This dissertation studies in depth the structure of the Discrete Ordered Median Problem (DOMP), to define new formulations and resolution algorithms. Furthermore we analyze an interesting extension for DOMP, namely MDOMP (Monotone Discrete Ordered Median Problem). This thesis is structured in three main parts.First, a widely theoretical and computational study is reported. It presents several new formulations for the Discrete Ordered Median Problem (DOMP) based on its similarity with some scheduling problems. Some of the new formulations present a considerably smaller number of constraints to define the problem with respect to some previously known formulations. Furthermore, the lower bounds provided by their linear relaxations improve the ones obtained with previous formulations in the literature even when strengthening is not applied. We also present a polyhedral study of the assignment polytope of our tightest formulation showing its proximity to the convex hull of the integer solutions of the problem. Several resolution approaches, among which we mention a branch and cut algorithm, are compared. Extensive computational results on two families of instances, namely randomly generated and from Beasley's OR-library, show the power of our methods for solving DOMP. One of the achievements of the new formulation consists in its tighter LP-bound. Secondly, DOMP is addressed with a new set partitioning formulation using an exponential number of variables. This chapter develops a new formulation in which each variable corresponds to a set of demand points allocated to the same facility with the information of the sorting position of their corresponding distances. We use a column generation approach to solve the continuous relaxation of this model. Then, we apply a branch-cut-and-price algorithm to solve to optimality small to moderate size of DOMP in competitive computational time.To finish, the third contribution of this dissertation is to analyze and compare formulations for the monotone discrete ordered median problem. These formulations combine different ways to represent ordered weighted averages of elements by using linear programs together with the p-median polytope. This approach gives rise to two efficient formulations for DOMP under a hypothesis of monotonicity in the lambda vectors. These formulations are theoretically compared and also compared with some other formulations valid for the case of general lambda vector. In addition, it is also developed another new formulation, for the general case, that exploits the efficiency of the rationale of monotonicity. This representation allows to solve very efficiently some DOMP instances where the monotonicity is only slightly lost. Detailed computational tests on all these formulations is reported in the dissertation. They show that specialized formulations allow to solve to optimality instances with sizes that are far beyond the limits of those that can solve in the general case. / Cette dissertation étudie en profondeur la structure du "Discrete Ordered Median Problem" (DOMP), afin de proposer de nouvelles formulations et de nouveaux algorithmes de résolution. De plus, une extension intéressante du DOMP nommée MDOMP ("Monotone Discrete Ordered Median Problem") a été étudiée.Cette thèse a été structurée en trois grandes parties.La première partie présente une étude riche aux niveaux théorique et expérimentale. Elle développe plusieurs formulations pour le DOMP qui sont basées sur des problèmes d'ordonnancement largement étudiés dans la littérature. Plusieurs d'entres elles nécessitent un nombre réduit de contraintes pour définir le problème en ce qui concerne certaines formulations connues antérieurement. Les bornes inférieures, qui sont obtenues par la résolution de la relaxation linéaire, donnent de meilleurs résultats que les formulations précédentes et ceci même avec tout processus de renforcement désactivé. S'ensuit une étude du polyhèdre de notre formulation la plus forte qui montre sa proximité entre l'enveloppe convexe des solutions entières de notre problème. Un algorithme de branch and cut et d'autres méthodes de résolution sont ensuite comparés. Les expérimentations qui montrent la puissance de nos méthodes s'appuient sur deux grandes familles d'instances. Les premières sont générées aléatoirement et les secondes proviennent de Beasley's OR-library. Ces expérimentations mettent en valeur la qualité de la borne obtenue par notre formulation.La seconde partie propose une formulation "set partitioning" avec un nombre exponentiel de variables. Dans ce chapitre, la formulation comporte des variables associées à un ensemble de demandes affectées à la même facilité selon l'ordre établi sur leurs distances correspondantes. Nous avons alors développé un algorithme de génération de colonnes pour la résolution de la relaxation continue de notre modèle mathématique. Cet algorithme est ensuite déployé au sein d'un Branch-and-Cut-and-Price afin de résoudre des instances de petites et moyennes tailles avec des temps compétitifs.La troisième partie présente l'analyse et la comparaison des différentes formulations du problème DOMP Monotone. Ces formulations combinent plusieurs manières de formuler l'ordre des éléments selon les moyennes pondérées en utilisant plusieurs programmes linéaires du polytope du p-median. Cette approche donne lieu à deux formulations performantes du DOMP sous l'hypothèse de monotonie des vecteurs lambda. Ces formulations sont comparées de manière théorique puis comparées à d'autres formulations valides pour le cas général du vecteur lambda. Une autre formulation est également proposée, elle exploite l'efficacité du caractère rationnel de la monotonie. Cette dernière permet de résoudre efficacement quelques instances où la monotonie a légèrement disparue. Ces formulations ont fait l'objet de plusieurs expérimentations dècrites dans ce manuscrit de thèse. Elles montrent que les formulations spécifiques permettent de résoudre des instances plus importantes que pour le cas général. / Este trabajo estudia en profundidad la estructura del problema disctreto de la mediana ordenada (DOMP, por su acrónimo en inglés) con el objetivo de definir nuevas formulaciones y algoritmos de resolución. Además, analizamos una interesante extensión del DOMP conocida como el problema monótono discreto de la mediana ordenada (MDOMP, de su acrónimo en inglés).Esta tesis se compone de tres grandes bloques.En primer lugar, se desarrolla un detallado estudio teórico y computacional. Se presentan varias formulaciones nuevas para el problema discreto de la mediana ordenada (DOMP) basadas en su similaridad con algunos problemas de secuenciación. Algunas de estas formulaciones requieren de un cosiderable menor número de restricciones para definir el problema respecto a algunas de las formulaciones previamente conocidas. Además, las cotas inferiores proporcionadas por las relajaciones lineales mejoran a las obtenidas con formulaciones previas de la literatura incluso sin reforzar la nueva formulación. También presentamos un estudio poliédrico del politopo de asignación de nuestra formulación más compacta mostrando su proximidad con la envolvente convexa de las soluciones enteras del problema. Se comparan algunos procedimientos de resolución, entre los que destacamos un algoritmo de ramificación y corte. Amplios resultados computacionales sobre dos familias de instancias -aleatoriamente generadas y utilizando la Beasley's OR-library- muestran la potencia de nuestros métodos para resolver el DOMP.En el segundo bloque, el problema discreto de la mediana ordenada es abordado con una formulación de particiones de conjuntos empleando un número exponencial de variables. Este capítulo desarrolla una nueva formulación en la que cada variable corresponde a un conjunto de puntos de demanda asignados al mismo servidor con la información de la posición obtenida de ordenar las distancias correspondientes. Utilizamos generación de columnas para resolver la relajación continua del modelo. Después, empleamos un algoritmo de ramificación, acotación y "pricing" para resolver a optimalidad tamaños moderados del DOMP en un tiempo computacional competitivo.Por último, el tercer bloque de este trabajo se dedica a analizar y comparar formulaciones para el problema monótono discreto de la mediana ordenada. Estas formulaciones combinan diferentes maneras de representar medidas de pesos ordenados de elementos utilizando programación lineal junto con el politopo de la $p$-mediana. Este enfoque da lugar a dos formulaciones eficientes para el DOMP bajo la hipótesis de monotonía en su vector $lambda$. Se comparan teóricamente las formulaciones entre sí y frente a algunas de las formulaciones válidas para el caso general. Adicionalmente, se desarrolla otra formulación válida para el caso general que explota la eficiencia de las ideas de la monotonicidad. Esta representación permite resolver eficientemente algunos ejemplos donde la monotonía se pierde ligeramente. Finalmente, llevamos a cabo un detallado estudio computacional, en el que se aprecia que las formulaciones ad hoc permiten resolver a optimalidad ejemplos cuyo tamaño supera los límites marcados en al caso general. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Master of Science / Department of Industrial and Manufacturing Systems Engineering / Todd W. Easton / Integer programming is an important discipline in operation research that positively impacts society. Unfortunately, no algorithm currently exists to solve IP's in polynomial time. Researchers are constantly developing new techniques, such as cutting planes, to help solve IPs faster. For example, DeLissa discovered the existence of equality cuts limited to zero and one coefficients for the multiple knapsack equality problem (MKEP). An equality cut is an improper cut because every feasible point satisfies the equality. However, such a cut always reduces the dimension of the linear relaxation space by at least one. This thesis introduces lifted equality cuts, which can have coefficients greater than or equal to two. Two main theorems provide the conditions for the existence of lifted equalities. These theorems provide the foundation for The Algorithm of Lifted Equality Cuts (ALEC), which finds lifted equality cuts in quadratic time. The computational study verifies the benefit of lifted equality cuts in random MKEP instances. ALEC generated millions of lifted equality cuts and reduced the solution time by an average of 15%. To the best of the author's knowledge, ALEC is the first algorithm that has found over 30.7 million cuts on a single problem, while reducing the solving time by 18%.

Polynomial continuation, a branch of numerical continuation, has been applied to several primary problems in kinematic geometry. The objective of the research presented in this document was to explore the possible extensions of the application of polynomial continuation, especially in the field of deployable structure design. The power of polynomial continuation as a design tool lies in its ability to find all solutions of a system of polynomial equations (even positive dimensional solution sets). A linkage design problem posed in polynomial form can be made to yield every possible feasible outcome, many of which may never otherwise have been found. Methods of polynomial continuation based design are illustrated here by way of various examples. In particular, the types of deployable structures which form planar rings, or frames, in their deployed configurations are used as design cases. Polynomial continuation is shown to be a powerful component of an equation-based design process. A polyhedral homotopy method, particularly suited to solving problems in kinematics, was synthesised from several researchers' published continuation techniques, and augmented with modern, freely available mathematical computing algorithms. Special adaptations were made in the areas of level-k subface identification, lifting value balancing, and path-following. Techniques of forming closure/compatibility equations by direct use of symmetry, or by use of transfer matrices to enforce loop closure, were developed as appropriate for each example. The geometry of a plane symmetric (rectangular) 6R foldable frame was examined and classified in terms of Denavit-Hartenberg Parameters. Its design parameters were then grouped into feasible and non-feasible regions, before continuation was used as a design tool; generating the design parameters required to build a foldable frame which meets certain configurational specifications. Two further deployable ring/frame classes were then used as design cases: (a) rings which form (planar) regular polygons when deployed, and (b) rings which are doubly plane symmetric and planar when deployed. The governing equations used in the continuation design process are based on symmetry compatibility and transfer matrices respectively. Finally, the 6, 7 and 8-link versions of N-loops were subjected to a witness set analysis, illustrating the way in which continuation can reveal the nature of the mobility of an unknown linkage. Key features of the results are that polynomial continuation was able to provide complete sets of feasible options to a number of practical design problems, and also to reveal the nature of the mobility of a real overconstrained linkage.

No description available.

Given a sequence of n topological pairs (X_i,A_i) for i=1,...,n, and a simplicial complex K, on n vertices, there is a topological space (X,A)^K by a construction of Buchstaber and Panov. Such spaces are called polyhedral products and they generalize the central notion of the moment-angle complex in toric topology. We study certain classes of polyhedral products from a homotopy theoretic point of view. The boundary of the 2-dimensional n-sided polygon, where n is greater than or equal to 3, may be viewed as a 1-dimensional simplicial complex with n vertices and n faces which we call the n-gon. When K is an n-gon for n at least 5, (D^2,S^1)^K is a hyperbolic space, by a theorem of Debongnie. We show that there is an infinite basis of the rational homotopy of the based loop space of (D^2,S^1)^K represented by iterated Samelson products. When K is an n-gon, for n at least 3, and P^m(p^r) is a mod p^r Moore space with m at least 3 and r at least 1, we show that the order of the elements in the p-primary torsion component in the homotopy groups of (Cone X, X)^K, where X is the loop space of P^m(p^r), is bounded above by p^{r+1}. This result provides new evidence in support of a conjecture of Moore. Moreover, this bound is the best possible and in fact, if a certain conjecture of M.J Barratt is assumed to be true, then this bound is also valid, and is the best possible, when K is an arbitrary simplicial complex.

This study aims to deduce an appropriate shape and density for an electronic free-cell that could be placed into a silo so that position and other desired physical parameters could be recorded. To determine how density and shape affects the trajectory and displacement of free cells, the trajectory and displacement of cylindrical, cuboid and triangular prism free-cells of equivalent volume was investigated in a discharging quasi 3D silo slice. The free-cells were placed at twelve different starting positions spread evenly over one half of the 3D slice. Tests were conducted using a monosized batch of spherical particles with a diameter of approximately 5 mm. Tests were also conducted in a binary mixture consisting of particles of different sizes (5 mm/4 mm) and the same density (1.28 g/cm3) and a binary mixture consisting of particles of different size (6 mm/5 mm) and different densities (1.16 g/cm3/1.28 g/cm3).The rotation of the free cells was also briefly discussed.Computer simulations were conducted using the Discrete Element Method (DEM). The simulation employed the spring-slider-dashpot contact model to represent the normal and tangential force components and the modified Euler integration scheme was applied to calculate the particle velocities and positions at each time step. One trial of each of the metal and plastic, cylindrical, cuboid and triangular prism free cells was compared with the average of three experimental trials. The trajectory and displacement of a representative particle positioned at the same starting position as the free cell was also obtained from DEM simulation and compared with the path and displacement of each of the free cells to determine which free cell followed the particle most closely and hence to determine a suitable free cell that would move with the rest of the grains. Spherical particles are idealised particles. Therefore tests were also conducted with a small number of polyhedral particles, to deduce their flow rate and the critical orifice width at which blockages were likely to form. Simulations were also conducted to test the feasibility of the DEM in modelling the behaviour of these polyhedral particles.Results indicate that for a free cell to move along the same trajectory and have the same displacement and velocity as an equivalent particle in the batch it should have a similar density to the majority of the other particles. A cylindrical free cell of similar density to the particles was found to follow the path of the representative particle more closely than the cuboid or triangular prism. Polyhedral particles were found to have a greater flow rate than spherical particles of equivalent volume.

Doctor en Sistemas de Ingeniería / En esta tesis se presentan los resultados del trabajo desarrollado por el autor durante el periodo en que fue estudiante de doctorado en el Departamento de Industrias de la Universidad de Chile. El trabajo se centra en la aplicación de técnicas de optimización entera-mixtas a problemas de planificación estratégica del sector eléctrico, donde el problema de corto plazo correspondiente al predespacho de unidades de generación en sistemas térmicos es el tema central en estudio. En lo relativo al modelamiento del problema de predespacho de unidades, se considera el análisis de las distintas formulaciones entera-mixtas disponibles en la literatura junto con una nueva basada en un formulaciones extendidas tipo red. Se investiga su desempeño sobre un conjunto de instancias reales desde el punto de vista de su eficiencia computacional al ser resueltas con softwares comerciales. Lo anterior incluye análisis de tiempos de solución, nodos utilizados e iteraciones de simplex realizadas para distintas tolerancias requeridas. Los experimentos muestran la calidad de la aproximación propuesta, siendo esta completamente competitiva respecto a las ya documentadas. Este resultado era esperable, dada la estructura totalmente unimodular de gran parte de la formulación propuesta, pero para nada justificable debido al tamaño de la misma. Lo anterior muestra que el efecto del preproceso de los softwares comerciales puede ser fundamental en algunas formulaciones. Por otro lado, respecto a la función objetivo del problema de predespacho de unidades, que por lo general se representa como una función cuadrática de la generación, se presenta una nueva manera de linealizar su comportamiento de modo que su inclusión en una formulación entera-mixta lineal tradicional sea eficiente. Esto último debe entenderse a partir de la necesidad que el tamaño de la aproximación no crezca de manera desmedida si el error requerido para la misma decrece. Si bien ya existía la posibilidad de hacer esto mediante la aplicación de la aproximación desarrollada por Ben-Tal y Nemirovsky para conos de segundo orden [2], acá se presenta un método alternativo, con mejores propiedades numéricas, un orden de magnitud mejor en calidad de aproximación, y cuya aplicación a problemas reales de predespacho de unidades genera mejores resultados respecto de las aproximaciones tradicionales. Por último, con el fin de mejorar el desempeño de la formulación entera-mixta presentada, se realiza el análisis poliedral de una de sus subestructuras esperando identificar desigualdades válidas que permitan mejorar su cota dual. Esta subestructura corresponde al knapsack semicontinuo con restricciones adicionales del tipo generalized upper bound. Se demuestra que bajo supuestos simples es posible identificar facetas tipo generalized flow cover en espacios restringidos de dimensión inferior. Luego se llevan estas desigualdades al espacio original utilizando procedimientos de lifting multidimensional independiente de la secuencia [38, 27, 16, 17] y se iii prueba que con supuestos adicionales también son facetas allí. Experimentos computacionales en instancias derivadas de problemas de UC muestran su eficiencia, donde más de un 50% del gap integral del nodo raíz se reduce aplicando en promedio solo tres de estos cortes. Además, en este contexto, también se ha implementado un solver ad-hoc para la solución eficiente de las relajaciones lineales de la formulación tipo red, con un speed-up del orden de 4x a 8x respecto a CPLEX barrier optimizer, pero que aún no está documentado.

Le développement des logiciels et leur restructuration deviennent de plus en plus complexes à cause de l'adoption massive des architectures parallèles, ce qui nécessite une expertise considérable de la part des développeurs. Bien que des nombreux modèles et langages de programmation permettent de créer des programmes efficaces, ils n'offrent pas de support spécifique à la restructuration des programmes existants afin d'en augmenter l'efficacité. En même temps, les approches automatiques sont trop conservatives et insuffisamment précises pour atteindre une partie substantielle de la performance du système sans que le développeur aie à fournir des informations sémantiques supplémentaires. Pour répondre à ces défis, nous adoptons l'approche de la restructuration interactive des programmes qui lie la manipulation semi-automatique des programmes avec la visualisation des logiciels. Dans cette thèse, l'approche de restructuration interactive est illustrée par l'extension du modèle polyédrique - une représentation des programmes moderne et puissante - pour permettre la manipulation de haut niveau ainsi que par la conception et l'évaluation d'une interface visuelle à manipulation directe pour la restructuration des programmes. Cette interface visualise l'information qui n'était pas immédiatement accessible dans la représentation textuelle et permet de manipuler des programmes sans en réécrire le code. Nous proposons également une représentation de l'optimisation de programme, calculée automatiquement, telle que le développeur puisse la comprendre et réutiliser facilement ainsi que la modifier d'une manière textuelle ou visuelle dans le cadre du partenariat homme-machine. Afin de représenter plusieurs aspects de la restructuration des programmes, nous concevons et évaluons une nouvelle interaction qui permet de communiquer l'information supplémentaire et non-cruciale pour la tâche à accomplir. Après une étude empirique de la distribution d'attention des développeurs face aux représentations textuelles et visuelles des programmes, nous discutons des implications pour la conception des outils d'aide à la programmation dans le cadre du modèle d'interaction instrumentale. La restructuration interactive des programmes est supposée faciliter la manipulation des programmes dans le but d'optimisation, la rendre plus efficace et plus largement adopté. / Software development and program manipulation become increasingly complex with the massive adoption of parallel architectures, requiring significant expertise from developers. While numerous programming models and languages allow for creating efficient programs, they fall short at helping developers to restructure existing programs for more effective execution. At the same time, automatic approaches are overly conservative and imprecise to achieve a decent portion of the systems' performance without supplementary semantic information from the developer. To answer these challenges, we propose the interactive program restructuring approach, a bridge between semi-automatic program manipulation and software visualization. It is illustrated in this thesis by, first, extending a state-of-the-art polyhedral model for program representation so that it supports high-level program manipulation and, second, by designing and evaluating a direct manipulation visual interface for program restructuring. This interface provides information about the program that was not immediately accessible in the code and allows to manipulate programs without rewriting. We also propose a representation of an automatically computed program optimization in an understandable form, easily modifiable and reusable by the developer both visually and textually in a sort of human-machine partnership. To support different aspects of program restructuring, we design and evaluate a new interaction to communicate supplementary information, not critical for the task at hand. After an empirical study of developers' attention distribution when faced with visual and textual program representation, we discuss the implications for design of program manipulation tools in the instrumental interaction paradigm. We expect interactive program restructuring to make program manipulation for optimization more efficient and widely adopted.

付記する学位プログラム名: 充実した健康長寿社会を築く総合医療開発リーダー育成プログラム / 京都大学 / 新制・課程博士 / 博士(工学) / 甲第23227号 / 工博第4871号 / 新制||工||1760(附属図書館) / 京都大学大学院工学研究科高分子化学専攻 / (主査)教授 田中 一生, 教授 秋吉 一成, 教授 古賀 毅 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

No description available.