Deterministic global optimization algorithm based on outer approximation for the parameter estimation of nonlinear dynamic biological systems.

BMC Bioinformatics
Anton MiróLaureano Jiménez

Abstract

The estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are usually classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens. This work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to global minimum, is based on reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation meth...Continue Reading

Citations

Dec 7, 2013·Journal of the Royal Society, Interface·Alejandro F Villaverde, Julio R Banga
Mar 8, 2013·PloS One·Afnizanfaizal AbdullahSatya N V Arjunan
May 17, 2008·PLoS Computational Biology·Jong Min LeeJason A Papin
Mar 10, 2012·PloS One·Nuno F LagesAntónio E N Ferreira
Oct 31, 2015·BMC Systems Biology·Attila Gábor, Julio R Banga
Mar 1, 2019·Bioinformatics·Alejandro F VillaverdeJulio R Banga

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Software Mentioned

BARON
GAMS
CPLEX
BARON ( Branch And Reduce Optimization Navigator )

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