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Metodologia para projeto de biorreatores industriais via otimização multiobjetivo com base em parâmetros de desempenho calculados por técnicas de CFD / Methodology for industrial bioreactor design via multiobjective optimization based on performance parameters calculated by CFD techniquesAnsoni, Jonas Laerte 21 May 2015 (has links)
A crescente demanda por biocombustíveis e a concorrência dos combustíveis fósseis torna necessária a otimização dos meios já existentes e o desenvolvimento de novas tecnologias para produção de biocombustíveis, principalmente em projetos envolvendo biorreatores e fotobiorreatores (FBR) industriais. A dinâmica dos fluidos computacional (CFD) vem sendo utilizada em vários trabalhos para o estudo de parâmetros fluidodinâmicos que podem influenciar no rendimento dos processos químicos envolvidos, como tensão de cisalhamento, perfis de velocidade, tempo de residência e a influência da geometria sobre esses parâmetros. Contudo, não existe ainda um número abrangente de trabalhos que utilize técnicas de otimização acopladas com a resolução numérica do problema fluidodinâmico. Em alguns estudos, algoritmos de otimização são utilizados para determinar os melhores coeficientes das reações químicas. No entanto, não há estudos, até o momento, que reportem a otimização multiobjetivo simultânea dos parâmetros geométricos e do escoamento aplicados a equipamentos da indústria sucro-energética. Neste contexto, o presente trabalho de pesquisa tem como objetivo contribuir para o avanço científico e tecnológico através da implementação de um software aberto (PyCFD-O) que permita o acoplamento CFD-otimização e o desenvolvimento das bases de uma metodologia de projeto otimizado bem como de operação de biorreatores e FBRs de escala industrial. O PyCFD-O foi testado em dois estudos de caso que podem ser estendidos a um fermentador contínuo e um FBR. Os parâmetros geométricos de ambos os reatores foram otimizados de forma a minimizar simultaneamente a tensão de cisalhamento e a variância da distribuição do tempo de residência. O software PyCFD-O mostrou-se robusto, revelando que o processo global de otimização realiza de fato a busca pela fronteira de Pareto. Além da obtenção das geometrias otimizadas, também foram discutidos a influência dos parâmetros geométricos na hidrodinâmica do escoamento em ambos os casos. / The growing demand for biofuels and its competition with fossil fuels create the need to optimize the existing resources and development of new technologies for production of biofuels, particularly in projects involving industrial bioreactors and photobioreactors (PBR). Computational fluid dynamics (CFD) has been used in several studies for the study of fluid dynamics parameters that can influence the performance of the chemical process involved, such as shear stress, velocity profiles, residence time and the influence of these parameters on the reactor geometry. However, there are lacks of studies that utilize optimization techniques coupled with the numerical resolution of the fluid dynamic problem. The use of optimization algorithms has been reported in some cases, but there have not been reports on studies combining the optimization of flow parameters and multiobjective algorithms to choose ideal geometric parameters applied to the equipment of the sugar-energy industry. In this context, this research project aims to contribute to the advancement of scientific and technological knowledge trhough the implementation of open source software (PyCFD-O) for the CFD-optimization coupling and the development of the bases of a methodology for optimal design and operation of industrial scale bioreactors and PBR. The PyCFD-O software was tested in two case studies with characteristics that can be extended to a continuos fermenter and PBR. The geometric parameters of both reactors were simultaneously optimized in order to minimize the shear stress and the variance of residence time distribuition. The PyCFD-O software showed robustness, revealing that overall optimization process actually performs the search of Pareto frontier. In addition to the geometry optimization, the influence of the geometrical parameters of the hydrodynamic of the flow was discussed in both case studies.
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Framework multiobjetivo de ranqueamento e comparação de algoritmos de predição de estrutura terciária de proteínas / Multiobjective framework for ranking and comparion of tertiary protein structure prediction algorithmsMarciano, Michelle Duarte 05 December 2016 (has links)
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Previous issue date: 2016-12-05 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Determining the tertiary structure of a protein is very important, once that this is the
structure that allow us to know the function of a protein on living beings. There are many
algorithms that intend to do this prediction, but none of them does it with one hundred
percent of accuracy, being a case of NP-complete problem. Even sill not being able to predict
the tertiary structure of proteins with total precision, these algorithms are already used in
areas such as pharmacology and are extremely important. This project presents a multiobjective framework for the classification and ranking of these algorithms, thus allowing a
comparison among them. The goal is to help improving researches in the area, either in
individual algorithms or groups of research in the bioinformatics field. / A determinação da estrutura tridimensional de uma proteína é muito importante, uma vez que
esta estrutura é que fornece a função de uma proteína no corpo de seres vivos. Existem
muitos algoritmos que buscam fazer essa predição, mas nenhum deles faz isso com cem por
cento de eficiência, tratando-se de um problema NP-completo. Mesmo ainda não sendo
capazes de predizer com total precisão a estrutura terciária das proteínas, tais algoritmos já
são aproveitados em áreas como a farmacologia e são de grande importãncia. Este projeto
apresenta um framework multi-objetivo para classificação e ranqueamento desses algoritmos,
permitindo assim uma comparação entre eles. O objetivo é ajudar a melhorar as pesquisas na
área, seja em algoritmos isolados ou grupos de pesquisa da área de bioinformática.
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Desenvolvimento de estratégias de otimização contínua e discreta para problemas de fluxo de potência ótimo / Development of continuous and discrete optimization strategies to problems of optimal power flowAna Paula Mazzini 01 April 2016 (has links)
O objetivo do presente trabalho é a investigação e o desenvolvimento de estratégias de otimização contínua e discreta para problemas de Fluxo de Potência Ótimo (FPO), onde existe a necessidade de se considerar as variáveis de controle associadas aos taps de transformadores em-fase e chaveamentos de bancos de capacitores e reatores shunt como variáveis discretas e existe a necessidade da limitação, e/ou até mesmo a minimização do número de ações de controle. Neste trabalho, o problema de FPO será abordado por meio de três estratégias. Na primeira proposta, o problema de FPO é modelado como um problema de Programação Não Linear com Variáveis Contínuas e Discretas (PNLCD) para a minimização de perdas ativas na transmissão; são propostas três abordagens utilizando funções de discretização para o tratamento das variáveis discretas. Na segunda proposta, considera-se que o problema de FPO, com os taps de transformadores discretos e bancos de capacitores e reatores shunts fixos, possui uma limitação no número de ações de controles; variáveis binárias associadas ao número de ações de controles são tratadas por uma função quadrática. Na terceira proposta, o problema de FPO é modelado como um problema de Otimização Multiobjetivo. O método da soma ponderada e o método ε-restrito são utilizados para modificar os problemas multiobjetivos propostos em problemas mono-objetivos. As variáveis binárias associadas às ações de controles são tratadas por duas funções, uma sigmoidal e uma polinomial. Para verificar a eficácia e a robustez dos modelos e algoritmos desenvolvidos serão realizados testes com os sistemas elétricos IEEE de 14, 30, 57, 118 e 300 barras. Todos os algoritmos e modelos foram implementados em General Algebraic Modeling System (GAMS) e os solvers CONOPT, IPOPT, KNITRO e DICOPT foram utilizados na resolução dos problemas. Os resultados obtidos confirmam que as estratégias de discretização são eficientes e as propostas de modelagem para variáveis binárias permitem encontrar soluções factíveis para os problemas envolvendo as ações de controles enquanto os solvers DICOPT e KNITRO utilizados para modelar variáveis binárias não encontram soluções. / The aims of this study are the investigation and the development of continuous and discrete optimization strategies to Optimal Power Flow (OPF) problems, where the control variables are the tap ratios of on-load tap changing (OLTC) transformers and shunt susceptances of switchable capacitors and reactors banks. These controls are discrete variables and a need for the limitation and/or even the minimization of the number of control adjustments is required. In this work, three strategies for solving the OPF problem have been deviced. In the first strategy, the OPF problem is modeled as a nonlinear programming problem with continuous and discrete variables for active power losses minimization; Three approaches using discretization functions for handling discrete variables have been investigated. In the second proposal, the OPF problem with discrete OLTC transformers and continuous shunt susceptances of switchable capacitors and reactors banks has a limitation on the number of control adjustments; binary variables associated with control adjustments are handled by a quadratic function. In the third proposal, the OPF problem is modeled as a multiobjective optimization problem. The weighting method and the ε-constraint method are used to modify the proposed multiobjective problems onto single-objective problems. The binary variables associated with the controls are handled by sigmoidal and polynomial functions. The efficiency and robustness of the models and algorithms are shown for IEEE benchmark test-systems with up to 300 buses. All algorithms and models were implemented in GAMS modeling language and the results are obtained by means of CONOPT, IPOPT, KNITRO and DICOPT solvers. The results confirm that the discretization strategies are efficient and the proposed modeling for binary variables allows finding feasible solutions to problems involving the of controls while DICOPT and KNITRO solvers used to handle binary variables fail to find solutions.
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Optimisation par essaim particulaire : adaptation de tribes à l'optimisation multiobjectif / Particle swarm optimization : adaptation of tribes to the multiobjective optimizationSmairi, Nadia 06 December 2013 (has links)
Dans le cadre de l'optimisation multiobjectif, les métaheuristiques sont reconnues pour être des méthodes performantes mais elles ne rencontrent qu'un succès modéré dans le monde de l'industrie. Dans un milieu où seule la performance compte, l'aspect stochastique des métaheuristiques semble encore être un obstacle difficile à franchir pour les décisionnaires. Il est donc important que les chercheurs de la communauté portent un effort tout particulier sur la facilité de prise en main des algorithmes. Plus les algorithmes seront faciles d'accès pour les utilisateurs novices, plus l'utilisation de ceux-ci pourra se répandre. Parmi les améliorations possibles, la réduction du nombre de paramètres des algorithmes apparaît comme un enjeu majeur. En effet, les métaheuristiques sont fortement dépendantes de leur jeu de paramètres. Dans ce cadre se situe l'apport majeur de TRIBES, un algorithme mono-objectif d'Optimisation par Essaim Particulaire (OEP) qui fonctionne automatiquement,sans paramètres. Il a été mis au point par Maurice Clerc. En fait, le fonctionnement de l'OEP nécessite la manipulation de plusieurs paramètres. De ce fait, TRIBES évite l'effort de les régler (taille de l'essaim, vitesse maximale, facteur d'inertie, etc.).Nous proposons dans cette thèse une adaptation de TRIBES à l'optimisation multiobjectif. L'objectif est d'obtenir un algorithme d'optimisation par essaim particulaire multiobjectif sans paramètres de contrôle. Nous reprenons les principaux mécanismes de TRIBES auxquels sont ajoutés de nouveaux mécanismes destinés à traiter des problèmes multiobjectif. Après les expérimentations, nous avons constaté, que TRIBES-Multiobjectif est moins compétitif par rapport aux algorithmes de référence dans la littérature. Ceci peut être expliqué par la stagnation prématurée de l'essaim. Pour remédier à ces problèmes, nous avons proposé l'hybridation entre TRIBES-Multiobjectif et un algorithme de recherche locale, à savoir le recuit simulé et la recherche tabou. L'idée était d'améliorer la capacité d'exploitation deTRIBES-Multiobjectif. Nos algorithmes ont été finalement appliqués sur des problèmes de dimensionnement des transistors dans les circuits analogiques / Meta-heuristics are recognized to be successful to deal with multiobjective optimization problems but still with limited success in engineering fields. In an environment where only the performance counts, the stochastic aspect of meta-heuristics again seems to be a difficult obstacle to cross for the decision-makers. It is, thus, important that the researchers of the community concern a quite particular effort to ease the handling of those algorithms. The more the algorithms will be easily accessible for the novices, the more the use of these algorithms can spread. Among the possible improvements, reducing the number of parameters is considered as the most challenging one. In fact, the performance of meta-heuristics is strongly dependent on their parameters values. TRIBES presents an attempt to remedy this problem. In fact, it is a particle swarm optimization (PSO) algorithm that works in an autonomous way. It was proposed by Maurice Clerc. Indeed, like every other meta-heuristic, PSO requires many parameters to be fitted every time a new problem is considered. The major contribution of TRIBES is to avoid the effort of fitting them. We propose, in this thesis, an adaptation of TRIBES to the multiobjective optimization. Our aim is to conceive a competitive PSO algorithm free of parameters. We consider the main mechanisms of TRIBES to which are added new mechanisms intended to handle multiobjective problems. After the experimentations, we noticed that Multiobjective-TRIBESis not competitive compared to other multiobjective algorithms representative of the state of art. It can be explained by the premature stagnation of the swarm. To remedy these problems, we proposed the hybridization between Multiobjective-TRIBES and local search algorithms such as simulated annealing and tabu search. The idea behind the hybridization was to improve the capacity of exploitation of Multiobjective-TRIBES. Our algorithms were finally applied to sizing analogical circuits' problems
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位相最適化と形状最適化の統合による多目的構造物の形状設計(均質化法と力法によるアプローチ)井原, 久, Ihara, Hisashi, 下田, 昌利, Shimoda, Masatoshi, 畔上, 秀幸, Azegami, Hideyuki, 桜井, 俊明, Sakurai, Toshiaki 04 1900 (has links)
No description available.
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A New Contribution To Nonlinear Robust Regression And Classification With Mars And Its Applications To Data Mining For Quality Control In ManufacturingYerlikaya, Fatma 01 September 2008 (has links) (PDF)
Multivariate adaptive regression spline (MARS) denotes a modern
methodology from statistical learning which is very important
in both classification and regression, with an increasing number of applications in many areas of science, economy and technology.
MARS is very useful for high dimensional problems and shows a great promise for fitting nonlinear multivariate functions. MARS technique does not impose any particular class of relationship between the predictor variables and outcome variable of interest. In other words, a special advantage of MARS lies in its ability to estimate the contribution of the basis functions so that
both the additive and interaction effects of the predictors are allowed to determine the response variable.
The function fitted by MARS is continuous, whereas the one fitted by classical classification methods (CART) is not. Herewith, MARS becomes an alternative to CART. The MARS algorithm for estimating the model function consists of two complementary algorithms: the forward and backward stepwise algorithms. In the first step, the model is built by adding basis functions until a maximum level of complexity is reached. On the other hand, the backward stepwise algorithm is began by removing the least significant basis functions from the model.
In this study, we propose not to use the backward stepwise algorithm. Instead, we construct a penalized residual sum of squares (PRSS) for MARS as a Tikhonov regularization problem, which is also known as ridge regression. We treat this problem using continuous optimization techniques which we consider to
become an important complementary technology and alternative to the concept of the backward stepwise algorithm. In particular, we apply the elegant framework of conic quadratic programming which is an area of convex optimization that
is very well-structured, herewith, resembling linear programming and, hence, permitting the use of interior point methods. The boundaries of this optimization problem are determined by the multiobjective optimization approach which provides us many
alternative solutions.
Based on these theoretical and algorithmical studies, this MSc thesis work also contains applications on the data investigated in a TÜ / BiTAK project on quality control. By these applications, MARS and our new method are compared.
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Adaptive multiobjective memetic optimization: algorithms and applicationsDang, Hieu January 1900 (has links)
The thesis presents research on multiobjective optimization based on memetic computing and its applications in engineering. We have introduced a framework for adaptive multiobjective memetic optimization algorithms (AMMOA) with an information theoretic criterion for guiding the selection, clustering, and local refinements. A robust stopping criterion for AMMOA has also been introduced to solve non-linear and large-scale optimization problems. The framework has been implemented for different benchmark test problems with remarkable results.
This thesis also presents two applications of these algorithms. First, an optimal image data hiding technique has been formulated as a multiobjective optimization problem with conflicting objectives. In particular, trade-off factors in designing an optimal image data hiding are investigated to maximize the quality of watermarked images and the robustness of watermark. With the fixed size of a logo watermark, there is a conflict between these two objectives, thus a multiobjective optimization problem is introduced. We propose to use a hybrid between general regression neural networks (GRNN) and the adaptive multiobjective memetic optimization algorithm (AMMOA) to solve this challenging problem. This novel image data hiding approach has been implemented for many different test natural images with remarkable robustness and transparency of the embedded logo watermark. We also introduce a perceptual measure based on the relative Rényi information spectrum to evaluate the quality of watermarked images.
The second application is the problem of joint spectrum sensing and power control optimization for a multichannel, multiple-user cognitive radio network. We investigated trade-off factors in designing efficient spectrum sensing techniques to maximize the throughput and minimize the interference. To maximize the throughput of secondary users and minimize the interference to primary users, we propose a joint determination of the sensing and transmission parameters of the secondary users, such as sensing times, decision threshold vectors, and power allocation vectors. There is a conflict between these two objectives, thus a multiobjective optimization problem is used again in the form of AMMOA. This algorithm learns to find optimal spectrum sensing times, decision threshold vectors, and power allocation vectors to maximize the averaged opportunistic throughput and minimize the averaged interference to the cognitive radio network. / February 2016
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Multicast packing problem: abordagem multiobjetivoAndrade, Romerito Campos de 01 February 2013 (has links)
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Previous issue date: 2013-02-01 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This work presents a algorithmic study of Multicast Packing Problem considering a multiobjective
approach. The first step realized was an extensive review about the problem. This
review serverd as a reference point for the definition of the multiobjective mathematical model.
Then, the instances used in the experimentation process were defined, this instances were created
based on the main caracteristics from literature. Since both mathematical model and the
instances were definined, then several algoritms were created. The algorithms were based on
the classical approaches to multiobjective optimization: NSGA2 (3 versions), SPEA2 (3 versions).
In addition, the GRASP procedures were adapted to work with multiples objectives, two
vesions were created. These algorithms were composed by three recombination operators(C1,
C2 e C3), two operator for build solution, a mutation operator and a local search procedure.
Finally, a long experimentation process was performed. This process has three stages: the first
consisted of adjusting the parameters; the second was perfomed to indentify the best version for
each algorithm. After, the best versions for each algorithm were compared in order to identify
the best algorithm among all. The algorithms were evaluated based on quality indicators and
Hypervolume Multiplicative Epsilon / O presente trabalho apresenta um estudo algor?tmico do Multicast Packing Problem levando
em considera??o uma abordagem multiobjetivo. Para tal, faz-se uma extensa revis?o
sobre o problema em quest?o. Esta revis?o serviu como ponto de refer?ncia para defini??o de
um modelo matem?tico multiobjetivo, tendo em vista que n?o h? na literatura nenhum trabalho
que tenha tratado o tema neste aspecto. Em seguida, define-se os casos de teste utilizados no
processo de experimenta??o dos algoritmos. Uma vez que tanto modelo matem?tico multiobjetivo
quanto os casos de teste foram criados, ent?o desenvolve-se v?rios algoritmos com base
nas abordagens cl?ssicas para problemas de otimiza??o multiobjetivo: NSGA2 (3 vers?es) e
SPEA2 (3 vers?es). Al?m disso, adaptou-se a metaheur?stica GRASP (2 vers?es) para aplica??o
considerando o modelo proposto. Estes algoritmos foram compostos por tr?s operadores
de recombina??o (C1, C2, C3), dois operadores de constru??o de solu??o, um operador de
muta??o e um operador de busca local. Por fim, um extenso processo de experimenta??o dos
algoritmos ? realizado. Este processo possui tr?s etapas: a primeira etapa consistiu de ajustar
os par?metros que cada algoritmo necessita, neste caso o ajuste de par?metro foi realizado para
todas as vers?es do SPEA2, NSGA2 e GRASP; A segunda etapa consistiu de verificar, para
cada algoritmo, qual a melhor vers?o. Por fim, as melhores vers?es de cada algoritmo, no total
3 vers?es, foram comparadas entre si visando identificar qual o melhor algoritmo dentre todos.
Os algoritmos foram avaliados com base nos indicadores de qualidade Hypervolume e Epsilon
Multiplicativo. Os resultados dos experimentos foram avaliados atrav?s de testes estat?sticos
n?o-param?tricos (teste de Mann-Whitney e teste de Friedman). A avalia??o dos resultados foi
favor?ravel ao NSGA2-C2 segundo a metodologia de avalia??o utilizada
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Uma meta-heurística para uma classe de problemas de otimização de carteiras de investimentosSilva, Yuri Laio Teixeira Veras 16 February 2017 (has links)
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Previous issue date: 2017-02-16 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / The problem in investment portfolio selection consists in the allocation of resources to
a finite number of assets, aiming, in its classic approach, to overcome a trade-off between
the risk and expected return of the portfolio. This problem is one of the most important
topics targeted at today’s financial and economic issues. Since the pioneering works of
Markowitz, the issue is treated as an optimisation problem with the two aforementioned
objectives. However, in recent years, various restrictions and additional risk measurements
were identified in the literature, such as, for example, cardinality restrictions, minimum
transaction lot and asset pre-selection. This practice aims to bring the issue closer to the
reality encountered in financial markets. In that regard, this paper proposes a metaheuristic
called Particle Swarm for the optimisation of several PSPs, in such a way that allows
the resolution of the problem considering a set of restrictions chosen by the investor. / O problema de seleção de carteiras de investimentos (PSP) consiste na alocação de
recursos a um número finito de ativos, objetivando, em sua abordagem clássica, superar
um trade-off entre o retorno esperado e o risco da carteira. Tal problema ´e uma das
temáticas mais importantes voltadas a questões financeiras e econômicas da atualidade.
Desde os pioneiros trabalhos de Markowitz, o assunto é tratado como um problema de
otimização com esses dois objetivos citados. Entretanto, nos últimos anos, diversas restrições e mensurações de riscos adicionais foram consideradas na literatura, como, por
exemplo, restrições de cardinalidade, de lote mínimo de transação e de pré-seleção de
ativos. Tal prática visa aproximar o problema da realidade encontrada nos mercados
financeiros. Neste contexto, o presente trabalho propõe uma meta-heurística denominada
Adaptive Non-dominated Sorting Multiobjective Particle Swarm Optimization para
a otimização de vários problemas envolvendo PSP, de modo que permita a resolução do
problema considerando um conjunto de restri¸c˜oes escolhidas pelo investidor.
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Optimisation multicritère pour une gestion globale des ressources : application au cycle du cuivre en France / Multicriteria optimization for a global resource management : application to French copper cycleBonnin, Marie 11 December 2013 (has links)
L'amélioration de la gestion des ressources naturelles est nécessaire pour répondre aux nombreux enjeux liés à leur exploitation. Ce travail propose une méthodologie d'optimisation de leur gestion, appliquée au cas du cuivre en France. Quatre critères permettant de juger les stratégies de gestion ont été retenus : le coût, les impacts environnementaux, la consommation énergétique et les pertes de ressources. La première étape de cette méthodologie est l'analyse de la situation actuelle, grâce à une modélisation du cycle français du cuivre de 2000 à 2009. Cet examen a montré que la France importe la quasi-totalité de ses besoins sous forme de cuivre raffiné, et a une industrie de recyclage peu développée. Suite à ces premiers résultats, la problématique du traitement des déchets de cuivre, et notamment de leur recyclage, a été étudiée. Une stratégie de modélisation des flux recyclés, basée sur la construction de flowsheets, a été développée. La formulation mathématique générale du problème a ensuite été définie : il s'agit d'un problème mixte, non-linéaire et a priori multiobjectif, qui a une contrainte égalité forte (la conservation de la masse). Une étude des méthodes d'optimisation a conduit à choisir un algorithme génétique (AG). Une alternative a également été envisagée pour résoudre le problème multiobjectif par programmation linéaire en le linéarisant "sous contrainte". Ce travail a mis en évidence la nécessité de développer une filière de recyclage efficace des déchets électriques et électroniques en France. Il a de plus montré que le cuivre contenu dans les déchets ne permet pas de couvrir la demande et qu'il est nécessaire d'importer du cuivre, de préférence sous forme de débris. / Improving the natural resources management is necessary to address the many issues related to their exploitation. This work proposes an optimization methodology for their management, applied to the case of copper in France. Four criteria are identified to assess management strategies: cost, environmental impacts, energy consumption and resource losses. The first step of this methodology is the analysis of the current situation, by modelling the French copper cycle from 2000 to 2009. This analysis showed that France imports almost all of its needs as refined copper, and has an underdeveloped recycling industry. Following these initial results, the problematic of copper wastes, including recycling, has been investigated. A recycled flow modelling strategy has been developed, based on the construction of flowsheets. The general mathematical formulation of the problem is then defined. It is a non-linear, mixed and a priori multiobjective problem, with a strong equality constraint (mass conservation). A review of optimization methods has led to choose a genetic algorithm (GA). An alternative was also proposed to solve the multiobjective problem with linear programming, by linearizing it under constraint. This work has highlighted the necessity of developing an effective recycling field of wastes from electric and electronic equipment in France. It also showed that the copper contained in wastes does not meet the demand, so that France needs to import copper, preferably as scraps.
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