predictive-microbiology-software.bib

@misc{edpm2023,
  author = {Pleyer, J and Gaindrik, P}, 
  title = {e{DPM} - experimental {D}esign for {P}redictive {M}icrobiology},
  howpublished = {\url{https://github.com/Spatial-Systems-Biology-Freiburg/eDPM}},
  note = {Accessed: 21.09.2023}
}

@article{stigterObservabilityComplex2017,
  title = {Observability of {{Complex Systems}}: {{Finding}} the {{Gap}}},
  author = {Stigter, J D and Joubert, D and Molenaar, J},
  year = {2017},
  month = nov,
  journal = {Scientific Reports},
  pages = {1--9},
  doi = {10.1038/s41598-017-16682-x},
  abstract = {Scientific Reports, doi:10.1038/s41598-017-16682-x},
  annotation = {27 citations (Crossref) [2023-02-16]},
  file = {/Users/cfleck/Zotero/storage/9EVSV94N/0290141B-6D60-4F59-9694-ABC7377DD8CF.pdf;/Users/cfleck/Zotero/storage/IPSRN4W2/Stigter et al. - 2017 - Observability of Complex Systems Finding the Gap.pdf}
}

@article{lyTutorialFisher2017,
  title = {A Tutorial on {{Fisher}} Information},
  author = {Ly, A and Marsman, M and Verhagen, J and of Mathematical, RPPP Grasman Journal and {2017}},
  year = {2017},
  month = oct,
  journal = {Elsevier},
  volume = {80},
  pages = {40--55},
  doi = {10.1016/j.jmp.2017.05.006},
  abstract = {In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different statistical paradigms. First, in the \textbackslash ldots},
  langid = {english},
  annotation = {90 citations (Crossref) [2023-02-16]},
  file = {/Users/cfleck/Zotero/storage/7MCRXJX8/Ly et al. - 2017 - A tutorial on Fisher information.pdf;/Users/cfleck/Zotero/storage/I3ZYQCUZ/346B8D77-90D9-42DC-9654-92858DC781B5.pdf}
}

@article{gaborRobustEfficient2015,
  title = {Robust and Efficient Parameter Estimation in Dynamic Models of Biological Systems},
  author = {G{\'a}bor, Attila and Banga, Julio R.},
  year = {2015},
  month = dec,
  journal = {BMC Systems Biology},
  volume = {9},
  number = {1},
  pages = {74},
  issn = {1752-0509},
  doi = {10.1186/s12918-015-0219-2},
  urldate = {2020-03-05},
  abstract = {Background: Dynamic modelling provides a systematic framework to understand function in biological systems. Parameter estimation in nonlinear dynamic models remains a very challenging inverse problem due to its nonconvexity and ill-conditioning. Associated issues like overfitting and local solutions are usually not properly addressed in the systems biology literature despite their importance. Here we present a method for robust and efficient parameter estimation which uses two main strategies to surmount the aforementioned difficulties: (i) efficient global optimization to deal with nonconvexity, and (ii) proper regularization methods to handle ill-conditioning. In the case of regularization, we present a detailed critical comparison of methods and guidelines for properly tuning them. Further, we show how regularized estimations ensure the best trade-offs between bias and variance, reducing overfitting, and allowing the incorporation of prior knowledge in a systematic way. Results: We illustrate the performance of the presented method with seven case studies of different nature and increasing complexity, considering several scenarios of data availability, measurement noise and prior knowledge. We show how our method ensures improved estimations with faster and more stable convergence. We also show how the calibrated models are more generalizable. Finally, we give a set of simple guidelines to apply this strategy to a wide variety of calibration problems. Conclusions: Here we provide a parameter estimation strategy which combines efficient global optimization with a regularization scheme. This method is able to calibrate dynamic models in an efficient and robust way, effectively fighting overfitting and allowing the incorporation of prior information.},
  langid = {english},
  annotation = {92 citations (Crossref) [2023-02-16]},
  file = {/Users/cfleck/Zotero/storage/CCWZH5Y5/Gábor und Banga - 2015 - Robust and efficient parameter estimation in dynam.pdf}
}


@article{baranyiDynamicApproach1994,
  title = {A Dynamic Approach to Predicting Bacterial Growth in Food},
  author = {Baranyi, J{\'o}zsef and Roberts, Terry A.},
  year = {1994},
  month = nov,
  journal = {International Journal of Food Microbiology},
  volume = {23},
  number = {3-4},
  pages = {277--294},
  issn = {01681605},
  doi = {10.1016/0168-1605(94)90157-0},
  urldate = {2023-08-01},
  abstract = {A new member of the family of growth models described by Baranyi et al. (1993a) is introduced in which the physiological state of the cells is represented by a single variable. The duration of lag is determined by the value of that variable at inoculation and by the post-inoculation environment. When the subculturing procedure is standardized, as occurs in laboratory experiments leading to models, the physiological state of the inoculum is relatively constant and independent of subsequent growth conditions. It is shown that, with cells with the same pre-inoculation history, the product of the lag parameter and the maximum specific growth rate is a simple transformation of the initial physiological state. An important consequence is that it is sufficient to estimate this constant product and to determine how the environmental factors define the specific growth rate without modelling the environment dependence of the lag separately. Assuming that the specific growth rate follows the environmental changes instantaneously, the new model can also describe the bacterial growth in an environment where the factors, such as temperature, pH and a w, change with time.},
  langid = {english},
  annotation = {1824 citations (Crossref) [2023-08-01]},
  file = {/Users/cfleck/Zotero/storage/38IA8Z5A/Baranyi und Roberts - 1994 - A dynamic approach to predicting bacterial growth .pdf}
}

@misc{jupyterteamJupyterNotebook,
  title = {Jupyter {{Notebook}}},
  author = {Jupyter Team},
  howpublished = {https://jupyter.org}
}

@article{vilasPredictiveFood2016,
  title = {Toward Predictive Food Process Models: {{A}} Protocol for Parameter Estimation},
  author = {Vilas, Carlos and {Arias-M{\'e}ndez}, Ana and Garc{\'i}a, M{\'i}riam R and Alonso, Antonio A and {Balsa-Canto}, E},
  year = {2016},
  month = may,
  journal = {Critical Reviews in Food Science and Nutrition},
  volume = {27},
  pages = {1--14},
  doi = {10.1080/10408398.2016.1186591},
  langid = {english},
  annotation = {15 citations (Crossref) [2023-02-16]},
  file = {/Users/cfleck/Zotero/storage/9IYMHGYN/Vilas et al. - 2016 - Toward predictive food process models A protocol .pdf}
}

@article{sunParameterEstimation2011,
  title = {Parameter {{Estimation Using Meta-Heuristics}} in {{Systems Biology}}: {{A Comprehensive Review}}.},
  author = {Sun, Jianyong and Garibaldi, Jonathan M and Hodgman, Charlie},
  year = {2011},
  month = mar,
  journal = {IEEE/ACM transactions on computational biology and bioinformatics / IEEE, ACM},
  doi = {10.1109/TCBB.2011.63},
  abstract = {This paper gives a comprehensive review of the application of meta-heuristics to optimization problems in systems biology, mainly focussing 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 meta-heuristic 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 meta-heuristics developed for these problems follow, along with outlines of their advantages and disadvantages. Several important issues in applying meta-heuristics to the systems biology modelling 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.},
  langid = {english},
  pmid = {21464505},
  annotation = {84 citations (Crossref) [2023-02-16]},
  file = {/Users/cfleck/Zotero/storage/PIVI3FYI/Sun et al. - 2011 - Parameter Estimation Using Meta-Heuristics in Syst.pdf}
}

@article{atkinsonDevelopmentsDesignExperiments1982,
  title = {Developments in the {{Design}} of {{Experiments}}, {{Correspondent Paper}}},
  author = {Atkinson, A. C.},
  year = {1982},
  journal = {International Statistical Review / Revue Internationale de Statistique},
  volume = {50},
  number = {2},
  pages = {161--177},
  publisher = {{[Wiley, International Statistical Institute (ISI)]}},
  issn = {03067734, 17515823},
  doi = {10.2307/1402599},
  abstract = {A survey is given of recent developments in the design of experiments, based on the literature of the last five years. Optimum design theory emerges as a unifying theme, even in such classical areas as incomplete block designs. /// Cet article rassemble, en se basant sur les publications apparues ces cinq derni\&\#xe8;res ann\&\#xe9;es, les plus r\&\#xe9;cents developpements en mati\&\#xe8;re de planification d'exp\&\#xe9;riences. La th\&\#xe9;orie de planification optimale (optimum design) \&\#xe9;merge comme th\&\#xe9;orie unificatrice, m\&\#xea;me dans des domaines aussi classiques que la planification comportant des blocs incomplets.}
}

@article{balsa-cantoe.bangaj.r.COMPUTINGOPTIMALDYNAMIC2008,
  title = {Computing optimal dynamic experiments for model calibration in {{Predictive Microbiology}}},
  author = {Balsa-Canto, E. Banga, J.R.},
  year = {2008},
  journal = {Journal of Food Process Engineering},
  volume = {31},
  doi = {10.1111/j.1745-4530.2007.00147.x},
  abstract = {The potential of mathematical models describing the microbial behavior during food processing and storage largely depends on their predictive capabilities and, in this concern, model calibration plays a crucial role. Unfortunately, model calibration may only be performed successfully if the sources of information are sufficiently rich. Therefore, a careful experimental design is required. This contribution formulated the optimal experimental design (OED) problem as a general dynamic optimization problem where the objective was to optimize a certain criterion depending on the Fisher information matrix. This formulation allows for more flexibility in the experimental design, including initial conditions, sampling times, experimental durations, time-dependent manipulable variables and number of experiments as degrees of freedom. Moreover, the use of robust confidence regions for the parameter estimates was suggested as an alternative to evaluate the quality of the proposed experimental schemes. The OED for the calibration of the thermal death time and Ratkowsky-type secondary models was considered for illustrative purposes, showing how the usually disregarded E-optimality criterion results in the experimental schemes offering the best compromise precision/decorrelation among the parameters. PRACTICAL APPLICATIONS This work addresses a general methodology for designing optimal dynamic experiments for the purpose of model calibration. This methodology is general in the sense that it may be applied to any type of food processing model, being particularly relevant for predictive microbiology and quality assessment as the experimentation is both time consuming and expensive. The main advantages of the proposed technique are twofold: on one hand, it is able to significantly reduce the overall experimental burden, contributing not only to simplify the experimental planning, devising the most adequate experiments, but also minimizing the number of experiments, and on the other hand, the resultant experiments provide the maximum quantity and quality of information to improve the predictive capabilities of the models under consideration, of key importance for process design, optimization and control.}
}

@article{bangaImprovingFoodProcessing2003,
  ids = {BANGA2003131},
  title = {Improving Food Processing Using Modern Optimization Methods},
  author = {Banga, Julio R. and {Balsa-Canto}, Eva and Moles, Carmen G. and Alonso, Antonio A.},
  year = {2003},
  journal = {Trends in Food Science \& Technology},
  volume = {14},
  number = {4},
  pages = {131--144},
  issn = {0924-2244},
  doi = {10.1016/s0924-2244(03)00048-7},
  abstract = {In this contribution, computer-aided optimization is presented as the ultimate tool to improve food processing. The state of the art is reviewed, especially focusing in recent developments using modern optimization techniques. Their potential for industrial applications is also discussed in the light of several important examples. Finally, future trends and research needs are outlined.}
}

@article{bernaertsConceptsToolsPredictive2004,
  title = {Concepts and {{Tools}} for {{Predictive Modeling}} of {{Microbial Dynamics}}},
  author = {Bernaerts, Kristel and Dens, Els and Vereecken, Karen and Geeraerd, Annemie H. and Standaert, Arnout R. and Devlieghere, Frank and Debevere, Johan and Van Impe, Jan F.},
  year = {2004},
  month = sep,
  journal = {Journal of Food Protection},
  volume = {67},
  number = {9},
  pages = {2041--2052},
  issn = {0362-028X},
  doi = {10.4315/0362-028X-67.9.2041},
  abstract = {Description of microbial cell (population) behavior as influenced by dynamically changing environmental conditions intrinsically needs dynamic mathematical models. In the past, major effort has been put into the modeling of microbial growth and inactivation within a constant environment (static models). In the early 1990s, differential equation models (dynamic models) were introduced in the field of predictive microbiology. Here, we present a general dynamic model-building concept describing microbial evolution under dynamic conditions. Starting from an elementary model building block, the model structure can be gradually complexified to incorporate increasing numbers of influencing factors. Based on two case studies, the fundamentals of both macroscopic (population) and microscopic (individual) modeling approaches are revisited. These illustrations deal with the modeling of (i) microbial lag under variable temperature conditions and (ii) interspecies microbial interactions mediated by lactic acid production (product inhibition). Current and future research trends should address the need for (i) more specific measurements at the cell and/or population level, (ii) measurements under dynamic conditions, and (iii) more comprehensive (mechanistically inspired) model structures. In the context of quantitative microbial risk assessment, complexity of the mathematical model must be kept under control. An important challenge for the future is determination of a satisfactory trade-off between predictive power and manageability of predictive microbiology models.}
}

@article{derlindenImpactExperimentDesign2013,
  title = {The Impact of Experiment Design on the Parameter Estimation of Cardinal Parameter Models in Predictive Microbiology},
  author = {Derlinden, Eva Van and Mertens, Laurence and Impe, Jan F. Van},
  year = {2013},
  journal = {Food Control},
  volume = {29},
  number = {2},
  pages = {300--308},
  issn = {0956-7135},
  doi = {10.1016/j.foodcont.2012.06.018},
  abstract = {In predictive food microbiology, cardinal parameter models are often applied to describe the effect of temperature, pH and/or water activity on the microbial growth rate. To identify the model parameters, full factorial designs are often used, in spite of the high experimental burden and cost related to this method. In this work, the impact of the selected experimental scheme on the estimation of the parameters of the cardinal model describing the effect of temperature, pH and/or water activity has been evaluated. In a first step, identification of a simple model describing only the effect of temperature, pH or water activity was considered. The comparison of an equidistant design and a D-optimal (based) design showed that the latter, which is based on the model's sensitivity functions, yields more realistic parameter estimates than the typical equidistant design. By selecting the experimental levels based on the sensitivity functions, a more realistic description of the behavior around optimal conditions can be obtained. In the second step, focus was on the efficient and accurate estimation of the ten parameters of the extended cardinal model that describes the combined effect of temperature, pH and water activity on the microbial growth rate. Again, equidistant level selection is compared to a D-optimal (based) experimental design. In addition, a full factorial and a Latin-square approach are evaluated. From the simulation case studies presented, it can be stated that all parameters can be equally well defined from an equidistant design as from a D-optimal-based design. In addition, reducing the experimental load by constructing a Latin-square design does not hamper the parameter estimation procedure. This work confirms the observation of a previous study, i.e., for complex cases a Latin-square design is an attractive alternative for a full factorial design as it yields equally accurate and reliable parameter estimates while reducing the experimental workload.},
  keywords = {Experimental design,Full factorial design,Latin-square design,Parameter estimation,Secondary cardinal parameter model}
}

@article{franceschiniModelbasedDesignExperiments2008,
  ids = {franceschiniModelbasedDesign2008},
  title = {Model-Based Design of Experiments for Parameter Precision: {{State}} of the Art},
  author = {Franceschini, Gaia and Macchietto, Sandro},
  year = {2008},
  journal = {Chemical Engineering Science},
  volume = {63},
  number = {19},
  pages = {4846--4872},
  issn = {0009-2509},
  doi = {10.1016/j.ces.2007.11.034},
  abstract = {Due to the wide use and key importance of mathematical models in process engineering, experiment design is becoming an essential tool for the rapid building and validation of these mechanistic models. Several experiment design techniques have been developed in the past and applied successfully to a wide range of systems. This paper is focused on the so-called model-based design of experiments (DOE) and aims at presenting an up-to-date state of the art in this important field. In order to provide an adequate and thorough background to this technique, a detailed description of the key elements of a model identification procedure (the model itself, the experiment, the statistical tools, etc.) and the major steps of a model-building strategy are introduced before focusing on the experiment design for parameter precision, which is the topic of this survey. An overview and critical analysis of the state of the art in this sector are proposed. The main contributions to model-based experiment design procedures in terms of novel criteria, mathematical formulations and numerical implementations are highlighted. A list of the most recent applications of these techniques in various fields (from chemical kinetics to biological modelling) is then presented highlighting the key role of model-based DOE in the process engineering area.},
  keywords = {Mathematical modelling,Model validation,Model-based experiment design,Non-linear dynamics,Optimisation,Parameter identification,Process engineering}
}

@book{friedenExploratoryData2010,
  title = {Exploratory {{Data Analysis Using Fisher Information}}},
  author = {Frieden, Roy and Gatenby, Robert A},
  year = {2010},
  month = may,
  publisher = {{Springer Science \& Business Media}},
  address = {{London}},
  doi = {10.1007/978-1-84628-777-0},
  abstract = {This book uses a mathematical approach to deriving the laws of science and technology, based upon the concept of Fisher information. The approach that follows from these ideas is called the principle of Extreme Physical Information (EPI). The authors show how to use EPI to determine the theoretical input/output laws of unknown systems. Will benefit readers whose math skill is at the level of an undergraduate science or engineering degree.},
  isbn = {978-1-84628-777-0},
  langid = {english}
}

@article{garciaQualityShelflifePrediction2015,
  title = {Quality and Shelf-Life Prediction for Retail Fresh Hake ({{Merluccius}} Merluccius)},
  author = {Garc{\'i}a, M{\'i}riam R. and Vilas, Carlos and Herrera, Juan R. and Bern{\'a}rdez, Marta and {Balsa-Canto}, Eva and Alonso, Antonio A.},
  year = {2015},
  journal = {International Journal of Food Microbiology},
  volume = {208},
  pages = {65--74},
  issn = {0168-1605},
  doi = {10.1016/j.ijfoodmicro.2015.05.012},
  abstract = {Fish quality has a direct impact on market price and its accurate assessment and prediction are of main importance to set prices, increase competitiveness, resolve conflicts of interest and prevent food wastage due to conservative product shelf-life estimations. In this work we present a general methodology to derive predictive models of fish freshness under different storage conditions. The approach makes use of the theory of optimal experimental design, to maximize data information and in this way reduce the number of experiments. The resulting growth model for specific spoilage microorganisms in hake (Merluccius merluccius) is sufficiently informative to estimate quality sensory indexes under time-varying temperature profiles. In addition it incorporates quantitative information of the uncertainty induced by fish variability. The model has been employed to test the effect of factors such as fishing gear or evisceration, on fish spoilage and therefore fish quality. Results show no significant differences in terms of microbial growth between hake fished by long-line or bottom-set nets, within the implicit uncertainty of the model. Similar conclusions can be drawn for gutted and un-gutted hake along the experiment horizon. In addition, whenever there is the possibility to carry out the necessary experiments, this approach is sufficiently general to be used in other fish species and under different stress variables.},
  keywords = {Core predictions,Fish shelf-life,Optimal experimental design,Predictive microbiology,Quality Index Method,Uncertainty analysis,Variability analysis}
}

@article{kreutzSystemsBiology2009,
  title = {Systems Biology: Experimental Design.},
  author = {Kreutz, Clemens and Timmer, Jens},
  year = {2009},
  month = feb,
  journal = {The FEBS journal},
  volume = {276},
  number = {4},
  pages = {923--942},
  doi = {10.1111/j.1742-4658.2008.06843.x},
  abstract = {Experimental design has a long tradition in statistics, engineering and life sciences, dating back to the beginning of the last century when optimal designs for industrial and agricultural trials were considered. In cell biology, the use of mathematical modeling approaches raises new demands on experimental planning. A maximum informative investigation of the dynamic behavior of cellular systems is achieved by an optimal combination of stimulations and observations over time. In this minireview, the existing approaches concerning this optimization for parameter estimation and model discrimination are summarized. Furthermore, the relevant classical aspects of experimental design, such as randomization, replication and confounding, are reviewed.},
  langid = {english},
  pmid = {19215298}
}

@article{logistRobustMultiobjectiveOptimal2011,
  title = {Robust Multi-Objective Optimal Control of Uncertain (Bio)Chemical Processes},
  author = {Logist, Filip and Houska, Boris and Diehl, Moritz and Impe, Jan F. Van},
  year = {2011},
  journal = {Chemical Engineering Science},
  volume = {66},
  number = {20},
  pages = {4670--4682},
  issn = {0009-2509},
  doi = {10.1016/j.ces.2011.06.018},
  abstract = {Dynamic optimization or optimal control problems are omnipresent in the (bio)chemical industry. In addition, these problems often involve multiple and conflicting objectives, leading to a so-called set of Pareto optimal solutions, instead of one single optimum. Alternatively, robustness of the obtained solutions with respect to model uncertainties, e.g., guaranteeing that critical constraints are not violated, is of the highest importance in process industry. Moreover, robustness can also be interpreted as an additional and conflicting objective, since more robust solutions typically induce a performance decrease. The current manuscript exploits advanced deterministic techniques to efficiently and accurately generate Pareto sets in the presence of model uncertainty. The developed procedures allow the presentation of robust Pareto sets, i.e., Pareto sets in which robustness is an additional objective. Based on these Pareto sets, all trade-offs can clearly be assessed by the decision maker. Two illustrative case studies are presented for the optimal design and operation of a jacketed tubular reactor with conflicting conversion and energy objectives and a fed-batch bioreactor with conflicting productivity and yield aims.},
  keywords = {(Bio)chemical reactors,Dynamic optimization,Multi-objective optimization,Optimal control,Robust optimization,Uncertainty}
}

@book{perez-rodriguezPredictiveMicrobiologyFoods2012,
  title = {Predictive {{Microbiology}} in {{Foods}}},
  author = {{Perez-Rodriguez}, Fernando and Valero, Antonio},
  year = {2012},
  month = dec,
  publisher = {{Springer Science \& Business Media}},
  address = {{New York, NY}},
  doi = {10.1007/978-1-4614-5520-2},
  abstract = {Predictive microbiology is a recent area within food microbiology, which studies the responses of microorganisms in foods to environmental factors (e.g., temperature, pH) through mathematical functions. These functions enable scientists to predict the behavior of pathogens and spoilage microorganisms under different combinations of factors. The main goal of predictive models in food science is to assure both food safety and food quality. Predictive models in foods have developed significantly in the last 20 years due to the emergence of powerful computational resources and sophisticated statistical packages. This book presents the concepts, models, most significant advances, and future trends in predictive microbiology. It will discuss the history and basic concepts of predictive microbiology. The most frequently used models will be explained, and the most significant software and databases (e.g., Combase, Sym,\"A\^oPrevius) will be reviewed. Quantitative Risk Assessment, which uses predictive modeling to account for the transmission of foodborne pathogens across the food chain, will also be covered. \hspace{0pt}},
  isbn = {1-4614-5520-0},
  langid = {english}
}

@book{rossumPythonLanguageReference2010,
  title = {The {{Python}} Language Reference},
  author = {van Rossum, Guido and Drake, Fred L.},
  year = {2010},
  series = {Python Documentation Manual / {{Guido}} van {{Rossum}}; {{Fred L}}. {{Drake}} [Ed.]},
  edition = {Release 3.0.1 [Repr.]},
  number = {Pt. 2},
  publisher = {{Python Software Foundation}},
  address = {{Hampton, NH}},
  isbn = {978-1-4414-1269-0},
  langid = {english}
}

@article{stamatiOptimalExperimentalDesign2016,
  title = {Optimal Experimental Design for Discriminating between Microbial Growth Models as Function of Suboptimal Temperature: {{From}} in Silico to in Vivo},
  author = {Stamati, I. and Akkermans, S. and Logist, F. and Noriega, E. and Impe, J. Van},
  year = {2016},
  journal = {Food Research International},
  volume = {89},
  pages = {689--700},
  issn = {0963-9969},
  doi = {10.1016/j.foodres.2016.08.001},
  abstract = {Temperature is an important food preservation factor, affecting microbial growth. Secondary predictive models can be used for describing the impact of this factor on microbial growth. In other words, the microbial behavior can be described in a dynamic environment with the use of a primary and secondary model. Two models for describing the effect of temperature on the microbial growth rate are the cardinal temperature model with inflection (CTMI) (Rosso et al., 1993) and its adapted version (aCTMI) (Le Marc et al., 2002). Although Escherichia coli is commonly modeled using CTMI, there are indications that aCTMI may be more appropriate (Van Derlinden and Van Impe, 2012a). For clarifying this, the method of Optimal experiment design for model discrimination (OED/MD) will be used in this work (Donckels et al., 2009; Schwaab et al., 2008). Results from an in silico study point out the required direction. Whereas the results of the in vivo study give a more realistic answer to the research question. Finally, discrimination unravelled the appropriate model for the needed use.},
  keywords = {Dynamic modeling,Model discrimination,Optimal experiment design,Optimization,Predictive microbiology}
}

@article{stornDifferentialEvolutionSimple1997,
  title = {Differential {{Evolution}} \textendash{} {{A Simple}} and {{Efficient Heuristic}} for Global {{Optimization}} over {{Continuous Spaces}}},
  author = {Storn, Rainer and Price, Kenneth},
  year = {1997},
  journal = {Journal of Global Optimization},
  volume = {4},
  number = {11},
  pages = {341--359},
  issn = {0925-5001, 1573-2916},
  doi = {10.1023/A:1008202821328},
  abstract = {{$<$}p{$>$}A new heuristic approach for minimizing possiblynonlinear and non-differentiable continuous spacefunctions is presented. By means of an extensivetestbed it is demonstrated that the new methodconverges faster and with more certainty than manyother acclaimed global optimization methods. The newmethod requires few control variables, is robust, easyto use, and lends itself very well to parallelcomputation.{$<$}/p{$>$}},
  langid = {english}
}

@article{telenOptimalExperimentDesign2012,
  title = {Optimal Experiment Design for Dynamic Bioprocesses: {{A}} Multi-Objective Approach},
  author = {Telen, D. and Logist, F. and Derlinden, E. Van and Tack, I. and Impe, J. Van},
  year = {2012},
  journal = {Chemical Engineering Science},
  volume = {78},
  pages = {82--97},
  issn = {0009-2509},
  doi = {10.1016/j.ces.2012.05.002},
  abstract = {Dynamic process models can be used for operating, controlling and optimising important bioprocesses, e.g., pharmaceuticals production, enzyme production and brewing. After selecting an appropriate process model structure, parameter estimates have to be obtained based on real-life experiments. To reduce the amount of labour and often cost intensive experiments optimal experiment design (OED) is an indispensable tool. In optimal experiment design, dynamic input profiles have to be determined in order to obtain informative experiments. In the particular case of optimal experiment design for parameter estimation, a scalar measure of the Fisher Information Matrix is used as an objective function. Over the years, different criteria have been developed. However, the important question that remains is which criterion to choose. In this work, an approach to tackle the criterion selection is presented. In addition, a multi-objective optimisation approach is implemented, which enables to combine two, often competing optimisation criteria. The developed approach is illustrated with two case studies. The first case study is a fed-batch bioreactor model and the second case study is a Lotka Volterra fishing model.},
  keywords = {Bioprocess,Criterion selection,Dynamic optimisation,Multi-objective optimisation,Optimal experiment design,Parameter estimation}
}

@article{versyckIntroducingOptimal1999,
  ids = {versyckIntroducingOptimal1999a},
  title = {Introducing Optimal Experimental Design in Predictive Modeling: A Motivating Example.},
  author = {Versyck, K J and Bernaerts, K and Geeraerd, A H and Van Impe, J F},
  year = {1999},
  month = oct,
  journal = {International Journal of Food Microbiology},
  volume = {51},
  number = {1},
  pages = {39--51},
  url = {http://eutils.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&id=10563462&retmode=ref&cmd=prlinks},
  abstract = {Predictive microbiology emerges more and more as a rational quantitative framework for predicting and understanding microbial evolution in food products. During the mathematical modeling of microbial growth and/or inactivation, great, but not always efficient, effort is spent on the determination of the model parameters from experimental data. In order to optimize experimental conditions with respect to parameter estimation, experimental design has been extensively studied since the 1980s in the field of bioreactor engineering. The so-called methodology of optimal experimental design established in this research area enabled the reliable estimation of model parameters from data collected in well-designed fed-batch reactor experiments. In this paper, we introduce the optimal experimental design methodology for parameter estimation in the field of predictive microbiology. This study points out that optimal design of dynamic input signals is necessary to maximize the information content contained within the resulting experimental data. It is shown that from few dynamic experiments, more pertinent information can be extracted than from the classical static experiments. By introducing optimal experimental design into the field of predictive microbiology, a new promising frame for maximization of the information content of experimental data with respect to parameter estimation is provided. As a case study, the design of an optimal temperature profile for estimation of the parameters D(ref) and z of an Arrhenius-type model for the maximum inactivation rate kmax as a function of the temperature, T, was considered. Microbial inactivation by heating is described using the model of Geeraerd et al. (1999). The need for dynamic temperature profiles in experiments aimed at the simultaneous estimation of the model parameters from measurements of the microbial population density is clearly illustrated by analytical elaboration of the mathematical expressions involved on the one hand, and by numerical simulations on the other.},
  langid = {english},
  pmid = {10563462},
  keywords = {Dynamic experiments,Optimal experimental design,Parameter estimation,Predictive microbiology,Thermal inactivation}
}

@article{virtanenSciPyFundamentalAlgorithms2020,
  title = {{{SciPy}} 1.0: Fundamental Algorithms for Scientific Computing in {{Python}}},
  shorttitle = {{{SciPy}} 1.0},
  author = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and Bright, Jonathan and {van der Walt}, St{\'e}fan J. and Brett, Matthew and Wilson, Joshua and Millman, K. Jarrod and Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and Kern, Robert and Larson, Eric and Carey, C. J. and Polat, {\.I}lhan and Feng, Yu and Moore, Eric W. and VanderPlas, Jake and Laxalde, Denis and Perktold, Josef and Cimrman, Robert and Henriksen, Ian and Quintero, E. A. and Harris, Charles R. and Archibald, Anne M. and Ribeiro, Ant{\^o}nio H. and Pedregosa, Fabian and {van Mulbregt}, Paul},
  year = {2020},
  month = mar,
  journal = {Nature Methods},
  volume = {17},
  number = {3},
  pages = {261--272},
  publisher = {{Nature Publishing Group}},
  issn = {1548-7105},
  doi = {10.1038/s41592-019-0686-2},
  abstract = {SciPy is an open-source scientific computing library for the Python programming language. Since its initial release in 2001, SciPy has become a de facto standard for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per year. In this work, we provide an overview of the capabilities and development practices of SciPy 1.0 and highlight some recent technical developments.},
  copyright = {2020 The Author(s)},
  langid = {english},
  keywords = {Biophysical chemistry,Computational biology and bioinformatics,Technology}
}

@article{walesGlobalOptimizationBasinHopping1997,
  title = {Global {{Optimization}} by {{Basin-Hopping}} and the {{Lowest Energy Structures}} of {{Lennard-Jones Clusters Containing}} up to 110 {{Atoms}}},
  author = {Wales, David J. and Doye, Jonathan P. K.},
  year = {1997},
  month = jul,
  journal = {The Journal of Physical Chemistry A},
  volume = {101},
  number = {28},
  pages = {5111--5116},
  issn = {1089-5639, 1520-5215},
  doi = {10.1021/jp970984n},
  langid = {english}
}

@article{balsa-canto_amigo2_2016,
	title = {{AMIGO2}, a toolbox for dynamic modeling, optimization and control in systems biology},
	volume = {32},
	issn = {1367-4803},
	url = {https://doi.org/10.1093/bioinformatics/btw411},
	doi = {10.1093/bioinformatics/btw411},
	abstract = {Motivation: Many problems of interest in dynamic modeling and control of biological systems can be posed as non-linear optimization problems subject to algebraic and dynamic constraints. In the context of modeling, this is the case of, e.g. parameter estimation, optimal experimental design and dynamic flux balance analysis. In the context of control, model-based metabolic engineering or drug dose optimization problems can be formulated as (multi-objective) optimal control problems. Finding a solution to those problems is a very challenging task which requires advanced numerical methods. Results: This work presents the AMIGO2 toolbox: the first multiplatform software tool that automatizes the solution of all those problems, offering a suite of state-of-the-art (multi-objective) global optimizers and advanced simulation approaches. Availability and Implementation: The toolbox and its documentation are available at: sites.google.com/site/amigo2toolbox . Contact:  ebalsa@iim.csic.esSupplementary information:  Supplementary data are available at Bioinformatics online.},
	number = {21},
	urldate = {2023-09-21},
	journal = {Bioinformatics},
	author = {Balsa-Canto, Eva and Henriques, David and Gábor, Attila and Banga, Julio R.},
	month = nov,
	year = {2016},
	pages = {3357--3359}
	}

@article{zhang_optimal_2018,
	title = {Optimal experimental design for predator–prey functional response experiments},
	volume = {15},
	url = {https://royalsocietypublishing.org/doi/full/10.1098/rsif.2018.0186},
	doi = {10.1098/rsif.2018.0186},
	abstract = {Functional response models are important in understanding predator–prey interactions. The development of functional response methodology has progressed from mechanistic models to more statistically motivated models that can account for variance and the over-dispersion commonly seen in the datasets collected from functional response experiments. However, little information seems to be available for those wishing to prepare optimal parameter estimation designs for functional response experiments. It is worth noting that optimally designed experiments may require smaller sample sizes to achieve the same statistical outcomes as non-optimally designed experiments. In this paper, we develop a model-based approach to optimal experimental design for functional response experiments in the presence of parameter uncertainty (also known as a robust optimal design approach). Further, we develop and compare new utility functions which better focus on the statistical efficiency of the designs; these utilities are generally applicable for robust optimal design in other applications (not just in functional response). The methods are illustrated using a beta-binomial functional response model for two published datasets: an experiment involving the freshwater predator Notonecta glauca (an aquatic insect) preying on Asellus aquaticus (a small crustacean), and another experiment involving a ladybird beetle (Propylea quatuordecimpunctata L.) preying on the black bean aphid (Aphis fabae Scopoli). As a by-product, we also derive necessary quantities to perform optimal design for beta-binomial regression models, which may be useful in other applications.},
	number = {144},
	urldate = {2023-09-21},
	journal = {Journal of The Royal Society Interface},
	author = {Zhang, Jeff F. and Papanikolaou, Nikos E. and Kypraios, Theodore and Drovandi, Christopher C.},
	month = jul,
	year = {2018},
	note = {Publisher: Royal Society},
	keywords = {D-optimality, exchange algorithm, Fisher information, functional response, optimal design, robust design},
	pages = {20180186}
  }

@article{busetto_near-optimal_2013,
	title = {Near-optimal experimental design for model selection in systems biology},
	volume = {29},
	issn = {1367-4803},
	url = {https://doi.org/10.1093/bioinformatics/btt436},
	doi = {10.1093/bioinformatics/btt436},
	abstract = {Motivation: Biological systems are understood through iterations of modeling and experimentation. Not all experiments, however, are equally valuable for predictive modeling. This study introduces an efficient method for experimental design aimed at selecting dynamical models from data. Motivated by biological applications, the method enables the design of crucial experiments: it determines a highly informative selection of measurement readouts and time points.Results: We demonstrate formal guarantees of design efficiency on the basis of previous results. By reducing our task to the setting of graphical models, we prove that the method finds a near-optimal design selection with a polynomial number of evaluations. Moreover, the method exhibits the best polynomial-complexity constant approximation factor, unless P = NP. We measure the performance of the method in comparison with established alternatives, such as ensemble non-centrality, on example models of different complexity. Efficient design accelerates the loop between modeling and experimentation: it enables the inference of complex mechanisms, such as those controlling central metabolic operation.Availability: Toolbox ‘NearOED’ available with source code under GPL on the Machine Learning Open Source Software Web site (mloss.org).Contact: busettoa@inf.ethz.chSupplementary information: Supplementary data are available at Bioinformatics online.},
	number = {20},
	urldate = {2023-09-21},
	journal = {Bioinformatics},
	author = {Busetto, Alberto Giovanni and Hauser, Alain and Krummenacher, Gabriel and Sunnåker, Mikael and Dimopoulos, Sotiris and Ong, Cheng Soon and Stelling, Jörg and Buhmann, Joachim M.},
	month = oct,
	year = {2013},
	pages = {2625--2632}
  }

@article{ratkowsky_relationship_1982,
	title = {Relationship between temperature and growth rate of bacterial cultures},
	volume = {149},
	url = {https://journals.asm.org/doi/abs/10.1128/jb.149.1.1-5.1982},
	doi = {10.1128/jb.149.1.1-5.1982},
	abstract = {The Arrhenius Law, which was originally proposed to describe the temperature dependence of the specific reaction rate constant in chemical reactions, does not adequately describe the effect of temperature on bacterial growth. Microbiologists have attempted to apply a modified version of this law to bacterial growth by replacing the reaction rate constant by the growth rate constant, but the modified law relationship fits data poorly, as graphs of the logarithm of the growth rate constant against reciprocal absolute temperature result in curves rather than straight lines. Instead, a linear relationship between in square root of growth rate constant (r) and temperature (T), namely, square root = b (T - T0), where b is the regression coefficient and T0 is a hypothetical temperature which is an intrinsic property of the organism, is proposed and found to apply to the growth of a wide range of bacteria. The relationship is also applicable to nucleotide breakdown and to the growth of yeast and molds.},
	number = {1},
	urldate = {2023-09-22},
	journal = {Journal of Bacteriology},
	author = {Ratkowsky, D A and Olley, J and McMeekin, T A and Ball, A},
	month = jan,
	year = {1982},
	note = {Publisher: American Society for Microbiology},
	pages = {1--5}
  }

@article{cintron-arias_sensitivity_2009,
	title = {A sensitivity matrix based methodology for inverse problem formulation},
	volume = {17},
	copyright = {De Gruyter expressly reserves the right to use all content for commercial text and data mining within the meaning of Section 44b of the German Copyright Act.},
	issn = {1569-3945},
	url = {https://www.degruyter.com/document/doi/10.1515/JIIP.2009.034/html},
	doi = {10.1515/JIIP.2009.034},
	abstract = {We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects in a score for a vector parameter defined using the norm of the vector of standard errors for components of estimates divided by the estimates. In some cases the method leads to reduction of the standard error for a parameter to less than 1\% of the estimate.},
	language = {en},
	number = {6},
	urldate = {2023-10-04},
	author = {Cintrón-Arias, A. and Banks, H. T. and Capaldi, A. and Lloyd, A. L.},
	month = aug,
	year = {2009},
	note = {Publisher: De Gruyter Section: Journal of Inverse and Ill-posed Problems},
	keywords = {Fisher Information matrix, Inverse problems, ordinary least squares, parameter selection, sensitivity matrix, standard errors},
	pages = {545--564}
	}


@article{balsa-cantoComputationalProcedures2008,
	title = {Computational procedures for optimal experimental design in biological systems},
	volume = {2},
	url = {https://digital-library.theiet.org/content/journals/10.1049/iet-syb_20070069},
	doi = {10.1049/iet-syb:20070069},
	language = {English},
	number = {4},
	journal = {IET systems biology},
	author = {Balsa-Canto, E and Banga, J R and Alonso, A A},
	month = jul,
	year = {2008},
	pages = {163--172}
  }

@article{banks_generalized_2010,
	title = {Generalized sensitivities and optimal experimental design},
	volume = {18},
	copyright = {De Gruyter expressly reserves the right to use all content for commercial text and data mining within the meaning of Section 44b of the German Copyright Act.},
	issn = {1569-3945},
	url = {https://www.degruyter.com/document/doi/10.1515/jiip.2010.002/html},
	doi = {10.1515/jiip.2010.002},
	abstract = {We consider the problem of estimating amodeling parameter θ using a weighted least squares criterion for given data y by introducing an abstract framework involving generalized measurement procedures characterized by probability measures. We take an optimal design perspective, the general premise (illustrated via examples) being that in any data collected, the information content with respect to estimating θ may vary considerably from one time measurement to another, and in this regard some measurements may be much more informative than others. We propose mathematical tools which can be used to collect data in an almost optimal way, by specifying the duration and distribution of time sampling in the measurements to be taken, consequently improving the accuracy (i.e., reducing the uncertainty in estimates) of the parameters to be estimated. We recall the concepts of traditional and generalized sensitivity functions and use these to develop a strategy to determine the “optimal” final time T for an experiment; this is based on the time evolution of the sensitivity functions and of the condition number of the Fisher information matrix. We illustrate the role of the sensitivity functions as tools in optimal design of experiments, in particular in finding “best” sampling distributions. Numerical examples are presented throughout to motivate and illustrate the ideas.},
	language = {en},
	number = {1},
	urldate = {2023-09-22},
	author = {Banks, H. T. and Dediu, Sava and Ernstberger, Stacey L. and Kappel, Franz},
	month = apr,
	year = {2010},
	note = {Publisher: De Gruyter 
  Section: Journal of Inverse and Ill-posed Problems},
	keywords = {design of experiments, Fisher information matrix, Least squares inverse problems, sensitivity and generalized sensitivity functions},
	pages = {25--83}
}

@article{guillaume_introductory_2019,
	title = {Introductory overview of identifiability analysis: {A} guide to evaluating whether you have the right type of data for your modeling purpose},
	volume = {119},
	issn = {1364-8152},
	shorttitle = {Introductory overview of identifiability analysis},
	url = {http://www.sciencedirect.com/science/article/pii/S1364815218307278},
	doi = {10.1016/j.envsoft.2019.07.007},
	abstract = {Identifiability is a fundamental concept in parameter estimation, and therefore key to the large majority of environmental modeling applications. Parameter identifiability analysis assesses whether it is theoretically possible to estimate unique parameter values from data, given the quantities measured, conditions present in the forcing data, model structure (and objective function), and properties of errors in the model and observations. In other words, it tackles the problem of whether the right type of data is available to estimate the desired parameter values. Identifiability analysis is therefore an essential technique that should be adopted more routinely in practice, alongside complementary methods such as uncertainty analysis and evaluation of model performance. This article provides an introductory overview to the topic. We recommend that any modeling study should document whether a model is non-identifiable, the source of potential non-identifiability, and how this affects intended project outcomes.},
	language = {en},
	urldate = {2020-03-09},
	journal = {Environmental Modelling \& Software},
	author = {Guillaume, Joseph H. A. and Jakeman, John D. and Marsili-Libelli, Stefano and Asher, Michael and Brunner, Philip and Croke, Barry and Hill, Mary C. and Jakeman, Anthony J. and Keesman, Karel J. and Razavi, Saman and Stigter, Johannes D.},
	month = sep,
	year = {2019},
	keywords = {Derivative based methods, Emulation, Hessian, Identifiability, Non-uniqueness, Response surface, Uncertainty},
	pages = {418--432}
  }

@article{wieland_structural_2021,
	title = {On structural and practical identifiability},
	volume = {25},
	issn = {2452-3100},
	url = {https://www.sciencedirect.com/science/article/pii/S245231002100007X},
	doi = {10.1016/j.coisb.2021.03.005},
	abstract = {We discuss issues of structural and practical identifiability of partially observed differential equations, which are often applied in systems biology. The development of mathematical methods to investigate structural nonidentifiability has a long tradition. Computationally efficient methods to detect and cure it have been developed recently. Practical nonidentifiability, on the other hand, has not been investigated at the same conceptually clear level. We argue that practical identifiability is more challenging than structural identifiability when it comes to modeling experimental data. We discuss that the classical approach based on the Fisher information matrix has severe shortcomings. As an alternative, we propose using the profile likelihood, which is a powerful approach to detect and resolve practical nonidentifiability.},
	urldate = {2023-09-22},
	journal = {Current Opinion in Systems Biology},
	author = {Wieland, Franz-Georg and Hauber, Adrian L. and Rosenblatt, Marcus and Tönsing, Christian and Timmer, Jens},
	month = mar,
	year = {2021},
	keywords = {Experimental design, Fisher information matrix, Identifiability, Model reduction, Nonlinear dynamics, Observability, ODE models, Practical identifiability, Profile likelihood, Structural identifiability},
	pages = {60--69}
  }

  @article{stigter_fast_2015,
	title = {A fast algorithm to assess local structural identifiability},
	volume = {58},
	issn = {0005-1098},
	url = {https://www.sciencedirect.com/science/article/pii/S0005109815001946},
	doi = {10.1016/j.automatica.2015.05.004},
	abstract = {The paper presents a novel method for assessing the local structural identifiability question for a general non-linear state-space model. The method is a combination of (i) the application of a singular value decomposition to a parametric output sensitivity matrix that is created by simply integrating the model once and, (ii) a symbolic computation for a reduced model that is guided by the SVD results and allows a confirmation of the conclusions regarding identifiability obtained in the first step. In case there is a lack of identifiability, the symbolic computation quickly results in determination of the exact structure of the nullspace and a suitable re-parametrisation. The method is discussed in detail and applied to three case studies, of which the last two are considerably large, containing 22 and 43 parameters to be identified, respectively.},
	urldate = {2023-09-22},
	journal = {Automatica},
	author = {Stigter, Johannes D. and Molenaar, Jaap},
	month = aug,
	year = {2015},
	keywords = {Identifiability, Parameter identification},
	pages = {118--124}
  }

@article{miao_identifiability_2011,
	title = {On {Identifiability} of {Nonlinear} {ODE} {Models} and {Applications} in {Viral} {Dynamics}},
	volume = {53},
	issn = {0036-1445},
	url = {https://epubs.siam.org/doi/10.1137/090757009},
	doi = {10.1137/090757009},
	abstract = {This erratum corrects an error in the coefficients of equation (6.23) in the original paper [H. Miao, X. Xia, A. S. Perelson, and H. Wu, SIAM Rev., 53 (2011), pp. 3--39].},
	number = {1},
	urldate = {2023-09-22},
	journal = {SIAM Rev.},
	author = {Miao, Hongyu and Xia, Xiaohua and Perelson, Alan S. and Wu, Hulin},
	month = jan,
	year = {2011},
	note = {Publisher: Society for Industrial and Applied Mathematics},
	pages = {3--39}
  }

@article{walter_identifiability_1996,
	series = {Mathematical {Modelling} and {Simulation} in {Agriculture} and {Bio}-{Industries} {Proceedings} of the 1st {IMACS}-{IFAC} {Symposium} {M}\{su2\}{SABI}},
	title = {On the identifiability and distinguishability of nonlinear parametric models},
	volume = {42},
	issn = {0378-4754},
	url = {https://www.sciencedirect.com/science/article/pii/0378475495001239},
	doi = {10.1016/0378-4754(95)00123-9},
	abstract = {Testing parametric models for identifiability and distinguishability is important when the parameters to be estimated have a physical meaning or when the model is to be used to reconstruct physically meaningful state variables that cannot be measured directly. Examples are used to explain why and indicate briefly how, with special emphasis on nonlinear models.},
	number = {2},
	urldate = {2023-09-22},
	journal = {Mathematics and Computers in Simulation},
	author = {Walter, Eric and Pronzato, Luc},
	month = oct,
	year = {1996},
	pages = {125--134}
  }

@article{holmberg_practical_1982,
	title = {On the practical identifiability of microbial growth models incorporating {Michaelis}-{Menten} type nonlinearities},
	volume = {62},
	issn = {0025-5564},
	url = {https://www.sciencedirect.com/science/article/pii/002555648290061X},
	doi = {10.1016/0025-5564(82)90061-X},
	abstract = {The reason for difficulties in obtaining unique estimates of the parameters μm and Ks of the Michaelis-Menten equation are analysed for a microbial batch growth process. With the aid of simulation studies in which the influences of different types of noise on the parameter estimates are compared, it is shown that, although theoretically identifiable in the deterministic case with ideal measurements, the parameters cannot in general be correctly determined from noisy measurements. The difficulties are further illuminated by estimation examples using real data. It certain situations, in which the value of the ratio Ks/so is high or in which only few and noisy measurements are available, the linear approximation of the Michaelis-Menten equation gives a better fit. The practical difficulties in obtaining correct values of the model parameters do not limit the applicability of the Michaelis-Menten model, which in most cases explains the bacterial growth behavior excellently. Rather, they underline the fact that care must be taken when utilizing parameter estimates for biological interpretations.},
	number = {1},
	urldate = {2023-09-22},
	journal = {Mathematical Biosciences},
	author = {Holmberg, Andrea},
	month = nov,
	year = {1982},
	pages = {23--43}
}

@article{kreutzProfileLikelihood2013,
	title = {Profile likelihood in systems biology},
	url = {http://doi.wiley.com/10.1111/febs.12276},
	doi = {10.1111/febs.12276},
	language = {English},
	journal = {The FEBS journal},
	author = {Kreutz, Clemens and Raue, Andreas and Kaschek, Daniel and Timmer, Jens},
	month = may,
	year = {2013}
  }

@article{dette_designing_1997,
	title = {Designing {Experiments} with {Respect} to ‘{Standardized}’ {Optimality} {Criteria}},
	volume = {59},
	copyright = {1997 Royal Statistical Society},
	issn = {1467-9868},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9868.00056},
	doi = {10.1111/1467-9868.00056},
	abstract = {We introduce a new class of `standardized' optimality criteria which depend on `standardized' covariances of the least squares estimators and provide an alternative to the commonly used criteria in design theory. Besides a nice statistical interpretation the new criteria satisfy an extremely useful invariance property which allows an easy calculation of optimal designs on many linearly transformed design spaces.},
	language = {en},
	number = {1},
	urldate = {2023-09-25},
	journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
	author = {Dette, Holger},
	year = {1997},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/1467-9868.00056},
	keywords = {A-optimality, Bonferroni t-intervals, D-optimality, Elfving's minimax criterion, ellipsoid of concentration, invariance, scaling of design space, standardized optimality criteria},
	pages = {97--110}
  }

@article{walter_qualitative_1990,
	title = {Qualitative and quantitative experiment design for phenomenological models—{A} survey},
	volume = {26},
	issn = {0005-1098},
	url = {https://www.sciencedirect.com/science/article/pii/000510989090116Y},
	doi = {10.1016/0005-1098(90)90116-Y},
	abstract = {Designing an experiment for parameter estimation involves two steps. The first one is qualitative, and consists of selecting a suitable configuration of the input/output ports so as to make, if possible, all the parameters of interest identifiable. The second step is quantitative, and based on the optimization of a suitable criterion (with respect to the input shapes, sampling schedule,…) so as to get the maximum information from the data to be collected. When the model is nonlinear in the parameters, the typical situation for phenomenological models, both steps present specific difficulties which are discussed in this paper. The practical importance of qualitative experiment design is illustrated by a very simple biological model. Various policies presented in the literature for quantitative experiment design are reviewed. Special emphasis is given to methods allowing uncertainty on the prior information to be taken into account.},
	number = {2},
	urldate = {2023-09-25},
	journal = {Automatica},
	author = {Walter, E. and Pronzato, L.},
	month = mar,
	year = {1990},
	keywords = {experiment design (not in the standard list), identifiability, Identification, modeling, parameter estimation},
	pages = {195--213}
  }

@article{espie_optimal_1989,
	title = {The optimal design of dynamic experiments},
	volume = {35},
	copyright = {Copyright © 1989 American Institute of Chemical Engineers},
	issn = {1547-5905},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/aic.690350206},
	doi = {10.1002/aic.690350206},
	abstract = {A robust and efficient algorithm is developed to calculate dynamic inputs for optimal experimental designs. Different objective functions are presented to allow designs for both model discrimination and the improvement of parameter precision. Time-varying inputs are calculated by reformulating the optimal design problem as an optimal control problem. This approach can provide large improvements in the ability to discriminate among a series of models, and then increase the accuracy of the resulting parameters.},
	language = {en},
	number = {2},
	urldate = {2023-09-25},
	journal = {AIChE Journal},
	author = {Espie, D. and Macchietto, S.},
	year = {1989},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/aic.690350206},
	pages = {223--229}
  }


@article{banga_dynamic_2005,
	title = {Dynamic optimization of bioprocesses: {Efficient} and robust numerical strategies},
	volume = {117},
	issn = {0168-1656},
	shorttitle = {Dynamic optimization of bioprocesses},
	url = {https://www.sciencedirect.com/science/article/pii/S0168165605001355},
	doi = {10.1016/j.jbiotec.2005.02.013},
	abstract = {The dynamic optimization (open loop optimal control) of non-linear bioprocesses is considered in this contribution. These processes can be described by sets of non-linear differential and algebraic equations (DAEs), usually subject to constraints in the state and control variables. A review of the available solution techniques for this class of problems is presented, highlighting the numerical difficulties arising from the non-linear, constrained and often discontinuous nature of these systems. In order to surmount these difficulties, we present several alternative stochastic and hybrid techniques based on the control vector parameterization (CVP) approach. The CVP approach is a direct method which transforms the original problem into a non-linear programming (NLP) problem, which must be solved by a suitable (efficient and robust) solver. In particular, a hybrid technique uses a first global optimization phase followed by a fast second phase based on a local deterministic method, so it can handle the nonconvexity of many of these NLPs. The efficiency and robustness of these techniques is illustrated by solving several challenging case studies regarding the optimal control of fed-batch bioreactors and other bioprocesses. In order to fairly evaluate their advantages, a careful and critical comparison with several other direct approaches is provided. The results indicate that the two-phase hybrid approach presents the best compromise between robustness and efficiency.},
	number = {4},
	urldate = {2023-09-25},
	journal = {Journal of Biotechnology},
	author = {Banga, Julio R. and Balsa-Canto, Eva and Moles, Carmen G. and Alonso, Antonio A.},
	month = jun,
	year = {2005},
	keywords = {Dynamic optimization, Global optimization, Non-linear bioprocesses, Optimal control},
	pages = {407--419}
  }

@incollection{banga_global_1996,
	address = {Boston, MA},
	series = {Nonconvex {Optimization} and {Its} {Applications}},
	title = {Global {Optimization} of {Chemical} {Processes} using {Stochastic} {Algorithms}},
	isbn = {978-1-4613-3437-8},
	url = {https://doi.org/10.1007/978-1-4613-3437-8_33},
	abstract = {Many systems in chemical engineering are difficult to optimize using gradient-based algorithms. These include process models with multimodal objective functions and discontinuities. Herein, a stochastic algorithm is applied for the optimal design of a fermentation process, to determine multiphase equilibria, for the optimal control of a penicillin reactor, for the optimal control of a non-differentiable system, and for the optimization of a catalyst blend in a tubular reactor. The advantages of the algorithm for the efficient and reliable location of global optima are examined. The properties of these algorithms, as applied to chemical processes, are considered, with emphasis on the ease of handling constraints and the ease of implementation and interpretation of results. For the five processes, the efficiency of computation is improved compared with selected stochastic and deterministic algorithms. Results closer to the global optimum are reported for the optimal control of the penicillin reactor and the non-differentiable system.},
	language = {en},
	urldate = {2023-09-25},
	booktitle = {State of the {Art} in {Global} {Optimization}: {Computational} {Methods} and {Applications}},
	publisher = {Springer US},
	author = {Banga, Julio R. and Seider, Warren D.},
	editor = {Floudas, C. A. and Pardalos, P. M.},
	year = {1996},
	doi = {10.1007/978-1-4613-3437-8_33},
	keywords = {Global Optimum, Simulated Annealing, Stochastic Algorithm, Success Ratio, Tubular Reactor},
	pages = {563--583}
  }

@article{esposito_global_2000,
	title = {Global {Optimization} for the {Parameter} {Estimation} of {Differential}-{Algebraic} {Systems}},
	volume = {39},
	issn = {0888-5885},
	url = {https://doi.org/10.1021/ie990486w},
	doi = {10.1021/ie990486w},
	abstract = {The estimation of parameters in semiempirical models is essential in numerous areas of engineering and applied science. In many cases these models are represented by a set of nonlinear differential-algebraic equations. This introduces difficulties from both a numerical and an optimization perspective. One such difficulty, which has not been adequately addressed, is the existence of multiple local minima. In this paper, two novel global optimization methods will be presented which offer a theoretical guarantee of convergence to the global minimum for a wide range of problems. The first is based on converting the dynamic system of equations into a set of algebraic constraints through the use of collocation methods. The reformulated problem has interesting mathematical properties which allow for the development of a deterministic branch and bound global optimization approach. The second method is based on the use of integration to solve the dynamic system of equations. Both methods will be applied to the problem of estimating parameters in differential-algebraic models through the error-in-variables approach. The mathematical properties of the formulation which lead to specialization of the algorithms will be discussed. Then, the computational aspects of both approaches will be presented and compared through their application to several problems involving reaction kinetics.},
	number = {5},
	urldate = {2023-09-25},
	journal = {Ind. Eng. Chem. Res.},
	author = {Esposito, William R. and Floudas, Christodoulos A.},
	month = may,
	year = {2000},
	note = {Publisher: American Chemical Society},
	pages = {1291--1310}
}

@article{ali_numerical_1997,
	title = {A {Numerical} {Comparison} of {Some} {Modified} {Controlled} {Random} {Search} {Algorithms}},
	volume = {11},
	issn = {1573-2916},
	url = {https://doi.org/10.1023/A:1008236920512},
	doi = {10.1023/A:1008236920512},
	abstract = {In this paper we propose a new version of the Controlled Random Search(CRS) algorithm of Price. The new algorithmhas been tested on thirteen global optimization test problems. Numericalexperiments indicate that the resulting algorithm performs considerablybetter than the earlier versions of the CRS algorithms. The algorithm,therefore, could offer a reasonable alternative to many currently availablestochastic algorithms, especially for problems requiring ’direct search‘type methods. Also a classification of the CRS algorithms is made based on’global technique‘ – ’local technique‘ and the relative performance ofclasses is numerically explored.},
	language = {en},
	number = {4},
	urldate = {2023-09-25},
	journal = {Journal of Global Optimization},
	author = {Ali, M. M. and Törn, A. and Viitanen, S.},
	month = dec,
	year = {1997},
	keywords = {controlled random search, Global optimization, β-distribution},
	pages = {377--385}
}

@article{runarsson_stochastic_2000,
	title = {Stochastic ranking for constrained evolutionary optimization},
	volume = {4},
	issn = {1941-0026},
	url = {https://ieeexplore.ieee.org/abstract/document/873238},
	doi = {10.1109/4235.873238},
	abstract = {Penalty functions are often used in constrained optimization. However, it is very difficult to strike the right balance between objective and penalty functions. This paper introduces a novel approach to balance objective and penalty functions stochastically, i.e., stochastic ranking, and presents a new view on penalty function methods in terms of the dominance of penalty and objective functions. Some of the pitfalls of naive penalty methods are discussed in these terms. The new ranking method is tested using a (/spl mu/, /spl lambda/) evolution strategy on 13 benchmark problems. Our results show that suitable ranking alone (i.e., selection), without the introduction of complicated and specialized variation operators, is capable of improving the search performance significantly.},
	number = {3},
	urldate = {2023-09-25},
	journal = {IEEE Transactions on Evolutionary Computation},
	author = {Runarsson, T.P. and Yao, Xin},
	month = sep,
	year = {2000},
	note = {Conference Name: IEEE Transactions on Evolutionary Computation},
	pages = {284--294}
}

@article{babu_differential_2007,
	title = {Differential evolution strategies for optimal design of shell-and-tube heat exchangers},
	volume = {62},
	issn = {0009-2509},
	url = {https://www.sciencedirect.com/science/article/pii/S0009250907003089},
	doi = {10.1016/j.ces.2007.03.039},
	abstract = {Differential evolution (DE) and its various strategies are applied for the optimal design of shell-and-tube heat exchangers in this study. The main objective in any heat exchanger design is the estimation of the minimum heat transfer area required for a given heat duty, as it governs the overall cost of the heat exchanger. Lakhs of configurations are possible with various design variables such as outer diameter, pitch, and length of the tubes, tube passes, baffle spacing, baffle cut, etc. Hence the design engineer needs an efficient strategy in searching for the global minimum. In the present study for the first time DE, an improved version of genetic algorithms (GAs), has been successfully applied with different strategies for 1,61,280 design configurations using Bell's method to find the heat transfer area. In the application of DE, 9680 combinations of the key parameters are considered. For comparison, GAs are also applied for the same case study with 1080 combinations of its parameters. For this optimal design problem, it is found that DE, an exceptionally simple evolution strategy, is significantly faster compared to GA and yields the global optimum for a wide range of the key parameters.},
	number = {14},
	urldate = {2023-09-25},
	journal = {Chemical Engineering Science},
	author = {Babu, B. V. and Munawar, S. A.},
	month = jul,
	year = {2007},
	keywords = {Bell's method, DE strategies, Differential evolution, Evolutionary computation, Genetic algorithms, Heat exchanger design, Optimization, Shell-and-tube heat exchanger},
	pages = {3720--3739}
  }

@inproceedings{Zielinski_DE,
  author = {K. Zielinski and P. Weitkemper and R. Laur and K.-D. Kammeyer, K. Zielinski, R. Laur},
  year = {2006},
  month = {May},
  title = {Examination of Stopping Criteria for Differential Evolution based on a Power Allocation Problem},
  address={Brasov, Romania},
  abstract={Usually the primary goal for the application of optimization algorithms is convergence to the global optimum, and the secondary goal is to use the least computational effort. By application of different stopping criteria the achievement of both objectives is influenced: If an optimization run is terminated too early, convergence may not be reached, but on the other hand computational resources may be wasted if the optimization run is stopped late. Because the two criteria that are applied mostly in evolutionary algorithms literature have some drawbacks, several stopping criteria are analyzed in this work, using the Differential Evolution algorithm. In contrast to a prior study a constrained optimization problem is used here. It consists of optimizing the power allocation for a CDMA (Code Division Multiple Access) system that includes a parallel interference cancellation technique.},
  booktitle={10th International Conference on Optimization of Electrical and Electronic Equipment}
}

@article{li_monte_1987,
	title = {Monte {Carlo}-minimization approach to the multiple-minima problem in protein folding.},
	volume = {84},
	url = {https://www.pnas.org/doi/abs/10.1073/pnas.84.19.6611},
	doi = {10.1073/pnas.84.19.6611},
	abstract = {A Monte Carlo-minimization method has been developed to overcome the multiple-minima problem. The Metropolis Monte Carlo sampling, assisted by energy minimization, surmounts intervening barriers in moving through successive discrete local minima in the multidimensional energy surface. The method has located the lowest-energy minimum thus far reported for the brain pentapeptide [Met5]enkephalin in the absence of water. Presumably it is the global minimum-energy structure. This supports the concept that protein folding may be a Markov process. In the presence of water, the molecules appear to exist as an ensemble of different conformations.},
	number = {19},
	urldate = {2023-09-26},
	journal = {Proceedings of the National Academy of Sciences},
	author = {Li, Z and Scheraga, H A},
	month = oct,
	year = {1987},
	note = {Publisher: Proceedings of the National Academy of Sciences},
	pages = {6611--6615}
}

@article{beichl_metropolis_2000,
	title = {The {Metropolis} {Algorithm}},
	volume = {2},
	issn = {1558-366X},
	url = {https://ieeexplore.ieee.org/abstract/document/814660},
	doi = {10.1109/5992.814660},
	abstract = {The Metropolis Algorithm has been the most successful and influential of all the members of the computational species that used to be called the "Monte Carlo method". Today, topics related to this algorithm constitute an entire field of computational science supported by a deep theory and having applications ranging from physical simulations to the foundations of computational complexity. Since the rejection method invention (J. von Neumann), it has been developed extensively and applied in a wide variety of settings. The Metropolis Algorithm can be formulated as an instance of the rejection method used for generating steps in a Markov chain.},
	number = {1},
	urldate = {2023-09-26},
	journal = {Computing in Science \& Engineering},
	author = {Beichl, I. and Sullivan, F.},
	month = jan,
	year = {2000},
	note = {Conference Name: Computing in Science \& Engineering},
	pages = {65--69}
}

@misc{scipybrute,
  author = {{T}he {SciPy} community},
  title = {Documentation scipy.optimize.brute},
  howpublished = {\url{https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.brute.html}},
  note = {Accessed: 26.09.2023}
}

@misc{scipydiffev,
  author = {{T}he {SciPy} community},
  title = {Documentation scipy.optimize.differential{\_}evolution},
  howpublished = {\url{https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.differential\_evolution.html}},
  note = {Accessed: 26.09.2023}
}

@misc{scipybashop,
  author = {{T}he {SciPy} community},
  title = {Documentation scipy.optimize.basinhopping},
  howpublished = {\url{https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.basinhopping.html}},
  note = {Accessed: 26.09.2023}
}

@article{gospavic_mathematical_2008,
	title = {Mathematical modelling for predicting the growth of {Pseudomonas} spp. in poultry under variable temperature conditions},
	volume = {127},
	issn = {0168-1605},
	url = {https://www.sciencedirect.com/science/article/pii/S0168160508004236},
	doi = {10.1016/j.ijfoodmicro.2008.07.022},
	abstract = {A dynamic growth model under variable temperature conditions was implemented and calibrated using raw data for microbial growth of Pseudomonas spp. in poultry under aerobic conditions. The primary model was implemented using measurement data under a set of fixed temperatures. The two primary models used for predicting the growth under constant temperature conditions were: Baranyi and modified Gompertz. For the Baranyi model the maximum specific growth rate and the lag phase at constant environmental conditions are expressed in exact form and it has been shown that in limit case when maximal cells concentration is much higher than the initial concentration the maximum specific growth rate is approximately equal to the specific growth rate. The model parameters are determined in a temperature range of 2–20 °C. As a secondary model the square root model was used for maximum specific growth rate in both models. In both models the main assumption, that the initial physiological state of the inoculum is constant and independent of the environmental parameters, is used, and a free parameter was implemented which was determined by minimizing the mean square error (MSE) relative to the measurement data. Two temperature profiles were used for calibration of the models on the initial conditions of the cells.},
	number = {3},
	urldate = {2023-09-27},
	journal = {International Journal of Food Microbiology},
	author = {Gospavic, Radovan and Kreyenschmidt, Judith and Bruckner, Stefanie and Popov, Viktor and Haque, Nasimul},
	month = oct,
	year = {2008},
	keywords = {Poultry spoilage, Predictive microbiology, Shelf life modelling, spp.},
	pages = {290--297}
}

@article{grijspeerdt_estimating_1999,
	title = {Estimating the parameters of the {Baranyi} model for bacterial growth},
	volume = {16},
	issn = {0740-0020},
	url = {https://www.sciencedirect.com/science/article/pii/S074000209990285X},
	doi = {10.1006/fmic.1999.0285},
	abstract = {The identifiability properties of the Baranyi model for bacterial growth were investigated, both structurally and applied to real-life data. Using the Taylor-series approach, it was formally proven that the model is structurally identifiable, i.e. it is now ascertained that it is certainly possible to give unique values to all parameters of the model, provided the bacterial growth data are of sufficiently good quality. The model also has acceptable practical identifiability properties in the presence of realistic data, which means that the confidence intervals on the parameter values are reasonable. However, there was a relatively high correlation between the maximum specific growth rate μmaxand the suitability indicator h0. An optimal experimental design to improve parameter estimation uncertainty was worked out, using the sampling times of the microbial growth curve as experimental degree of freedom. Using a D-optimal design criterion, it could be shown that the optimal sampling times were concentrated in four time periods (initial, start and end of exponential growth, end of experiment), each providing maximum information on a particular parameter. Because the optimal experimental design requires a priori estimates of the parameters, the propagation of the parameter uncertainty into the experimental design was assessed with a Monte Carlo simulation. In this way, 95\% confidence intervals could be established around the optimal sampling times to be used in the optimal experiment. Based on these intervals, a design was proposed and experimentally validated. The error on the parameter estimates was more than halved, their correlation diminished and the nonlinearity of the result improved.},
	language = {en},
	number = {6},
	urldate = {2022-10-12},
	journal = {Food Microbiology},
	author = {Grijspeerdt, K and Vanrolleghem, P},
	month = dec,
	year = {1999},
	pages = {593--605}
}

@article{wales_global_1997,
	title = {Global {Optimization} by {Basin}-{Hopping} and the {Lowest} {Energy} {Structures} of {Lennard}-{Jones} {Clusters} {Containing} up to 110 {Atoms}},
	volume = {101},
	issn = {1089-5639, 1520-5215},
	url = {https://pubs.acs.org/doi/10.1021/jp970984n},
	doi = {10.1021/jp970984n},
	language = {en},
	number = {28},
	urldate = {2022-11-02},
	journal = {J. Phys. Chem. A},
	author = {Wales, David J. and Doye, Jonathan P. K.},
	month = jul,
	year = {1997},
	pages = {5111--5116},
	file = {Submitted Version:/home/pgaindrik/snap/zotero-snap/common/Zotero/storage/IZRZZBV6/Wales and Doye - 1997 - Global Optimization by Basin-Hopping and the Lowes.pdf:application/pdf},
}