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Synthesizing Regularity Exposing Attributes in Large Protein Databasesde la Maza, Michael 01 May 1993 (has links)
This thesis describes a system that synthesizes regularity exposing attributes from large protein databases. After processing primary and secondary structure data, this system discovers an amino acid representation that captures what are thought to be the three most important amino acid characteristics (size, charge, and hydrophobicity) for tertiary structure prediction. A neural network trained using this 16 bit representation achieves a performance accuracy on the secondary structure prediction problem that is comparable to the one achieved by a neural network trained using the standard 24 bit amino acid representation. In addition, the thesis describes bounds on secondary structure prediction accuracy, derived using an optimal learning algorithm and the probably approximately correct (PAC) model.
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Function Variables for Constraint ProgrammingHnich, Brahim January 2003 (has links)
Quite often modelers with constraint programming (CP) use the same modelling patterns for different problems, possibly from different domains. This results in recurring idioms in constraint programs. Our approach can be seen as a three-step approach. First, we identify some of these recurring patterns in constraint programs. Second, we propose a general way of describing these patterns by introducing proper constructs that would cover a wide range of applications. Third, we propose automating the process of reproducing these idioms from these higher-level descriptions. The whole process can be seen as a way of encapsulating some of the expertise and knowledge often used by CP modelers and making it available in much simpler forms. Doing so, we are able to extend current CP languages with high-level abstractions that open doors for automation of some of the modelling processes. In particular, we introduce function variables and allow the statement of constraints on these variables using function operations. A function variable is a decision variable that can take a value from a set of functions as opposed to an integer variable that ranges over integers, or a set variable that ranges over a set of sets. We show that a function variable can be mapped into different representations in terms of integer and set variables, and illustrate how to map constraints stated on a function variable into constraints on integer and set variables. As a result, a function model expressed using function variables opens doors to the automatic generation of alternate CP models. These alternate models either use a different variable representation, or have extra implied constraints, or employ different constraint formulation, or combine different models that are linked using channelling constraints. A number of heuristics are also developed that allow the comparison of different constraint formulations. Furthermore, we present an extensive theoretical comparison of models of injection problems supported by asymptotic and empirical studies. Finally, a practical modelling tool that is built based on a high-level language that allows function variables is presented and evaluated. The tool helps users explore different alternate CP models starting from a function model that is easier to develop, understand, and maintain.
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Utilisation d'ontologies comme support à la recherche et à la navigation dans une collection de documentsSy, Mohameth-François 11 December 2012 (has links) (PDF)
Les ontologies modélisent la connaissance d'un domaine avec une hiérarchie de concepts. Cette thèse porte sur leur utilisation dans les Systèmes de Recherche d'Information (SRI) pour estimer la pertinence des documents par rapport à une requête. Nous calculons cette pertinence à l'aide d'un modèle des préférences de l'utilisateur et d'une mesure de similarité sémantique associée à l'ontologie. Cette approche permet d'expliquer à l'utilisateur pourquoi les documents sélectionnés sont pertinents grâce à une visualisation originale. La RI étant un processus itératif, l'utilisateur doit être guidé dans sa reformulation de requête. Une stratégie de reformulation de requêtes conceptuelles est formalisée en un problème d'optimisation utilisant les retours faits par l'utilisateur sur les premiers résultats proposés comme base d'apprentissage. Nos modèles sont validés sur la base de performances obtenues sur des jeux de tests standards et de cas d'études impliquant des experts biologistes.
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Impact des variations morphologiques sur la recherche d'information sur le WebEddamoun, Said January 2009 (has links) (PDF)
Notre travail de recherche est de type exploratoire. Il traite de l'apport des connaissances linguistiques à la recherche d'information sur le Web. Plus spécifiquement, nous avons étudié l'impact des variations morphologiques, notamment les variantes dérivées, en termes de fréquence, sur la pertinence des documents rapportés. À ce sujet, nous avons vérifié s'il y a une corrélation entre la fréquence des termes et des variantes morphologiques extraits des documents rapportés et la pertinence de ces mêmes documents. Les résultats obtenus n'ont pas permis de confirmer, d'une façon évidente, cette corrélation. En d'autres termes, si les données brutes laissent croire que, globalement, il y a une corrélation entre la fréquence des variables et la pertinence des documents, ce n'est pas le cas après l'examen des requêtes d'une façon individuelle, et, aussi, après l'application du test statistique de Jonckheere-Terpstra. En somme, la présence ou non d'une telle corrélation dépend, en partie, de la requête, des mots de la requête, de la nature et de la qualité des variantes. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Recherche d'information, Connaissances linguistiques, Variations morphologiques, Reformulation de requêtes, Traitement automatique des langues, Web.
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Automatizuotas grafinio modelio performulavimas į natūralią kalbą / Automated Reformulation of Graphical Model in Natural LanguageSrogis, Andrius 26 August 2013 (has links)
Grafinių modelių projektavimas yra plačiai naudojamas tiek mokslo, tiek verslo srytyse. Pasaulyje naudojama įvairių kalbų, skirtų tiek sistemų architektūrų, tiek verslo procesų projektavimui. Daugumai kalbų yra sukurta įvairių įrankių, leidžiančių jų naudotojams projektuoti įvairius procesus ar statines sistemas. Vienai labiausiai paplitusių kalbų (UML) trūksta metodikos ir įrankių, gebančių korektiškai perteikti natūralia kalba sistemų architektų aprašytus grafinius modelius asmenims, mažai kvalifikuotiems grafinių modelių sudaryme, skaityme. Perteikimas tuo natūralesnis ir labiau suprantamesnis, kuo jis artimesnis natūraliai kalbai. Yra metodikų ir įrankių atliekančių grafinio modelio verbalizavimą, tačiau nėra koncentruotų ties diagramomis UML kalba, kurios geba formuoti ne tik statiką, bet ir dinamiką. Pagrindinis darbo tikslas yra sukurti metodiką ir realizuoti įrankį, kuris gebėtų grafinį modelį išreikštą UML kalba performuluoti natūralia kalba. / The graphical model architecture design is widely used for scientific and enterprise purposes. There are many languages concentrated on enterprise processes and static systems designing. One of the most popular modeling language (UML) is missing methodology and tools suitable for correct reformulation of graphical models (formulated by the UML) in natural language. The main purpose of the graphical model reformulation in natural language is to make models easier to understand for people whose are not specialized in UML. Methodology and tool which is capable of reformulating graphical models in natural language already exists, but it isn’t concentrated on UML or capable of reformulating static and dynamic processes. The main goal of this work is to define a methodology and implement a tool, which would be capable of translating the graphical UML model to a natural language text.
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An investigation of computer based tools for mathematical programming modellingLucas, Cormac Anthony January 1986 (has links)
No description available.
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Desenvolvimento de linguiça suína, cozida e defumada, com adição de biomassa de banana verde e redução dos teores de sódio e gordura / Cooked and smoked pork sausage making with green banana biomass and sodium and fat reductionThomé, Bruna Rodrigues 11 August 2017 (has links)
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Previous issue date: 2017-08-11 / Food consumption patterns have changed according to concerns regarding environmental
sustainability, regional development, nutritional aspects and, mainly, health issues. The results
on changing this habit involve demand growth and the need for food that, besides nourishing
the organism, can also offer other healthy qualities. Therefore, meat products have become the
objects of many scientific studies, which, mainly, concern their nutritional composition. The
usage of replacements for fat, such as the green banana biomass (GBB), is an alternative that
can be sought in order to create this appeal for the consumers. The GBB is a kind of food that
can be added to several formulations without altering their original taste. It also has many
nutritional advantages, like the presence of fiber and resistant starch in it. However, there are
not studies that use the GBB in cooked pork sausage. Because of this, this study aims to make
cooked and smoked pork sausage with added green bananas biomass and to reduce its sodium
and fat levels. For this purpose, three formulations were developed: Control and Treatment
(TC), without adding the green bananas biomass and without reducing the sodium and fat
levels; Treatment 1 (T1), by adding 2,17% of GBB and reducing the sodium and fat levels in
15%; and Treatment 2 (T2), with added 3,12% GBB and a reduction of 20% on sodium level
and 30% on fat levels. Physicochemical, microbial and sensory analysis have been carried out
in three different times: one day after processing (t0), seven days after processing (t7) and
twenty-one days after processing (t21), and these analyses aimed to check possible alterations,
over time during storage, under refrigeration. We concluded, through the obtained results, that
the developed product, with added GBB and reduction on its sodium and fat levels, was in
accordance to the current physicochemical and microbial regulation standards, during the
storage time. As for the sensory analysis, excepting the scent aspect, we concluded that all other
aspects did not present statistical differences. The T2 treatment was the most indicated one
among the evaluated aspects. / Os padrões de consumo de alimentos têm experimentado mudanças em função das
preocupações sobre sustentabilidade ambiental, desenvolvimento regional, aspectos
nutricionais e, sobretudo, questões relacionadas à saúde. O resultado desta mudança de hábito
consiste no crescimento da demanda e necessidade por alimentos, que além de nutrir o
organismo ofereçam também características benéficas à saúde. Neste sentido, os produtos
derivados de carnes tornaram-se objetos constantes de estudos científicos, principalmente na
busca de estratégias e formulações que os tornem saudáveis em relação à sua composição
nutricional. O emprego de substitutos de gordura, como a biomassa de banana verde (BBV), é
uma das alternativas que pode ser buscada para conseguir este apelo diante dos consumidores.
A BBV é um alimento que pode ser incorporado em diversas formulações sem alterar o sabor
original, apresenta muitas vantagens nutricionais, principalmente pela presença de fibras e
amido resistente. No entanto, há a ausência de estudos utilizando a BBV em linguiça suína
cozida. Diante desse fato, objetivou-se neste trabalho, desenvolver uma linguiça suína, cozida
e defumada com adição de biomassa de banana verde e redução dos teores de sódio e gordura,
além de verificar a preferência e a intenção de compra da linguiça. Para tanto, foram
desenvolvidas três formulações, sendo Tratamento Controle (TC), sem adição de biomassa de
banana verde, sem redução nos teores de sódio e gordura; Tratamento 1 (T1), com adição de
2,17% de BBV e redução de 15% nos teores de sódio e gordura e Tratamento 2 (T2),
correspondeu à formulação com adição de 3,12 % de BBV e redução de 20% no teor de sódio
e 30% no teor de gordura. Foram realizadas análises físico-químicas, microbiológicas e
sensorial, em três tempos distintos, um dia após o processamento (t0), sete dias após o
processamento (t7) e vinte e um dias após o processamento (t21), a fim de verificar possíveis
alterações, ao longo do tempo de estocagem, sob refrigeração. Com os resultados obtidos, podese concluir que o produto desenvolvido com a adição de BBV e as reduções dos teores de sódio
e gordura estavam de acordo com os padrões físico-químicos e microbiológicos estabelecidos
pela legislação vigente, durante o período de estocagem. Em relação à análise sensorial, com
exceção do atributo aroma, todos os demais atributos não apresentaram diferença estatística. O
tratamento T2 apresentou maior preferência e intenção de compra entre os tratamentos
avaliados.
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Aumento da qualidade global de mortadela reformulada com a adição de gordura vegetal e marinha em substituição da gordura animal / Increase of overall quality of reformulated mortadella with the addition of vegetable and marine fat in substitution of animal fatErick Manuel Saldaña Villa 08 September 2015 (has links)
A carne exerce um papel crucial na evolução humana e é um componente importante em dietas saudáveis e balanceadas, uma vez que apresenta propriedades nutricionais, é fonte de proteína de alto valor biológico e de algumas vitaminas e minerais. No entanto, estudos recentes têm estabelecido uma relação direta entre o consumo de produtos cárneos e o aumento no risco de distúrbios graves de saúde, como câncer colo retal e doenças cardíacas. Assim, o desenvolvimento de produtos cárneos com níveis reduzidos de gordura, que sejam similares aos produtos tradicionais, apresentando boa aceitabilidade pelos consumidores, é essencial para a melhoria da saúde humana. No entanto, poucos trabalhos da literatura tem estudado a incorporação de pré-emulsões como substituto da gordura animal, especialmente em relação às caracteristicas sensoriais. O presente trabalho estudou o efeito da substituição de gordura animal por óleos vegetais e marinhos sobre as propriedades físicas, químicas e sensoriais de mortadela formulada com diferentes hidrocóloides. Na primeira parte do trabalho avaliaram-se as propriedades físicas, químicas e sensoriais da mortadela reformulada usando gordura vegetal hidrogenada como substituto de gordura animal, e foi verificado que o uso da gordura vegetal hidrogenada não é adequado como substituto da gordura animal devido à redução da qualidade nutricional, especificamente do perfil lipídico, e da qualidade sensorial, especificamente da dureza. Após isto, estudou-se a microestrutura, a textura sensorial descritiva e o perfil instrumental de textura da mortadela tradicional e light e, através dos resultados, os parâmetros de dureza e elasticidade foram considerados como referências na seguinte etapa da reformulação. Em seguida, otimizou-se o perfil lipídico e, através de uma estratégia sequencial de planejamento experimental, as proporções adequadas de óleos em préemulsões foram obtidas, assim como a dureza e a elasticidade foram otimizadas, em função da composição da pré-emulsão composta de alginato de sódio, goma guar e isolado proteico de leite. Avaliaram-se, então, as características sensoriais da mortadela e sua relação com a aceitação do consumidor. O atributo direcionador da preferêcia, segundo a correlação entre as respostas da análise descritiva e do teste de aceitação, foi a textura \"borrachenta\", confirmando-se assim que mesmo adicionando um hidrocolóide para diminuir a dureza, esta diminuição resultou em um novo atributo negativo. As perguntas Check- all-that-apply (CATA) juntamente com a Análise de Penalização e a PLSR de variáveis fictícias com a aceitação ajudaram a identificar o \"sabor estranho\", \"sabor caracteristico\", \"textura gelatinosa\" e \"textura firme\" como os principais atributos a serem modificados numa reformulação posterior. Dessa forma, conclui-se que através da estratégia de reformulação planejada, pode-se elaborar uma mortadela com um perfil lipídico em consonância com as recomendações de uma dieta saudável, levando em consideração a opinião do consumidor. / Meat plays a crucial role in human evolution and it is an important component in healthy and balanced diets, since it presents nutritional properties, it is source of proteins of high biological value, and some vitamins, and minerals. However, recent studies have established a direct relationship between the consumption of meat products and the increased risk of serious health disorders, such as colorectal cancer and coronary-heart diseases. Thus, the development of meat products with reduced fat levels that are similar to traditional products and with good consumer acceptability is essential for the improvement of the human health. However, few studies in the literature have studied the incorporation of pre-emulsion as animal fat substitute, especially regarding the sensory characteristics. The present study evaluated the effect of the animal fat substitution by vegetable and marine oils on the physical, chemical, and sensory properties of mortadella formulated with different hydrocolloids. In the first part of the study, the physical, chemical and sensory properties of reformulated mortadella using hydrogenated vegetable fat as animal fat replacer were evaluated and it was verified that the use of hydrogenated fat is not suitable as animal fat replacer due to a reduction in the nutritional quality, specifically regarding the lipid profile, and in the sensory quality, specifically regarding hardness. After this, the microstructure, the descriptive sensory texture and the instrumental profile of the traditional and light mortadella were studied and, through the results, the parameters of hardness and elasticity were considered as references to the next step of the reformulation. Then, the lipid profile was optimized and, through a sequential strategy of experimental design, the appropriate proportions of oils in preemulsions were obtained, as well as the hardness and elasticity were optimized according to the pre-emulsion composition composed of sodium alginate, guar gum and isolated milk protein. The sensory characteristics of the mortadella and their relationship with the consumer acceptance were then evaluated. According to the correlation between the answers of the descriptive analysis and the acceptance test, the driver of liking was the \"rubbery\" texture, thus confirming that, even by adding a hydrocolloid to reduce the hardness, this decrease resulted in a \"new negative attribute\". The questions Check-all-that-apply (CATA), along with the Penalty Analysis and the PLSR of dummy variables with the acceptance helped to identify the \"strange flavor\", \"characteristic flavor,\" \"gelatinous texture\" and \"firm texture\" as the key attributes to be modified at a later reformulation. Thus, it is concluded that, through the planned reformulation strategy, it was possible to develop a mortadella with a lipid profile in agreement with the recommendations of a healthy diet, taking into account the consumer\'s opinion.
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Francês com objetivos específicos para o curso de Secretariado Executivo: é possível uma aprendizagem recíproca de saberes profissionais e de linguagem? / French with specific objectives for the Executive Secretariat Course: is it possible a reciprocal learning of professional knowledge and language?Fábio Lucas Pierini 20 April 2012 (has links)
Este trabalho originou-se da necessidade de elaborar e complementar atividades que promovam o ensino e a aprendizagem do francês com objetivos específicos para o curso de Secretariado Executivo Trilíngue da Universidade Estadual de Maringá-PR. Durante o andamento do curso, percebemos que as tarefas de produção escrita poderiam ser potencializadas se tivessem como origem um texto oral, pois os alunos mobilizariam de forma mais proveitosa suas estratégias de compreensão. Para comprovar nossa hipótese, elaboramos uma tarefa na qual os alunos devessem passar uma mensagem gravada na secretária eletrônica para uma nota de serviço, que são situações de comunicação muito correntes no ofício do secretariado. Nossa previsão era que ao conhecer o formato do texto de destino, o aluno selecionaria com mais agilidade as informações necessárias no texto fonte, comprovando o movimento de reciprocidade entre os saberes profissionais (estrutura do texto, contexto de emprego, etc.) e os saberes linguísticos. De fato, após quase um ano de trabalho, nossos alunos foram capazes de compor a nota de serviço a partir de uma gravação na secretária eletrônica, pois utilizaram estratégias de mediação para ligar a compreensão do texto fonte à produção do texto de destino. O resultado do uso dessas estratégias foi um texto de destino que obedeceu às normas de composição esperadas e cumpriu sua função comunicativa, comprovando o papel das estratégias de mediação na aprendizagem do francês com objetivos específicos para o curso de Secretariado Executivo Trilíngue. / The aim of this work was to develop and supplement activities in order to promote the teaching and learning of French focusing the Trilingual Executive Secretariat Course of Universidade Estadual de Maringá state of Paraná Brazil. It was observed during the classes that the written production tasks could be improved if the oral text were taken into account, since the students would be able to mobilize the comprehension strategies in a more profitable way. To try the hypothesis, a communicative situation task was chosen among the most current of Secretariat work. For the elaborated task students should deliver a recorded message from an electronic machine into a memo. Our assumption was that students should select more accurately the necessary information of the source text, once they knew the format of the target text, confirming thus the exchange movement between their professional knowledge (text structure, job context, etc) and their linguistic knowledge. In fact, after almost one year of work, students were able to build up the memo, based in an electronic machine recording, by using mediation strategies to link the source text comprehension to the target text production. The use of such strategies showed that the target text followed the composition rules and accomplished its communicative function, proving the role of the mediation strategies in the learning of specific purpose French for the Executive Secretariat Course.
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Enhanced Formulations for Minimax and Discrete Optimization Problems with Applications to Scheduling and RoutingGhoniem, Ahmed 12 July 2007 (has links)
This dissertation addresses the development of enhanced formulations for minimax and mixed-integer programming models for certain industrial and logistical systems, along with the design and implementation of efficient algorithmic strategies. We first examine the general class of minimax mixed-integer 0-1 problems of the type that frequently arise in decomposition approaches and in a variety of location and scheduling problems. We conduct an extensive polyhedral analysis of this problem in order to tighten its representation using the Reformulation-Linearization/Convexification Technique (RLT), and demonstrate the benefits of the resulting lifted formulations for several classes of problems. Specifically, we investigate RLT-enhanced Lagrangian dual formulations for the class of minimax mixed-integer 0-1 problems in concert with deflected/conjugate subgradient algorithms. In addition, we propose two general purpose lifting mechanisms for tightening the mathematical programming formulations associated with such minimax optimization problems.
Next, we explore novel continuous nonconvex as well as lifted discrete formulations for the notoriously challenging class of job-shop scheduling problems with the objective of minimizing the maximum completion time (i.e., minimizing the makespan). In particular, we develop an RLT-enhanced continuous nonconvex model for the job-shop problem based on a quadratic formulation of the job sequencing constraints on machines. The tight linear programming relaxation that is induced by this formulation is then embedded in a globally convergent branch-and-bound algorithm. Furthermore, we design another novel formulation for the job-shop scheduling problem that possesses a tight continuous relaxation, where the non-overlapping job sequencing constraints on machines are modeled via a lifted asymmetric traveling salesman problem (ATSP) construct, and specific sets of valid inequalities and RLT-based enhancements are incorporated to further tighten the resulting mathematical program. The efficacy of our enhanced models is demonstrated by an extensive computational experiment using classical benchmark problems from the literature. Our results reveal that the LP relaxations produced by the lifted ATSP-based models provide very tight lower bounds, and directly yield a 0\% optimality gap for many benchmark problems, thereby substantially dominating other alternative mixed-integer programming models available for this class of problems. Notably, our lifted ATSP-based formulation produced a 0\% optimality gap via the root node LP relaxation for 50\% of the classical problem instances due to Lawrence.
We also investigate enhanced model formulations and specialized, efficient solution methodologies for applications arising in four particular industrial and sports scheduling settings. The first of these was posed to us by a major trucking company (Volvo Logistics North America), and concerns an integrated assembly and routing problem, which is a unique study of its kind in the literature. In this context, we examine the general class of logistical systems where it is desirable to appropriately ascertain the joint composition of the sequences of vehicles that are to be physically connected along with determining their delivery routes. Such assembly-routing problems occur in the truck manufacturing industry where different models of vehicles designed for a network of customers need to be composed into compatible groups (assemblies) and subsequently dispatched via appropriately optimized delivery routes that are restricted by the particular sequence in which the trucks are connected. A similar structure is exhibited in the business of shipping goods via boat-towed barges along inland waterways, or via trains through railroad networks. We present a novel modeling framework and column generation-based optimization approach for this challenging class of joint vehicle assembly-routing problems. In addition, we suggest several extensions to accommodate particular industrial restrictions where assembly sequence-dependent delivery routes are necessary, as well as those where limited driver- and equipment-related resources are available. Computational experience is provided using large-scale realistic data to demonstrate the applicability of our suggested methodology in practice.
The second application addressed pertains to a production planning problem faced by a major motorcycle manufacturing firm (Harley-Davidson Motor Company). We consider the problem of partitioning and sequencing the production of different manufactured items in mixed-model assembly lines, where each model has various specific options and designated destinations. We propose a mixed-integer programming formulation (MPSP1) for this problem that sequences the manufactured goods within production batches in order to balance the motorcycle model and destination outputs as well as the load demands on material and labor resources. An alternative (relaxed) formulation (MPSP2) is also presented to model a closely related case where all production decisions and outputs are monitored within a common sequence of batches, which permits an enhanced tighter representation via an additional set of hierarchical symmetry-defeating constraints that impart specific identities amongst batches of products under composition. The latter model inspires a third set partitioning-based formulation in concert with an efficient column generation approach that directly achieves the joint partitioning of jobs into batches along with ascertaining the sequence of jobs within each composed batch. Finally, we investigate a subgradient-based optimization strategy that exploits a non-differentiable optimization formulation, which is prompted by the flexibility in the production process as reflected in the model via several soft-constraints, thereby providing a real-time decision-making tool. Computational experience is presented to demonstrate the relative effectiveness of the different proposed formulations and the associated optimization strategies for solving a set of realistic problem instances.
The third application pertains to the problem of matching or assigning subassembly parts in assembly lines, where we seek to minimize the total deviation of the resulting final assemblies from a vector of nominal and mean quality characteristic values. We introduce three symmetry-defeating enhancements for an existing assignment-based model, and highlight the critical importance of using particular types of symmetry-defeating hierarchical constraints that preserve the model structure. We also develop an alternative set partitioning-based formulation in concert with a column generation approach that efficiently exploits the structure of the problem. A special complementary column generation feature is proposed, and we provide insights into its vital role for the proposed column generation strategy, as well as highlight its benefits in the broader context of set partitioning-based formulations that are characterized by columns having relatively dense non-zero values. In addition, we develop several heuristic procedures. Computational experience is presented to demonstrate the relative effectiveness of the different adopted strategies for solving a set of realistic problem instances.
Finally, we analyze a doubles tennis scheduling problem in the context of a training tournament as prompted by a tennis club in Virginia, and develop two alternative 0-1 mixed-integer programming models, each with three different objective functions that attempt to balance the partnership and the opponentship pairings among the players. Our analysis and computational experience demonstrate the superiority of one of these models over the other, and reflect the importance of model structure in formulating discrete optimization problems. Furthermore, we design effective symmetry-defeating strategies that impose certain decision hierarchies within the models, which serve to significantly enhance algorithmic performance. In particular, our study provides the insight that the special structure of the mathematical program to which specific tailored symmetry-defeating constraints are appended can greatly influence their pruning effect. We also propose a novel nonpreemptive multi-objective programming strategy in concert with decision hierarchies, and highlight its effectiveness and conceptual value in enhancing problem solvability. Finally, four specialized heuristics are devised and are computationally evaluated along with the exact solution schemes using a set of realistic practical test problems.
Aside from the development of specialized effective models and algorithms for particular interesting and challenging applications arising in different assembly, routing, and scheduling contexts, this dissertation makes several broader contributions that emerge from the foregoing studies, which are generally applicable to solving formidable combinatorial optimization problems. First, we have shown that it is of utmost importance to enforce symmetry-defeating constraints that preserve the structure of mathematical programs to which they are adjoined, so that their pruning effects are most efficiently coupled with the branch-and-bound strategies that are orchestrated within mathematical programming software packages. In addition, our work provides the insight that the concept of symmetry compatible formulations plays a crucial role in the effectiveness of implementing any particular symmetry-defeating constraints. In essence, if the root node LP solution of the original formulation does not conform relatively well with the proposed symmetry-defeating hierarchical constraints, then a significant branching effort might be required to identify a good solution that is compatible with the pattern induced by the selected symmetry-defeating constraints. Therefore, it is advisable to enforce decision hierarchies that conform as much as possible with the problem structure as well as with the initial LP relaxation.
Second, we have introduced an alternative concept for defeating symmetry via augmented objective functions. This concept prompts the incorporation of objective perturbation terms that discriminate amongst subsets of originally undistinguishable solution structures and, in particular, leads to the development of a nonpreemptive multiobjective programming approach based on, and combined with, symmetry-defeating constraints. Interestingly, nonpreemptive multiobjective programming approaches that accommodate symmetry-defeating hierarchical objective terms induce a root node solution that is compatible with the imposed symmetry-defeating constraints, and hence affords an automated alternative to the aforementioned concept of symmetry compatible formulations.
Third, we have proposed a new idea of complementary column generation in the context of column generation approaches that generally provide a versatile framework for analyzing industrial-related, integrated problems that involve the joint optimization of multiple operational decisions, such as assembly and routing, or partitioning and scheduling. In such situations, we have reinforced the insight that assignment-related problems that involve collections of objects (production batches, final assemblies, etc.) whose permutation yields equivalent symmetric solutions may be judiciously formulated as set partitioning models. The latter can then be effectively tackled via column generation approaches, thereby implicitly obviating the foregoing combinatorial symmetric reflections through the dynamic generation of attractive patterns or columns. The complementary column generation feature we have proposed and investigated in this dissertation proves to be particularly valuable for such set partitioning formulations that involve columns having relatively dense non-zero values. The incorporation of this feature guarantees that every LP iteration (involving the solution of a restricted master program and its associated subproblem) systematically produces a consistent set of columns that collectively qualify as a feasible solution to the problem under consideration. Upon solving the problem to optimality as a linear program, the resultant formulation encompasses multiple feasible solutions that generally include optimal or near-optimal solutions to the original integer-restricted set partitioning formulation, thereby yielding a useful representation for designing heuristic methods as well as exact branch-and-price algorithms. In addition, using duality theory and considering set partitioning problems where the number of patterns needed to collectively compose a feasible solution is bounded, we have derived a lower bound on the objective value that is updated at every LP phase iteration. By virtue of this sequence of lower bounds and the availability of upper bounds via the restricted master program at every LP phase iteration, the LP relaxation of the set partitioning problem is efficiently solved as using a pre-specified optimality tolerance. This yields enhanced algorithmic performance due to early termination strategies that successfully mitigate the tailing-off effect that is commonly witnessed for simplex-based column generation approaches. / Ph. D.
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