Optimisation globale à complexité réduite: Application à divers problèmes industriels

In this paper we introduce two main ideas : We reformulate global optimization problems in term of boundary value problem (BVP). This allow us to introduce new optimization algorithms using what is known to solve BVPs. Indeed, current optimization methods, including non-deterministic ones, are based on discretization of initial value problems for differential equations. On the other hand, we introduce low complexity sensitivity evaluation techniques using incomplete sensitivity concept, reduced complexity models and multi-level discretizations. Sensitivity knowledge permits to distinguish between points of a Pareto front in multi-criteria optimization problems characterizing these points from a robustness point of view

A Multi-Layer Line Search Method to Improve the Initialization of Optimization Algorithms

International audienceWe introduce a novel metaheuristic methodology to improve the initializationof a given deterministic or stochastic optimization algorithm. Our objectiveis to improve the performance of the considered algorithm, calledcore optimization algorithm, by reducing its number of cost function evaluations,by increasing its success rate and by boosting the precision of itsresults. In our approach, the core optimization is considered as a suboptimizationproblem for a multi-layer line search method. The approachis presented and implemented for various particular core optimization algorithms:Steepest Descent, Heavy-Ball, Genetic Algorithm, Differential Evolutionand Controlled Random Search. We validate our methodology byconsidering a set of low and high dimensional benchmark problems (i.e.,problems of dimension between 2 and 1000). The results are compared tothose obtained with the core optimization algorithms alone and with twoadditional global optimization methods (Direct Tabu Search and ContinuousGreedy Randomized Adaptive Search). These latter also aim at improvingthe initial condition for the core algorithms. The numerical results seemto indicate that our approach improves the performances of the core optimizationalgorithms and allows to generate algorithms more efficient thanthe other optimization methods studied here. A Matlab optimization packagecalled ”Global Optimization Platform” (GOP), implementing the algorithmspresented here, has been developed and can be downloaded at:http://www.mat.ucm.es/momat/software.ht

Be-CoDiS: A mathematical model to predict the risk of human diseases spread between countries. Validation and application to the 2014-15 Ebola Virus Disease epidemic

Ebola virus disease is a lethal human and primate disease that currently requires a particular attention from the international health authorities due to important outbreaks in some Western African countries and isolated cases in the United Kingdom, the USA and Spain. Regarding the emergency of this situation, there is a need of development of decision tools, such as mathematical models, to assist the authorities to focus their efforts in important factors to eradicate Ebola. In this work, we propose a novel deterministic spatial-temporal model, called Be-CoDiS (Between-Countries Disease Spread), to study the evolution of human diseases within and between countries. The main interesting characteristics of Be-CoDiS are the consideration of the movement of people between countries, the control measure effects and the use of time dependent coefficients adapted to each country. First, we focus on the mathematical formulation of each component of the model and explain how its parameters and inputs are obtained. Then, in order to validate our approach, we consider two numerical experiments regarding the 2014-15 Ebola epidemic. The first one studies the ability of the model in predicting the EVD evolution between countries starting from the index cases in Guinea in December 2013. The second one consists of forecasting the evolution of the epidemic by using some recent data. The results obtained with Be-CoDiS are compared to real data and other models outputs found in the literature. Finally, a brief parameter sensitivity analysis is done. A free Matlab version of Be-CoDiS is available at: http://www.mat.ucm.es/momat/software.htmComment: 34 pages; Version 5; Work in Progres

A Variance-Expected Compliance Model for Structural Optimization

t The goal of this paper is to find robust structures for a given main load and its perturbations. In the first part, we show the mathematical formulation of an original variance-expected compliance model used for structural optimization. In the second part, we study the interest of this model on two 3D benchmark test cases and compare the obtained results with those given by an expected compliance mode

A Multi-Layer Line Search Method to Improve the Initialization of Optimization Algorithms (Preprint submitted to Optimization Online)

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.ht

Nonlinear Advection-Diffusion-Reaction Phenomena Involved in the Evolution and Pumping of Oil in Open Sea: Modeling, Numerical Simulation and Validation Considering the Prestige and Oleg Naydenov Oil Spill Cases.

The main goal of this article is to improve upon a previous model used to simulate the evolution of oil spots in the open sea and the effect of a skimmer ship pumping oil out from the spots. The concentration of the pollutant is subject to the effects of wind and sea currents, diffusion, and the pumping action of a skimmer (i.e., cleaning) ship that follows a pre-assigned trajectory. This implies that the mathematical model is of the advection-diffusion-reaction type. A drawback of our previous model was that diffusion was propagating with infinite velocity; in this article, we use an improved modeling relying on a nonlinear diffusion term, implying that diffusion propagates with finite velocity. To reduce numerical diffusion when approximating the advection part of the model, we consider second order discretization schemes with nonlinear flux limiters. We consider also absorbing boundary conditions to insure accurate results near the boundary. To reduce CPU time we use an operator-splitting scheme for the time discretization. Finally, we also introduce the modeling of coastlines and dynamic sources of pollutant. The novel approach we advocate in this article is validated by comparing our numerical results with real life measurements from the Oleg Naydenov and the Prestige oil spills, which took place in Spain in 2015 and 2002, respectively

Semi-Deterministic vs. Genetic Algorithms for Global Optimization of Multichannel Optical Filters

A new global optimization algorithm is presented and applied to the design of high-channel-count multichannel filters based on sampled Fiber Bragg Gratings. We focus on the realization of particular designs corresponding to multichannel filters that consist of 16 and 38 totally reflective identical channels spaced 100 GHz. The results are compared with those obtained by a hybrid genetic algorithm and by the classical sinc method

Asymptotic stability of a coupled Advection-Diffusion-Reaction system arising in bioreactor processes.

In this work, we perform an asymptotic analysis of a coupled system of two Advection-Diffusion-Reaction equations with Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacterias), called biomass, and a diluted organic contaminant (e.g., nitrates), called substrate, in a continuous flow bioreactor. This system exhibits, under suitable conditions, two stable equilibrium states: one steady state in which the biomass becomes extinct and no reaction is produced, called washout, and another steady state, which corresponds to the partial elimination of the substrate. We use the method of linearization to give sufficient conditions for the asymptotic stability of the two stable equilibrium configurations. Finally, we compare our asymptotic analysis with the usual asymptotic analysis associated to the continuous bioreactor when it is modeled with ordinary differential equations

Un nouvel algorithme d’optimisation globale est utilisé pour la conception d’un mélangeur microfluidique. Notre objectif est de modifier la forme de ce dispositif afin de réduire le temps de mélange pour le repliement de protéines.

A new semi-deterministic global optimization algorithm is used for the design of a fast-micro-mixer. Our aim is to reduce the mixing time for protein folding by modifying the device shape.Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasTRUEpu