] J. Tomshine and Y.N. Kaznessis, “Optimization of a Stochastically Simulated Gene Network Model via Simulated Annealing,” Biophysical J., vol. 91, pp. 3196-3205, 2006.
[154] K.-Y. Tsai and F.-S. Wang, “Evolutionary Optimization with Data Collocation for Reverse Engineering of Biological Networks,” Bioinformatics, vol. 21, no. 7, pp. 1180-1188, 2005.
[155] S. Tsutsui, M. yamamura, and T. Higuchi, “Multi-Parent Recombination with Simplex Crossover in Real-Coded Genetic Algorithm,” Proc. Genetic and Evolutionary Computation Conf., pp. 657-664, 1999.
[156] P.A. Vanrolleghem and D. Dochain, “Model Identification,” Advanced Instrumentation, Data Integration, and Control of Biotechnological Process, J. Van Impe, P.A. Vanrolleghem, and D. Iserentant, eds., pp. 251-318, Kluwer Academic Publishers, 1998.
[157] T.D. Vo, W.N.P. Lee, and P.O. Palsson, “Systems Analysis of Energy Metabolism Elucidates the Affected Respiratory Chain Complex in Leigh's Syndrome,” Molecular Genetics and Metabolism, vol. 91, no. 1, pp. 15-22, 2007.
[158] E.O. Voit and J. Almeida, “Decoupling Dynamical Systems for Pathway Identification from Metabolic Profiles,” Bioinformatics, vol. 20, no. 11, pp. 1670-1681, 2004.
[159] V. Vyshemirsky and M. Girolami, “Biobayes: A Software Package for Bayesian Inference in Systems Biology,” Bioinformatics, vol. 24, no. 17, pp. 1933-1934, 2008.
[160] F.-S. Wang and P.-K. Liu, “Inverse Problems of Biochemical Systems Using Hybrid Differential Evolution and Data Collocation,” Int'l J. Systems and Synthetic Biology, vol. 1, pp. 21-38, 2010.
[161] Y. Wang, T. Joshi, X.-S. Zhang, D. Xu, and L. Chen, “Inferring Gene Regulatory Networks from Multiple Microarray Databases,” Bioinformatics, vol. 22, no. 19, pp. 2413-2420, 2006.
[162] K.Q. Weinberger, F. Sha, Q. Zhu, and L.K. Saul, “Graph Laplacian Regularization for Large-Scale Semidefinite Programming,” Advanced in Neural Information Processing System, 2007.
[163] D.H. Wolpert and W.G. Macready, “No Free Lunch Theorems for Optimization,” IEEE Trans. Evolutionary Computation, vol. 1, no. 1, pp. 67-82, Apr. 1997.
[164] R. Xu, G.K. Venayagamoorthy, and D.C. WunschII, “Modeling of Gene Regulatory Networks with Hybrid Differential Evolution and Particle Swarm Optimization,” Neural Networks, vol. 20, pp. 917-927, 2007.
[165] J. Yang, S. Wongsa, V. Kadirkamanathan, S.A. Billings, and P.C. Wright, “Metabolic Flux Estimation—A Self-Adaptive Evolutionary Algorithm with Singular Value Decomposition,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 4, no. 1, pp. 126-138, Jan.-Mar. 2007.
[166] J. Yang, S. Woongsa, V. Kadirkamanathan, S.A. Billings, and P.C. Wright, “Differential Evolution and Its Application to Metabolic Flux Analysis,” Proc. Evo Workshops '05, F. Rothlauf et al., eds., pp. 115-124, 2005.
[167] Evolutionary Computation in Dynamics and Uncertain Environments, ser. Studies in Computational Intelligence, S.X. Yang, Y.-S. Ong, and Y.C. Jin, eds., vol. 51, Springer, 2007.
[168] Y. Ye, “Interior Algorithms for Linear, Quadratic and Linearly Constrained Nonlinear Programming,” PhD thesis, Dept. of ESS, Stanford Univ., 1987.
[169] M.K.S. Yeung, J. Tegner, and J.J. Collins, “Reverse Engineering Gene Networks Using Singular Value Decomposition and Robust Regression,” Proc. Nat'l Academy of Sciences USA, vol. 99, no. 9, pp. 6163-6168, 2002.
[170] L. You, “Toward Computational Systems Biology,” Cell Biochemistry and Biophysics, vol. 40, pp. 167-184, 2004.
[171] D.E. Zak, G.E. Gonye, J.S. Schwaber, and F.J. DoyleIII, “Importance of Input Perturbations and Stochastic Gene Expression in the Reverse Engineering of Genetic Regulatory Networks: Insights from and Identifiability Analysis of an in Silico Network,” Genome Research, vol. 13, pp. 2396-2405, 2003.
[172] W. Zhang and X. Xie, “DEPSO: Hybrid Particle Swarm with Differential Evolution Operator,” Proc. IEEE Int'l Conf. Systems, Man and Cybernetics, pp. 3816-3821, 2003.
[173] Z. Zhou, Y.-S. Ong, P.B. Nair, A.J. Keane, and K.Y. Lum, “Combining Global and Local Surrogate Models to Accelerate Evolutionary Optimization,” IEEE Trans. Systems, Man, and Cybernetics, Part C: Applications and Rev., vol. 37, no. 1, pp. 66-76, Jan. 2007.
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