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In this work, we propose a novel methodology to adjust parameters of compartmental epidemiological models. It is based on solving a multi-objective optimization problem that consists in fitting some of the model outputs to real observations. First, according to the available data of the considered epidemic, we define a multi-objective optimization problem where the model parameters are the optimization variables. Then, this problem is solved by considering a particular optimization algorithm called ParWASF-GA (ParallelWeighting Achievement Scalarizing Function Genetic Algorithm). Finally, the decision maker chooses, within the set of possible solutions, the values of parameters that better suit his/her preferences. In order to illustrate the benefit of using our approach, it is applied to estimate the parameters of a deterministic epidemiological model, called Be-CoDiS (Between-Countries Disease Spread), used to forecast the possible spread of human diseases within and between countries. We consider data from different Ebola outbreaks from 2014 up to 2019. In all cases, the proposed methodology helps to obtain reasonable predictions of the epidemic magnitudes with the considered model.

We introduce a novel metaheuristic methodology to improve the initialization of a given deterministic or stochastic optimization algorithm. Our objective is to improve the performance of the considered algorithm, called core optimization algorithm, by reducing its number of cost function evaluations, by increasing its success rate and by boosting the precision of its results. In our approach, the core optimization is considered as a suboptimization problem for a multi-layer line search method. The approach is presented and implemented for various particular core optimization algorithms: Steepest Descent, Heavy-Ball, Genetic Algorithm, Differential Evolution and Controlled Random Search. We validate our methodology by considering a set of low and high dimensional benchmark problems (i.e., problems of dimension between 2 and 1000). The results are compared to those obtained with the core optimization algorithms alone and with two additional global optimization methods (Direct Tabu Search and Continuous Greedy Randomized Adaptive Search). These latter also aim at improving the initial condition for the core algorithms. The numerical results seem to indicate that our approach improves the performances of the core optimization algorithms and allows to generate algorithms more efficient than the other optimization methods studied here. A Matlab optimization package called ”Global Optimization Platform” (GOP), implementing the algorithms presented here, has been developed and can be downloaded at: http://www.mat.ucm.es/momat/software.htm

In this work, we develope a numerical method to solve infinite time differential games in closed-loop equilibria. Differential games are thought to be run in dynamic decissions and competitive situations, such as marketing investments and pricing policies in a company. Closed-loop equilibria allow us to obtain strategies as a function of ourselves and our competitor. We apply our algorithm to a real data set of two competitive firms. We show how our algorithm is able to develop a different price-advertising strategy to get bigger benefits

Climate change is affecting the ecosystem and many of the factors associated with human and animal diseases. In particular, significant changes in insect-borne diseases have been shown. The clearest example is found in Europe regarding the bluetongue virus (BTV), a disease of ruminants transmitted by insects (Culicoides spp.). Traditionally this disease was distributed below the 40th parallel, but since 2006 spread to northern Europe where the situation is now endemic. This spread of BTV has been produced by several factors. First, there is a direct relationship between the increased of temperature and the presence of Culicoides. It is also important to highlight the role of the wind in the movement of insects, and could be a significant mode of transmission of vector-borne diseases (such as bluetongue) from endemic areas to free areas. In Spain, the introduction of Culicoides by the wind has not formally been proved, but many experts and epidemiological data has hypothesized it, especially in the first outbreaks occurred in 2004 in the Iberian Peninsula. The objective of the model described here has been, first, to predict the number of Culicoides introduced by the wind and its potential survival in Spain and, secondly, to assess the impact that a potential increase in temperature could have on the distribution and survival Culicoides in Spain. This model will help to identify locations and time periods at highest risk for mosquitoes introduction and survival, and will help to optimize efforts and better prevent and control future outbreaks of bluetongue in the country.

In this work, we describe a model to simulate the spread of withinand between- farms transmission of Classical swine fever virus (CSFV). It is a spatial hybrid model, based on the combination of a stochastic individual based model for between-farm spread with a Susceptible-Infected model for within- farm spread. An important characteristic of this model is the use, as an input, of the information available in real databases. The aim of this model is to quantify the magnitude, duration and risk zones of potential CSFV epidemics to provide support for the decision making process in future CSFV outbreaks. Model parameters and assumptions are provided and an illustration of the model’s results is performed by using available data from the Spanish region of Segovia. The outputs are also compared with those given by another model.

In this paper, we consider two particular devices used for protein folding. The first one is a microfluidic mixer that perform a folding process by mixing a protein solution with a solvent. We are interested in minimizing its mixing time by choosing suitable shape and flow conditions. The second one is related to food processing and we focus on the modeling and simulation of the temperature evolution inside a high pressure food treatment device. Some of the effects of such treatments is to unfold, and thus inactivate, certain enzymes inside the food sample. The behavior and stability of the proposed model is checked by numerical examples. Furthermore, a simplified version of this model is presented and compared in terms of accuracy and computational time.

Classical swine fever is a viral disease of pigs that causes severe commercial restrictions to the affected areas. The knowledge of its spread patterns and risk factors would help to implement specific measures for controlling future outbreaks. In this article, we introduce a spatial hybrid model, based on the combination of a stochastic individual based model for between-farm spread with a Susceptible-Infected model for within-farm spread, to simulate the spread of this disease in a given region. Then, this model is validated by comparing the results given by numerical experiments considering the Spanish province of Segovia with other studies based on real outbreaks. Finally, a brief sensitivity analysis of the model parameters is performed.

Abordamos el problema inverso que consiste en identificar el coeficiente de intercambio de calor H entre un material y el medio que lo rodea, supuesto que H es función de la temperatura y que sólo se conocen ciertas mediciones experimentales (con posible error) de la misma. La dificultad mayor reside en que el coeficiente que se pretende identificar es una función que depende de la solución de la ecuación de estado. Se presenta un algoritmo numérico desarrollado para resolver este tipo de problemas, el cual mejora el descrito en [1].

In this paper, we first remember the mathematical formulation of an original variance expected compliance model used for structural optimization. It allows to find structures robust for the main load and its perturbations. In the second part, we valid this model on a 3-D benchmark test case and compare the obtained results with those given by a classical expected compliance model.

International audience; In this article, we focus on the design of code division multiple access filters (used in data transmission) composed of a particular optical fiber called sampled fiber Bragg grating (SFBG).More precisely, we consider an inverse problem that consists in determining the effective refractive index profile of an SFBG that produces a given reflected spectrum. In order to solve this problem, we use an original multilayers semi-deterministic global optimization method based on the search of suitable initial conditions for a given optimization algorithm. The results obtained with our optimization algorithms are compared, in term of complexity and final design, with those given by an hybrid genetic algorithm (the method generally considered in the literature for designing SFBGs).

Classical swine fever (CSF) is a highly contagious viral disease of pigs and wild boars that causes severe commercial restrictions to the affected countries. The knowledge of spread patterns and risk factors that are involved in the transmission of CSF would help to implement specific measures and to reduce the disease spread in future outbreaks. In this article, we introduce a new spatial hybrid model developed for the spread of CSF. It is based on the combination of a stochastic individual Based model with a Susceptible-Infected model. The coefficients and parameters of the models are estimated using real data.

In this paper, we envision global optimization as finding, for a given calculation complexity, a suitable initial guess of a considered optimization algorithm. One can imagine that this possibility clearly improve the capacity of existing optimization algorithms, including stochastic ones. This approach is validated on several large dimension nonlinear minimization problems. Results are compared with those obtained by a geneti algorithm

High Pressure (HP) Processing has turned out to be very effective in order to prolong the shelf life of some foods. This paper deals with the modelling and simulation of the effect of the combination of high pressure with thermal treatments on food. The behaviour and stability of this model are checked by various numerical examples. Furthermore, a simplified version of the model is presented and compared with the full model in terms of accuracy and computational time. The models developed provide a useful tool to design suitable industrial equipments and optimize the processes.

This paper is concerned with the numerical solution of multiobjective control problems associated with linear (resp., nonlinear) partial differential equations. More precisely, for such problems, we look for Nash equilibria, which are solutions to noncooperative games. First, we study the continuous case. Then, to compute the solution of the problem, we combine finite-difference methods for the time discretization, finite-element methods for the space discretization, and conjugate gradient algorithms (resp., a suitable algorithm) for the iterative solution of the discrete control problems. Finally, we apply the above methodology to the solution of several tests problems.

En esta memoria se abordan dos problemas relacionados con la teoría de control de ecuaciones en derivadas parciales.en el primer capitulo se estudia la controlabilidad aproximada de ecuaciones parabólicas semilineales y se obtienen tanto resultados de controlabilidad como contraejemplos. En el segundo se analiza la factorización de una ecuación elíptica lineal y se establece un paralelismo con la factorización lu del sistema discretizado correspondiente

El objetivo de esta tesis es el diseño e implementación de un algoritmo numérico para la solución de juegos diferenciales, tanto deterministas como estocásticos, en equilibrios de Nash en bucle cerrado ya horizonte infinito. Estos juegos son de especial relevancia puesto que, en la literatura, suelen ser los más comunes debido a sus amplias aplicaciones. Este algoritmo se denomina RaBVItG (Radial Basis and Value Iteration for Games) dadas las principales características de su diseño. Desde nuestro punto de vista, este algoritmo puede considerarse innovador, puesto que en la literatura no hemos encontrado un competidor que resuelva tanto juegos deterministas como estocásticos. Además, cuenta con un diseño "sin mallado", de tal forma que pueden resolverse juegos con N jugadores, donde N es mucho mayor que 2 (en la literatura suelen plantearse algoritmos para mallados con 2 jugadores). En este trabajo, utilizaremos los artículos [13] (en el caso determinista) y [76] (en el caso estocástico) como dos referencias con las que poder compararnos siempre que sea posible. Los principales resultados se enmarcan, por un lado, en la eficiencia del algoritmo. Comparado, por ejemplo, con [13], RaBVItG presenta menor tiempo de cálculo y menor error, en general, debido a la ventaja que supone no tener que usar un mallado. Otro conjunto de resultados de interés son las aplicaciones del algoritmo a dos casos prácticos de dos áreas de conocimiento: marketing y psicología matemática. Estos dos campos, a su vez, están abriendo líneas futuras de investigación donde poder usar el algoritmo y sus sucesivas mejoras...

Se modeliza el tratamiento a altas presiones de alimentos, haciendo especial énfasis en su simulación computacional, para diseñar metodologías que contribuyan a la optimización de los procesos. Los modelos que se utilizan son complejos y requieren sofisticadas herramientas numéricas para su resolución aproximada. Pero además, en las ecuaciones aparecen parámetros físicos característicos de los materiales que son sensibles a los cambios de presión y temperatura y no suelen ser conocidos para presiones distintas de la atmosférica. En la primera parte se presenta un modelo matemático que permite trabajar con fluidos compresible cuya simulación numérica describe el comportamiento térmico y fluidodinámico de la muestra de alimento, cuando es sometida a un tratamiento a altas presiones. Este modelo se acopla con ecuaciones cinéticas que modelizan la actividad degradante de diversas enzimas; su resolución numérica permite estimar la inactivación de estas enzimas tras el uso de diversos tratamientos. El resto de la memoria está motivada por la mencionada falta de información relativa a los parámetros físicos de este tipo de problemas. Se pretende identificar los valores que, para cada material en concreto, toman esos coeficientes en un rango de temperaturas y presiones dados, partiendo de una cantidad (lo menor posible) de mediciones de la temperatura. Esto nos coloca en el contexto de los problemas inversos, y en él se diseñan algoritmos numéricos mediante los que se consigue identificar dos de estos parámetros: para un modelo simplificado planteado como un problema de valor inicial en dimensión uno, el coeficiente de intercambio de calor, que puede depender de la presión y/o de la temperatura (que es la incógnita de la ecuación diferencial ordinaria); y para un segundo modelo simplificado que se plantea como una ecuación en derivadas parciales con condiciones de contorno mixtas, el coeficiente de conductividad térmica (dependiente de la presión).