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Jakobsson S.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Patriksson M.,Chalmers University of Technology | Patriksson M.,Gothenburg University | Rudholm J.,Chalmers University of Technology | And 3 more authors.
Optimization and Engineering | Year: 2010

We propose an algorithm for the global optimization of expensive and noisy black box functions using a surrogate model based on radial basis functions (RBFs). A method for RBF-based approximation is introduced in order to handle noise. New points are selected to minimize the total model uncertainty weighted against the surrogate function value. The algorithm is extended to multiple objective functions by instead weighting against the distance to the surrogate Pareto front; it therefore constitutes the first algorithm for expensive, noisy and multiobjective problems in the literature. Numerical results on analytical test functions show promise in comparison to other (commercial) algorithms, as well as results from a simulation based optimization problem. © 2009 Springer Science+Business Media, LLC. Source

Voronov A.,Chalmers University of Technology | Akesson K.,Chalmers University of Technology | Ekstedt F.,Fraunhofer Chalmers Research Center for Industrial Mathematics
CEUR Workshop Proceedings | Year: 2011

Models of configurable products can have hundreds of variables and thousands of configuration constraints. A product engineer usually has a limited responsibility area, and thus is interested in only a small subset of the variables that are relevant to the responsibility area. It is important for the engineer to have an overview of possible products with respect to the responsibility area, with all irrelevant information omitted. Configurations with some variables omitted we will call partial configurations, and we will call a partial configuration valid if it can be extended to a complete configuration satisfying all configuration constraints. In this paper we consider exact ways to compute valid partial configurations: we present two new algorithms based on Boolean satisfiability solvers, as well as ways to use knowledge compilation methods (Binary Decision Diagrams and Decomposable Negation Normal Form) to compute valid partial configurations. We also show that the proposed methods are feasible on configuration data from two automotive companies. Source

Sunnaker M.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Schmidt H.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Jirstrand M.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Cedersund G.,Fraunhofer Chalmers Research Center for Industrial Mathematics | And 3 more authors.
BMC Systems Biology | Year: 2010

Background: Systems biology models tend to become large since biological systems often consist of complex networks of interacting components, and since the models usually are developed to reflect various mechanistic assumptions of those networks. Nevertheless, not all aspects of the model are equally interesting in a given setting, and normally there are parts that can be reduced without affecting the relevant model performance. There are many methods for model reduction, but few or none of them allow for a restoration of the details of the original model after the simplified model has been simulated.Results: We present a reduction method that allows for such a back-translation from the reduced to the original model. The method is based on lumping of states, and includes a general and formal algorithm for both determining appropriate lumps, and for calculating the analytical back-translation formulas. The lumping makes use of efficient methods from graph-theory and ε{lunate}-decomposition and is derived and exemplified on two published models for fluorescence emission in photosynthesis. The bigger of these models is reduced from 26 to 6 states, with a negligible deviation from the reduced model simulations, both when comparing simulations in the states of the reduced model and when comparing back-translated simulations in the states of the original model. The method is developed in a linear setting, but we exemplify how the same concepts and approaches can be applied to non-linear problems. Importantly, the method automatically provides a reduced model with back-translations. Also, the method is implemented as a part of the systems biology toolbox for matlab, and the matlab scripts for the examples in this paper are available in the supplementary material.Conclusions: Our novel lumping methodology allows for both automatic reduction of states using lumping, and for analytical retrieval of the original states and parameters without performing a new simulation. The two models can thus be considered as two degrees of zooming of the same model. This is a conceptually new development of model reduction approaches, which we think will stimulate much further research and will prove to be very useful in future modelling projects. © 2010 Sunnåker et al; licensee BioMed Central Ltd. Source

Sunnaker M.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Sunnaker M.,ETH Zurich | Cedersund G.,Linkoping University | Cedersund G.,Albert Ludwigs University of Freiburg | And 2 more authors.
BMC Systems Biology | Year: 2011

Background: Models of biochemical systems are typically complex, which may complicate the discovery of cardinal biochemical principles. It is therefore important to single out the parts of a model that are essential for the function of the system, so that the remaining non-essential parts can be eliminated. However, each component of a mechanistic model has a clear biochemical interpretation, and it is desirable to conserve as much of this interpretability as possible in the reduction process. Furthermore, it is of great advantage if we can translate predictions from the reduced model to the original model.Results: In this paper we present a novel method for model reduction that generates reduced models with a clear biochemical interpretation. Unlike conventional methods for model reduction our method enables the mapping of predictions by the reduced model to the corresponding detailed predictions by the original model. The method is based on proper lumping of state variables interacting on short time scales and on the computation of fraction parameters, which serve as the link between the reduced model and the original model. We illustrate the advantages of the proposed method by applying it to two biochemical models. The first model is of modest size and is commonly occurring as a part of larger models. The second model describes glucose transport across the cell membrane in baker's yeast. Both models can be significantly reduced with the proposed method, at the same time as the interpretability is conserved.Conclusions: We introduce a novel method for reduction of biochemical models that is compatible with the concept of zooming. Zooming allows the modeler to work on different levels of model granularity, and enables a direct interpretation of how modifications to the model on one level affect the model on other levels in the hierarchy. The method extends the applicability of the method that was previously developed for zooming of linear biochemical models to nonlinear models. © 2011 Sunnåker et al; licensee BioMed Central Ltd. Source

Berglund M.,Gothenburg University | Berglund M.,Chalmers University of Technology | Sunnaker M.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Sunnaker M.,ETH Zurich | And 6 more authors.
Mathematical Medicine and Biology | Year: 2012

Non-linear mixed effects (NLME) models represent a powerful tool to simultaneously analyse data from several individuals. In this study, a compartmental model of leucine kinetics is examined and extended with a stochastic differential equation to model non-steady-state concentrations of free leucine in the plasma. Data obtained from tracer/tracee experiments for a group of healthy control individuals and a group of individuals suffering from diabetes mellitus type 2 are analysed. We find that the interindividual variation of the model parameters is much smaller for the NLME models, compared to traditional estimates obtained from each individual separately. Using the mixed effects approach, the population parameters are estimated well also when only half of the data are used for each individual. For a typical individual, the amount of free leucine is predicted to vary with a standard deviation of 8.9% around a mean value during the experiment. Moreover, leucine degradation and protein uptake of leucine is smaller, proteolysis larger and the amount of free leucine in the body is much larger for the diabetic individuals than the control individuals. In conclusion, NLME models offers improved estimates for model parameters in complex models based on tracer/tracee data and may be a suitable tool to reduce data sampling in clinical studies. © The Author 2011. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. Source

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