Rozprawy doktorskie: „Mathematical programming”

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Koch, Thorsten. "Rapid mathematical programming". [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=973541415.

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Moreno, Dávila Julio Moreno Davila Julio. "Mathematical programming for logic inference /". [S.l.] : [s.n.], 1990. http://library.epfl.ch/theses/?nr=784.

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Sharifi, Mokhtarian Faranak. "Mathematical programming with LFS functions". Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=56762.

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Differentiable functions with a locally flat surface (LFS) have been recently introduced and studied in convex optimization. Here we extend this motion in two directions: to non-smooth convex and smooth generalized convex functions. An important feature of these functions is that the Karush-Kuhn-Tucker condition is both necessary and sufficient for optimality. Then we use the properties of linear LFS functions and basic point-to-set topology to study the "inverse" programming problem. In this problem, a feasible, but nonoptimal, point is made optimal by stable perturbations of the parameters. The results are applied to a case study in optimal production planning.

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Steffy, Daniel E. "Topics in exact precision mathematical programming". Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39639.

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The focus of this dissertation is the advancement of theory and computation related to exact precision mathematical programming. Optimization software based on floating-point arithmetic can return suboptimal or incorrect resulting because of round-off errors or the use of numerical tolerances. Exact or correct results are necessary for some applications. Implementing software entirely in rational arithmetic can be prohibitively slow. A viable alternative is the use of hybrid methods that use fast numerical computation to obtain approximate results that are then verified or corrected with safe or exact computation. We study fast methods for sparse exact rational linear algebra, which arises as a bottleneck when solving linear programming problems exactly. Output sensitive methods for exact linear algebra are studied. Finally, a new method for computing valid linear programming bounds is introduced and proven effective as a subroutine for solving mixed-integer linear programming problems exactly. Extensive computational results are presented for each topic.

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5

Smith, Barbara Mary. "Bus crew scheduling using mathematical programming". Thesis, University of Leeds, 1986. http://etheses.whiterose.ac.uk/1053/.

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This thesis describes a bus crew scheduling system, IMPACS, which has been demonstrated to be successful for a wide variety of scheduling conditions, and is at present in regular use by three British bus companies including the largest, London Buses Ltd. The background to the bus crew scheduling problem 1S described and the existing literature on methods for solution is reviewed. In IMPACS, the crew scheduling problem is formulated as an integer linear programme using a formulation which is an extension of set covering; a very large set of possible duties is generated, from which the duties forming the schedule are selected in such a way as to minimise the total cost. The variables of the set covering problem correspond to the duties generated and the constraints to the pieces of work in the bus schedule. For realistic schedules, it is impossible to generate all legal duties, and there are often too many pieces of work to allow each one to give rise to a constraint. IMPACS contains several heuristic methods which reduce the set covering problem to a manageable size, while still allowing good quality schedules to be compiled. Techniques for speeding up the solution of the set covering problem have been investigated, and in particular a branching strategy which exploits features of the crew scheduling problem has been developed.

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Aras, Raghav. "Mathematical programming methods for decentralized POMDPs". Thesis, Nancy 1, 2008. http://www.theses.fr/2008NAN10092/document.

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Nous étudions le problème du contrôle optimale décentralisé d'un processus de Markoff partiellement observé sur un horizon fini. Mathématiquement, ce problème se défini comme un DEC-POMDP. Plusieurs problèmes des domaines de l'intélligence artificielles et recherche opérationelles se formalisent comme des DEC-POMDPs. Résoudre un DEC-POMDP dans une mannière exacte est un problème difficile (NEXP-dur). Pourtant, des algorithmes exactes sont importants du point de vue des algorithmes approximés pour résoudre des problèmes pratiques. Les algorithmes existants sont nettement inefficace même pour des DEC-POMDP d'une très petite taille. Dans cette thèse, nous proposons une nouvelle approche basée sur la programmation mathématique. En utilisant la forme séquentielle d'une politique, nous montrons que ce problème peut être formalisé comme un programme non-linéaire. De plus, nous montrons comment transformer ce programme nonl-linéaire un des programmes linéaire avec des variables bivalents et continus (0-1 MIPs). L'éxpérience computationelle sur quatres problèmes DEC-POMDP standards montrent que notre approche trouve une politique optimale beaucoup plus rapidement que des approches existantes. Le temps réduit des heures aux seconds ou minutes
In this thesis, we study the problem of the optimal decentralized control of a partially observed Markov process over a finite horizon. The mathematical model corresponding to the problem is a decentralized POMDP (DEC-POMDP). Many problems in practice from the domains of artificial intelligence and operations research can be modeled as DEC-POMDPs. However, solving a DEC-POMDP exactly is intractable (NEXP-hard). The development of exact algorithms is necessary in order to guide the development of approximate algorithms that can scale to practical sized problems. Existing algorithms are mainly inspired from POMDP research (dynamic programming and forward search) and require an inordinate amount of time for even very small DEC-POMDPs. In this thesis, we develop a new mathematical programming based approach for exactly solving a finite horizon DEC-POMDP. We use the sequence form of a control policy in this approach. Using the sequence form, we show how the problem can be formulated as a mathematical progam with a nonlinear object and linear constraints. We thereby show how this nonlinear program can be linearized to a 0-1 mixed integer linear program (MIP). We present two different 0-1 MIPs based on two different properties of a DEC-POMDP. The computational experience of the mathematical programs presented in the thesis on four benchmark problems (MABC, MA-Tiger, Grid Meeting, Fire Fighting) shows that the time taken to find an optimal joint policy is one or two orders or magnitude lesser than the exact existing algorithms. In the problems tested, the time taken drops from several hours to a few seconds or minutes

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Aras, Raghav Charpillet François Dutech Alain. "Mathematical programming methods for decentralized POMDPs". S. l. : Nancy 1, 2008. http://www.scd.uhp-nancy.fr/docnum/SCD_T_2008_0092_ARAS.pdf.

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Hochreiter, Ronald. "Applied Mathematical Programming and Modelling 2016". edp sciences, 2017. http://dx.doi.org/10.1051/itmconf/20171400001.

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The 12th International Conference on Applied Mathematical Programming and Modelling (APMOD 2016) was held in Brno, Czech Republic in June 8-10, 2016. In this volume eight research papers are collected which depict the broad range of topics the conference series covers.

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Reeves, Laurence H. "Mathematical Programming Applications in Agroforestry Planning". DigitalCommons@USU, 1991. https://digitalcommons.usu.edu/etd/6495.

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Agroforestry as a sustainable production system has been recognized as a land use system with the potential to slow encroachment of agriculture onto forested lands in developing countries. However, the acceptance of nontraditional agroforestry systems has been hampered in some areas due to the risk-averse nature of rural agriculturalists. By explicitly recognizing risk in agroforestry planning, a wider acceptance of agroforestry is possible. This thesis consists of a collection of three papers that explore the potential of modern stock portfolio theory to reduce financial risk in agroforestry planning. The first paper presents a theoretical framework that incorporates modern stock portfolio theory through mathematical programming. This framework allows for the explicit recognition of financial risk by using a knowledge of past net revenue trends and fluctuations for various cropping systems, with the assumption that past trend behavior is indicative of future behavior. The paper demonstrates how financial risk can be reduced by selecting cropping systems with stable and/or negatively correlated net revenues, thereby reducing the variance of future net revenues. Agroforestry systems generally entail growing simultaneously some combination of plant and/or animal species. As a result, interactions between crops usually cause crop yields within systems to deviate from what would be observed under monocultural conditions, thus requiring some means of incorporating these interactions into mathematical models. The second paper presents two approaches to modeling such interactions, depending on the nature of the interaction. The continuous system approach is appropriate under conditions where yield interactions are linear between crops and allows for a continuous range of crop mixtures. The discrete system approach should be used where nonlinear interactions occur. Under this second approach, decision variables are defined as fixed crop mixtures with known yields. In the third paper, the techniques presented above were applied to a case study site in Costa Rica. Using MOTAD programming and a discrete system approach, a set of minimum-risk farm plans were derived for a hypothetical farm. For the region studied, results indicate that reductions in risk require substantial reductions in expected net revenue.

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Violin, Alessia. "Mathematical programming approaches to pricing problems". Doctoral thesis, Università degli studi di Trieste, 2014. http://hdl.handle.net/10077/10863.

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2012/2013
There are many real cases where a company needs to determine the price of its products so as to maximise its revenue or profit. To do so, the company must consider customers’ reactions to these prices, as they may refuse to buy a given product or service if its price is too high. This is commonly known in literature as a pricing problem. This class of problems, which is typically bilevel, was first studied in the 1990s and is NP-hard, although polynomial algorithms do exist for some particular cases. Many questions are still open on this subject. The aim of this thesis is to investigate mathematical properties of pricing problems, in order to find structural properties, formulations and solution methods that are as efficient as possible. In particular, we focus our attention on pricing problems over a network. In this framework, an authority owns a subset of arcs and imposes tolls on them, in an attempt to maximise his/her revenue, while users travel on the network, seeking for their minimum cost path. First, we provide a detailed review of the state of the art on bilevel pricing problems. Then, we consider a particular case where the authority is using an unit toll scheme on his/her subset of arcs, imposing either the same toll on all of them, or a toll proportional to a given parameter particular to each arc (for instance a per kilometre toll). We show that if tolls are all equal then the complexity of the problem is polynomial, whereas in case of proportional tolls it is pseudo-polynomial. We then address a robust approach taking into account uncertainty on parameters. We solve some polynomial cases of the pricing problem where uncertainty is considered using an interval representation. Finally, we focus on another particular case where toll arcs are connected such that they constitute a path, as occurs on highways. We develop a Dantzig-Wolfe reformulation and present a Branch-and-Cut-and-Price algorithm to solve it. Several improvements are proposed, both for the column generation algorithm used to solve the linear relaxation and for the branching part used to find integer solutions. Numerical results are also presented to highlight the efficiency of the proposed strategies. This problem is proved to be APX-hard and a theoretical comparison between our model and another one from the literature is carried out.
Un problème classique pour une compagnie est la tarification de ses produits à vendre sur le marché, de façon à maximiser les revenus. Dans ce contexte, il est important que la société prenne en compte le comportement de ses clients potentiels, puisque si le prix est trop élevé, ils peuvent décider de ne rien acheter. Ce problème est communément connu dans la littérature comme un problème de tarification ou "pricing". Une approche de programmation biniveau pour ce problème a été introduite dans les années 90, révélant sa difficulté. Cependant, certains cas particuliers peuvent être résolus par des algorithmes polynomiaux, et il y a encore de nombreuses questions ouvertes sur le sujet. Cette thèse de doctorat porte sur les propriétés mathématiques des problèmes de tarification, fixant l’objectif de déterminer différentes formulations et méthodes de résolution les plus efficaces possibles, en se concentrant sur les problèmes appliqués aux réseaux de différents types. Dans les problèmes de tarification sur réseau, nous avons deux entités : une autorité qui possède un certain sous-ensemble d’arcs, et impose des péages, avec l’intention de maximiser les revenus provenant de celle-ci, et des utilisateurs qui choisissent leur chemin de moindre coût sur l’ensemble du réseau. Dans la première partie de la thèse une analyse détaillée de l’état de l’art sur les problèmes de tarification biniveau est présentée, suivie, dans la deuxième partie, par une analyse de cas particuliers polynomiaux. En particulier, nous considérons le cas où l’autorité utilise un péage unitaire sur son sous-ensemble d’arcs, soit en choisissant le même péage sur chaque arc, soit en choisissant un péage proportionnel à un paramètre donné pour chaque arc (par exemple, un péage par kilomètre). Dans le premier cas de péages égaux, il est démontré que la complexité du problème est polynomiale, tandis que dans le second cas de péages proportionnels, elle est pseudo-polynomiale. Ensuite, nous présentons une première approche d’optimisation robuste pour les problèmes de tarification sur réseau, de manière à inclure de l’incertitude sur la valeur exacte des paramètres dans le modèle, qui est typique dans les problèmes réels. Cette incertitude est représentée en utilisant des intervalles pour les paramètres et nous proposons, pour certains cas, des algorithmes de résolution polynomiaux. La troisième et dernière partie de la thèse concerne un cas difficile, le problème de tarification sur réseau dans lequel les arcs sont connectés de manière à constituer un chemin, comme c’est le cas pour les autoroutes. Initialement, nous prouvons que ce problème est APX-dur, renforçant le résultat connu jusqu’à maintenant. Ensuite, nous présentons des nouvelles formulations plus fortes, et en particulier, nous développons une reformulation de type Danztig-Wolfe, résolue par un algorithme de Branch-and-Cut-and-Price. Enfin, nous proposons différentes stratégies pour améliorer les performances de l’algorithme, pour ce qui concerne l’algorithme de génération de colonnes utilisé pour résoudre la relaxation linéaire, et pour ce qui concerne la résolution du problème avec variables binaires. Les résultats numériques complètent les résultats théoriques, en mettant en évidence l’efficacité des stratégies proposées.
Un classico problema aziendale è la determinazione del prezzo dei prodotti da vendere sul mercato, in modo tale da massimizzare le entrate che ne deriveranno. In tale contesto è importante che l’azienda tenga in considerazione il comportamento dei propri potenziali clienti, in quanto questi ultimi potrebbero ritenere che il prezzo sia troppo alto e decidere dunque di non acquistare. Questo problema è comunemente noto in letteratura come problema di tariffazione o di “pricing”. Tale problema è stato studiato negli anni novanta mediante un approccio bilivello, rivelandone l’alta complessità computazionale. Tuttavia alcuni casi particolari possono essere risolti mediante algoritmi polinomiali, e ci sono sono ancora molte domande aperte sull’argomento. Questa tesi di dottorato si focalizza sulle proprietà matematiche dei problemi di tariffazione, ponendosi l’obiettivo di determinarne formulazioni e metodi risolutivi più efficienti possibili, concentrandosi sui problemi applicati a reti di vario tipo. Nei problemi di tariffazione su rete si hanno due entità: un’autorità che possiede un certo sottoinsieme di archi e vi impone dei pedaggi, con l’intento di massimizzare le entrate che ne derivano, e gli utenti che scelgono il proprio percorso a costo minimo sulla rete complessiva (a pedaggio e non). Nella prima parte della tesi viene affrontata una dettagliata analisi dello stato dell’arte sui problemi di tariffazione bilivello, seguita, nella seconda parte, dall’analisi di particolari casi polinomiali del problema. In particolare si considera il caso in cui l’autorità utilizza uno schema di pedaggio unitario sul suo sottoinsieme di archi, imponendo o lo stesso pedaggio su ogni arco, o un pedaggio proporzionale a un dato parametro relativo ad ogni arco (ad esempio un pedaggio al chilometro). Nel primo caso di pedaggi uguali, si dimostra che la complessità del problema è polinomiale, mentre nel secondo caso di pedaggi proporzionali è pseudo-polinomiale. In seguito viene affrontato un approccio di ottimizzazione robusta per alcuni problemi di tariffazione su rete, in modo da includere nei modelli un’incertezza sul valore esatto dei parametri,tipica dei problemi reali. Tale incertezza viene rappresentata vincolando i parametri in degli intervalli e si propongono, per alcuni casi, algoritmi risolutivi polinomiali. La terza e ultima parte della tesi riguarda un caso computazionalmente difficile, in cui gli archi tariffabili sono connessi in modo tale da costituire un cammino, come avviene per le autostrade. Inizialmente si dimostra che tale problema è APX-hard, rafforzando il risultato finora conosciuto. In seguito si considerano formulazioni piùforti, e in particolare si sviluppa una riformulazione di Danztig-Wolfe, risolta tramite un algoritmo di Branch-and-Cut-and-Price. Infine si propongono diverse strategie per migliorare le performance dell’algoritmo, sia per quanto riguarda l’algoritmo di generazione di colonne utilizzato per risolvere il rilassamento lineare, sia per quanto riguarda la risoluzione del problema con variabili binarie. Risultati numerici complementano quelli teorici ed evidenziano l’efficacia delle strategie proposte.
XXV Ciclo
1985

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11

Violin, Alessia. "Mathematical programming approaches to pricing problems". Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209173.

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There are many real cases where a company needs to determine the price of its products so as to maximise its revenue or profit.

To do so, the company must consider customers' reactions to these prices, as they may refuse to buy a given product or service if its price is too high. This is commonly known in literature as a pricing problem.

This class of problems, which is typically bilevel, was first studied in the 1990s and is NP-hard, although polynomial algorithms do exist for some particular cases. Many questions are still open on this subject.

The aim of this thesis is to investigate mathematical properties of pricing problems, in order to find structural properties, formulations and solution methods that are as efficient as possible. In particular, we focus our attention on pricing problems over a network. In this framework, an authority owns a subset of arcs and imposes tolls on them, in an attempt to maximise his/her revenue, while users travel on the network, seeking for their minimum cost path.

First, we provide a detailed review of the state of the art on bilevel pricing problems.

Then, we consider a particular case where the authority is using an unit toll scheme on his/her subset of arcs, imposing either the same toll on all of them, or a toll proportional to a given parameter particular to each arc (for instance a per kilometre toll). We show that if tolls are all equal then the complexity of the problem is polynomial, whereas in case of proportional tolls it is pseudo-polynomial.

We then address a robust approach taking into account uncertainty on parameters. We solve some polynomial cases of the pricing problem where uncertainty is considered using an interval representation.

Finally, we focus on another particular case where toll arcs are connected such that they constitute a path, as occurs on highways. We develop a Dantzig-Wolfe reformulation and present a Branch-and-Cut-and-Price algorithm to solve it. Several improvements are proposed, both for the column generation algorithm used to solve the linear relaxation and for the branching part used to find integer solutions. Numerical results are also presented to highlight the efficiency of the proposed strategies. This problem is proved to be APX-hard and a theoretical comparison between our model and another one from the literature is carried out.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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Bettinelli, A. "MATHEMATICAL PROGRAMMING ALGORITHMS FOR TRANSPORTATION PROBLEMS". Doctoral thesis, Università degli Studi di Milano, 2010. http://hdl.handle.net/2434/150079.

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The thesis deals with the study of transportation problems, and in particular focuses on developing new exact and heuristic algorithms for two interesting variants of the well known Vehicle Routing Problem: the multi-depot heterogeneous-fleet vehicle routing problem with time windows and the multi-depot heterogeneous-fleet pickup and delivery problem with soft time windows. The studied problems consider additional real-world requirements, often neglected in the literature. They lead to more involved problems but on the other hand more realistic ones, that call for powerful optimization methods in order to tackle such difficult applications. The proposed algorithms are based on mathematical programming techniques, such as branch-and-price, column generation and dynamic programming. The performance of the algorithms is analyzed with extensive computational experiments and compared with the most effective algorithms from the literature, showing the usefulness of the proposed methods.

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Costa, Alberto. "Applications of Reformulations in Mathematical Programming". Phd thesis, Palaiseau, Ecole polytechnique, 2012. https://pastel.hal.science/docs/00/74/60/83/PDF/Phd_Costa.pdf.

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La programmation mathématique est une technique qui peut être utilisée pour résoudre des problèmes concrets où l'on veut maximiser, ou minimiser, une fonction objectif soumise à des contraintes sur les variables décisionnelles. Les caractéristiques les plus importantes de la programmation mathématique sont la création d'un modèle pour décrire le problème (aussi appelé formulation), et la mise en œuvre d'algorithmes efficaces pour le résoudre (aussi appelés solveurs). Dans cette thèse, on s'occupe du premier point. Plus précisemment, on étudie certains problèmes qui proviennent de domaines diffèrents, et en commençant par les modèles les plus naturels pour les décrire, on présente des formulations alternatives, qui partagent certaines propriétés avec le modèle original mais qui sont en quelque sorte meilleures (par exemple au niveau du temps d'exécution nécessaire pour obtenir la solution par le solveur). Ces nouveaux modèles sont appelés reformulations. On suit la classification des reformulations proposée par Liberti dans [Reformulations in Mathematical Programming: Definitions and Systematics, RAIRO-OR, 43(1):55-86, 2009]: exact reformulations (aussi appellées opt-reformulations), narrowings, relaxations. Cette thèse concerne trois applications de la programmation mathématique où les reformulations ont été fondamentales pour obtenir une bonne solution. Le premier problème étudié est le partitionnement de graphes sur la base de la maximisation de la modularité. Comme ce problème est NP-difficile, plusieurs heuristiques sont proposées. On s'occupe d'un algorithme séparatif hiérarchique qui fonctionne en divisant récursivement une classe en deux nouvelles classes de façon optimale. Cet étape de division est accomplie en résolvant un programme binaire quadratique et convexe. Il est reformulé de manière exacte pour obtenir une forme plus compacte sans modifier l'ensemble des solutions optimales (exact reformulation). On considère aussi l'impact donné par la réduction du nombre des solutions symétriques globalement optimales. Les temps d'exécution sont considérablement réduits par rapport à la formulation originelle. Le deuxième problème étudié dans cette thèse est le placement de cercles égaux dans un carré (Packing Equal Circles in a Square, ou PECS), où l'on veut placer des cercles égaux dans un carré de côté 1 sans avoir de superposition et en maximisant le rayon commun. L'une des raisons pour laquelle le problème est difficile à résoudre vient de la présence de plusieurs solutions symétriques optimales, et par conséquent un arbre de séparation-et-évaluation (ou Branch-and-Bound) très large. Certaines solutions symétriques optimales sont rendues irréalisables en ajoutant des contraintes pour briser les symétries (Symmetry Breaking Constraints, ou SBCs) à la formulation, en obtenant ainsi un narrowing. Le temps d'exécution et la dimension de l'arbre de Branch-and-Bound sont tous les deux meilleurs par rapport à la formulation originelle. La troisième application considérée dans cette thèse est le calcul de la relaxation convexe pour des problèmes multilinéaires, et la comparaison de la formulation ''primale'' avec celle obtenue par une représentation ''duale''. Bien que ces deux relaxations soient déjà connues, il est intéressant de voir que la relaxation duale conduit à des meilleures performances de calcul
Mathematical programming is a technique that can be used to solve real-world optimization problems, where one wants to maximize, or minimize, an objective function subject to some constraints on the decision variables. The key features of mathematical programming are the creation of a model for describing the problem (the so called formulation), and the implementation of efficient algorithms to solve it (also called solvers). In this thesis, we focus on the first point. More precisely, we study some problems arising from different domains, and starting from the most natural models for describing them, we propose alternative formulations, which share some properties with the original models but are somehow better (for instance in terms of computational time needed to obtain the solution by the solver). These new models are called reformulations. We follow the classification of reformulations proposed by Liberti in [Reformulations in Mathematical Programming: Definitions and Systematics, RAIRO-OR, 43(1):55-86, 2009]: exact reformulations (also called opt-reformulations), narrowings, relaxations. This thesis is concerned with three mathematical programming applications where the reformulation was crucial to obtain a good solution. The first problem tackled herein is graph clustering by means of modularity maximization. Since this problem is NP-hard, several heuristics are proposed. We focus on a divisive hierarchical algorithm which works by recursively splitting a cluster into two new clusters in an optimal way. This splitting step is performed by solving a convex binary quadratic program. This is reformulated exactly to a more compact form without changing the optimal solutions set (exact reformulation). We also evaluate the impact provided by the reduction of the number of symmetric global optima of the problem, which is also an important topic of the next part of this thesis. The computational times are considerably reduced with respect to the original formulation. The second problem tackled in the thesis is the Packing of Equal Circles in a Square (PECS), where one wants to place non-overlapping equal circles in a unit square in such a way as to maximize the common radius. One of the reasons why the problem is hard to solve is the presence of several symmetric optimal solutions, and consequently a very large Branch-and-Bound tree. Some of the symmetric optima are made infeasible by adjoining some Symmetry Breaking Constraints (SBCs) to the formulation, thereby obtaining a narrowing. Both computational time and size of the Branch-and-Bound tree outperform the ones provided by the original formulation. The third application considered in the thesis is that of computing the convex relaxation for multilinear problems, and to compare the "primal" formulation and another one obtained using a "dual" representation. Although these two relaxations are both already known in the literature, we make a striking observation, i. E. , that the dual relaxation leads to a faster and more stable solution process as regards CPU time

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14

Costa, Alberto. "Applications of Reformulations in Mathematical Programming". Phd thesis, Ecole Polytechnique X, 2012. http://pastel.archives-ouvertes.fr/pastel-00746083.

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La programmation mathématique est une technique qui peut être utilisée pour résoudre des problèmes concrets où l'on veut maximiser, ou minimiser, une fonction objectif soumise à des contraintes sur les variables décisionnelles. Les caractéristiques les plus importantes de la programmation mathématique sont la création d'un modèle pour décrire le problème (aussi appelé formulation), et la mise en œuvre d'algorithmes efficaces pour le résoudre (aussi appelés solveurs). Dans cette thèse, on s'occupe du premier point. Plus précisemment, on étudie certains problèmes qui proviennent de domaines diffèrents, et en commençant par les modèles les plus naturels pour les décrire, on présente des formulations alternatives, qui partagent certaines propriétés avec le modèle original mais qui sont en quelque sorte meilleures (par exemple au niveau du temps d'exécution nécessaire pour obtenir la solution par le solveur). Ces nouveaux modèles sont appelés reformulations. On suit la classification des reformulations proposée par Liberti dans [Reformulations in Mathematical Programming: Definitions and Systematics, RAIRO-OR, 43(1):55-86, 2009]: exact reformulations (aussi appellées opt-reformulations), narrowings, relaxations. Cette thèse concerne trois applications de la programmation mathématique où les reformulations ont été fondamentales pour obtenir une bonne solution. Le premier problème étudié est le partitionnement de graphes sur la base de la maximisation de la modularité. Comme ce problème est NP-difficile, plusieurs heuristiques sont proposées. On s'occupe d'un algorithme séparatif hiérarchique qui fonctionne en divisant récursivement une classe en deux nouvelles classes de façon optimale. Cet étape de division est accomplie en résolvant un programme binaire quadratique et convexe. Il est reformulé de manière exacte pour obtenir une forme plus compacte sans modifier l'ensemble des solutions optimales (exact reformulation). On considère aussi l'impact donné par la réduction du nombre des solutions symétriques globalement optimales. Les temps d'exécution sont considérablement réduits par rapport à la formulation originelle. Le deuxième problème étudié dans cette thèse est le placement de cercles égaux dans un carré (Packing Equal Circles in a Square, ou PECS), où l'on veut placer des cercles égaux dans un carré de côté 1 sans avoir de superposition et en maximisant le rayon commun. L'une des raisons pour laquelle le problème est difficile à résoudre vient de la présence de plusieurs solutions symétriques optimales, et par conséquent un arbre de séparation-et-évaluation (ou Branch-and-Bound) très large. Certaines solutions symétriques optimales sont rendues irréalisables en ajoutant des contraintes pour briser les symétries (Symmetry Breaking Constraints, ou SBCs) à la formulation, en obtenant ainsi un narrowing. Le temps d'exécution et la dimension de l'arbre de Branch-and-Bound sont tous les deux meilleurs par rapport à la formulation originelle. La troisième application considérée dans cette thèse est le calcul de la relaxation convexe pour des problèmes multilinéaires, et la comparaison de la formulation ''primale'' avec celle obtenue par une représentation ''duale''. Bien que ces deux relaxations soient déjà connues, il est intéressant de voir que la relaxation duale conduit à des meilleures performances de calcul.

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15

Borg, Andreas. "Designing for the incorporation of programming in mathematical education : Programming as an instrument for mathematical problem solving". Licentiate thesis, Karlstads universitet, Institutionen för pedagogiska studier (from 2013), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-85625.

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This study explored Swedish upper secondary school students’ use of programming for mathematical purposes. The aim of the study was to investigate the process through which students learn how to use a programming environment as a technical artefact during mathematical problem solving and how the orchestration of such learning situations could facilitate this process. In order to study the students’ use of the programming environment, design-based research was used as the main methodological approach. The design involved the development of specific mathematical tasks to be tried out with students, as well as the orchestration of the learning situation within the classroom e.g., by preparing scaffolding to be offered to the students. The subsequent implementation of the design was analysed so that, in accordance with the cyclic approach of design-based research, it could be revised ahead of the following design cycle. The study involved two complete design cycles. In the study, the Instrumental Approach was used as the theoretical framework and the instrumental genesis of the students in using a programming environment for mathematical purposes was thus of special interest. In order to analyse this process and the associated mental schemes developed by the students, Vergnaud’s concept of scheme served as an analytical framework. The findings revealed how the students, despite having basic knowledge in programming, experienced several difficulties when trying to use the programming environment as a technical mathematical artefact. These difficulties were related both to the fact that the mathematical affordances offered by the programming environment were unclear to many of the students, as well as to the handling of more specific computational concepts such as nested loops. The findings also revealed that the transformation of mathematical notations and ideas into programming code caused students difficulties.
This study explored Swedish upper secondary school students’ use of programming for mathematical purposes. The aim of the study was to investigate the process through which students learn how to use a programming environment as a technical artefact during mathematical problem solving and how the orchestration of such learning situations could facilitate this process. In order to study the students’ use of the programming environment, design-based research was used as the main methodological approach and the Instrumental Approach served as the theoretical framework. The design involved the development of mathematical tasks to be tried out with students, as well as the orchestration of the learning situation within the classroom. The findings revealed how the students experienced several difficulties when trying to use the programming environment as a technical mathematical artefact. These difficulties were related to the fact that the mathematical affordances offered by the programming environment initially were unclear to many of the students, as well as to the handling of more specific computational concepts such as nested loops. The findings also revealed that the transformation of mathematical notations and ideas into programming code caused students difficulties.

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Heipcke, Susanne. "Combined modelling and problem solving in mathematical programming and constraint programming". Thesis, University of Buckingham, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.297665.

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Sundbom, Tobias. "Mathematical programming based approaches in credit scoring". Thesis, Uppsala University, Department of Mathematics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-120980.

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Chuang, Poon-Hwei. "Fuzzy mathematical programming in civil engineering systems". Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/7802.

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Nahum, Carole. "Second order sensitivity analysis in mathematical programming". Thesis, McGill University, 1989. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74349.

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We consider a nonlinear mathematical program, with twice continuously differentiable functions.
If a point x$ sb0$ does not satisfy a certain Second Order Sufficient Condition (SOS) for optimality (that does not require any constraint qualification, see, e.g., BEN-ISRAEL, BEN-TAL and ZLOBEC (81)), then we prove that the knowledge of the second order properties (derivative, Hessian) of the functions is not enough to conclude that the point is optimal.
When the functions are continuously perturbed, what is the local behavior of an optimal solution x$ sb0$ and of the associate optimal value? The stability and sensitivity of the mathematical model are addressed. We present a new method for solving this problem. Our approach does not rely on the classical Lagrangian coefficients (which cannot be always defined) but rather on power series expansions because we use the primal formulations of optimality.
In the regular case, when Strict complementarity slackness holds, we recover Fiacco's results (FIACCO (83)). On the other hand, when Strict complementarity slackness does not hold, we extensively generalize Shapiro's Theorems (SHAPIRO (85)) since we do not assume Robinson's second order condition (ROBINSON (80)) but the SOS condition.
In the non-regular case, no general algorithm for computing the derivative of the optimizing point with respect to the parameters had been presented up to now.
The approach is extended to analyze the evolution of the set of Pareto minima of a multiobjective nonlinear program. In particular, we define the derivative of a point-to-set map. Our notion seems more adequate than the contingent derivative (AUBIN (81)), though the latter can easily be deduced from the former. This allows to get information about the sensitivity of the set of Pareto minima. A real-life example shows the usefulness and the simplicity of our results. Also, an application of our method to industry planning (within a general framework of Input Optimization) is made in the ideal case of a linear model.

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Patsiatzis, Dimitrios. "Optimal process plant layout using mathematical programming". Thesis, University College London (University of London), 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.406748.

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Esche, Alexander. "Mathematical Programming and Magic| The Gathering(RTM)". Thesis, Northern Illinois University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10689404.

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In this paper mathematical programming techniques were used to determine the optimal strategy for playing Magic: The Gathering^®. Games with the cards Lightning Bolt, Mountain, and Vexing Devil were evaluated using the minimax algorithm to determine the winner when all information about the cards is assumed known to both players. Computation time was shortened through the use of an evaluation function, a random forest algorithm that had been trained on 1000 completed games. A winning percentage was established for each pair of decks where the number of creatures was less than eight. Using linear programming, the optimal mixed strategy was then calculated. By repeating the simulations, a standard deviation for the winning percentages was estimated. Techniques from robust optimization were then used to determine the optimal strategy under different possible variations. Last, an imperfect information player was constructed that made choices based on guessing the order of the cards in its deck and the composition of the opponent's deck, playing through the perfect information games of these guesses, and making the choice that won in most of these simulations. With decks of eight or fewer creatures, this imperfect information player played below or near a player who used an aggressive heuristic. When the number of possible creatures was increased to 16, the imperfect information player's performance was better than the aggressive heuristic.

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Viaud, Quentin. "Mathematical programming methods for complex cutting problems". Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0350.

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Cette thèse s’intéresse à un problème de bin-packing en deux dimensions avec des défauts sur les bins rencontré dans l’industrie verrière. Les plans de découpe sont guillotine 4-stage exact, les objets à couper sans défauts.Une possible résolution utilise la décomposition de Dantzig-Wolfe puis une génération de colonnes et un branch-and-price. Cela est impossible dans notre cas du fait d’instances de trop grande taille. Nous résolvons d’abord le problème de pricing sans défauts par un algorithme incrémental de labelling basé sur un programme dynamique (DP), représenté par un problème de flot dans un hypergraphe. Notre méthode est générique pour les problèmes de sac-à-dos guillotine mais ne résout pas de larges instances en un temps de calcul raisonnable. Nous résolvons alors le problème de bin-packing sans défauts grâce à un DP et une heuristique de diving. Le DP génère des colonnes “non propres”,ne pouvant pas participer à une solution entière. Nous adaptons le diving pour ce cas sans perte d’efficacité. Nous l’étendons alors au cas avec défauts. Nous réparons d’abord heuristiquement une solution du problème sans défauts. La fixation des colonnes dans le diving sans-défaut est ensuite modifiée pour gérer les défauts. Les résultats industriels valident nos méthodes
This thesis deals with a two-dimensional bin-packing problem with defects on bins from the glass industry. Cutting patterns have to be exact 4-stage guillotine and items defect-free. A standard way to solve it isto use Dantzig-Wolfe reformulation with column generation and branch-and price.This is impossible in our case due to large instance size. We first study and solve the defect-free pricing problem with an incremental labelling algorithm based on a dynamic program (DP), represented as a flow problem in a hypergraph. Our method is generic for guillotine knapsack problems but fails to solve large instance in a short amount of time. Instead we solve the defect freebin-packing problem with a DP and a diving heuristic. This DP generatesnon-proper columns, cutting patterns that cannot be in an integer solution.We adapt standard diving heuristic to this “non-proper” case while keeping itseffectiveness. We then extend the diving heuristic to deal with defects. Ourfirst proposal heuristically repairs a given defect-free solution. Secondly the defect-free diving heuristic is adjusted to handle defects during column fixing.Our industrial results outline the effectiveness of our methods

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Colombo, F. "MATHEMATICAL PROGRAMMING ALGORITHMS FOR NETWORK OPTIMIZATION PROBLEMS". Doctoral thesis, Università degli Studi di Milano, 2014. http://hdl.handle.net/2434/234164.

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In the thesis we consider combinatorial optimization problems that are defined by means of networks. These problems arise when we need to take effective decisions to build or manage network structures, both satisfying the design constraints and minimizing the costs. In the thesis we focus our attention on the four following problems: - The Multicast Routing and Wavelength Assignment with Delay Constraint in WDM networks with heterogeneous capabilities (MRWADC) problem: this problem arises in the telecommunications industry and it requires to define an efficient way to make multicast transmissions on a WDM optical network. In more formal terms, to solve the MRWADC problem we need to identify, in a given directed graph that models the WDM optical network, a set of arborescences that connect the source of the transmission to all its destinations. These arborescences need to satisfy several quality-of-service constraints and need to take into account the heterogeneity of the electronic devices belonging to the WDM network. - The Homogeneous Area Problem (HAP): this problem arises from a particular requirement of an intermediate level of the Italian government called province. Each province needs to coordinate the common activities of the towns that belong to its territory. To practically perform its coordination role, the province of Milan created a customer care layer composed by a certain number of employees that have the task to support the towns of the province in their administrative works. For the sake of efficiency, the employees of this customer care layer have been partitioned in small groups and each group is assigned to a particular subset of towns that have in common a large number of activities. The HAP requires to identify the set of towns assigned to each group in order to minimize the redundancies generated by the towns that, despite having some activities in common, have been assigned to different groups. Since, for both historical and practical reasons, the towns in a particular subset need to be adjacent, the HAP can be effectively modeled as a particular graph partitioning problem that requires the connectivity of the obtained subgraphs and the satisfaction of nonlinear knapsack constraints. - Knapsack Prize Collecting Steiner Tree Problem (KPCSTP): to implement a Column Generation algorithm for the MRWADC problem and for the HAP, we need also to solve the two corresponding pricing problems. These two problems are very similar, both of them require to find an arborescence, contained in a given directed weighted graph, that minimizes the difference between its cost and the prizes associated with the spanned nodes. The two problems differ in the side constraints that their feasible solutions need to satisfy and in the way in which the cost of an arborescence is defined. The ILP formulations and the resolution methods that we developed to tackle these two problems have many characteristics in common with the ones used to solve other similar problems. To exemplify these similarities and to summarize and extend the techniques that we developed for the MRWADC problem and for the HAP, we also considered the KPCSTP. This problem requires to find a tree that minimizes the difference between the cost of the used arcs and the profits of the spanned nodes. However, not all trees are feasible: the sum of the weights of the nodes spanned by a feasible tree cannot exceed a given weight threshold. In the thesis we propose a computational comparison among several optimization methods for the KPCSTP that have been either already proposed in the literature or obtained modifying our ILP formulations for the two previous pricing problems. - The Train Design Optimization (TDO) problem: this problem was the topic of the second problem solving competition, sponsored in 2011 by the Railway Application Section (RAS) of the Institute for Operations Research and the Management Sciences (INFORMS). We participated to the contest and we won the second prize. After the competition, we continued to work on the TDO problem and in the thesis we describe the improved method that we have obtained at the end of this work. The TDO problem arises in the freight railroad industry. Typically, a freight railroad company receives requests from customers to transport a set of railcars from an origin rail yard to a destination rail yard. To satisfy these requests, the company first aggregates the railcars having the same origin and the same destination in larger blocks, and then it defines a trip plan to transport the obtained blocks to their correct destinations. The TDO problem requires to identify a trip plan that efficiently uses the limited resources of the considered rail company. More formally, given a railway network, a set of blocks and the segments of the network in which a crew can legally drive a train, the TDO problem requires to define a set of trains and the way in which the given blocks can be transported to their destinations by these trains, both satisfying operational constraints and minimizing the transportation costs.

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Lee, Seungjae. "Mathematical programming algorithms for equilibrium road traffic assignment". Thesis, University College London (University of London), 1995. http://discovery.ucl.ac.uk/1318036/.

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The equilibrium approach to representing interactions between the supply and demand sides of traffic assignment has been used widely in the estimation of traffic flows on road networks. Although this approach is quite reasonable, there is a considerable gap between the observed and modelled values of cost and flow. This gap can be reduced by relaxing some of the restrictive assumptions behind the models used in order to enhance their realism. This study investigates the solutions of various advanced road traffic assignment models. Priority and signal controlled junctions are modelled in traffic assignment in order to enhance the realism of junction analysis. A multiclass assignment is modelled to represent different groups of users. These problems are known to be non-separable because traffic cannot be segmented in such a way that the costs incurred by any one segment vary only with the flow within that segment. Existence, uniqueness and stability properties of solutions to these problems are investigated. These analyses are important to know the reliability and repeatability of any solutions that are calculated. Analyses of these properties lead to some guidelines for using these detailed models. A number of new solution algorithms are developed to solve the resulting traffic assignment problems. These algorithms belong to the general category of simplicial decomposition which solves the problem by dividing it into two subproblems: a linear and a master subproblem which are solved alternately. One of the advantages of these algorithms is that they operate in a lower dimensional space than that of original feasible region and hence allow large-scale problems to be solved with improved accuracy and speed of convergence. These improved algorithms give many choices to the traffic management studies. Two substantial networks have been used to compare the performance of new algorithms on the various models developed. They have performed favourably by comparison with existing algorithms. A small example network has been used to investigate existence, uniqueness and stability properties using the models. In a priority controlled model, a unique stable solution has been obtained using the model whilst in a signal controlled model, multiple and unstable solutions have been obtained. In a multiclass model, a unique solution has been obtained in terms of the total class flow whilst multiple solutions have been obtained in terms of each class flow. These results correspond well to the theoretical analyses of these models, which has shown to have indeterminate behaviour and by the nature of these models assumed, the degree of non-separability is ordered according to priority controlled, multiclass and signal controlled models.

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COSTA, PEDRO FRANCA FERREIRA DA. "OPTIMIZATION OF THE OFFLOADING LOGISTICS USING MATHEMATICAL PROGRAMMING". PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=25301@1.

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O crescimento da produção diária de petróleo e os elevados custos envolvidos na logística de petróleo, mais precisamente na logística upstream, pela sua complexidade, e em particular, na logística de produção e ainda, somando-se a atual queda do preço do barril, resultam que os impactos econômicos que as falhas no processo logístico podem causar, tornam-se cada vez mais relevantes. Neste contexto, foi desenvolvido um modelo de programação linear que promove a otimização da operação de alivio de plataformas conjugada à programação da janela de atendimento das diversas embarcações a fim de não haja necessidade de interromper a produção de nenhuma plataforma e que todas as demandas sejam cumpridas. Em qualquer circunstância o método utilizado busca a minimização dos custos operacionais através da redução das distancias percorridas e do número de navios afretados. O modelo matemático foi aplicado em um estudo de caso composto por três cenários distintos. O resultado obtido fundamenta a tomada de decisão que definirá o numero de navios aliviadores a serem afretados durante um determinado período.
The growth of daily oil production and the high costs involved in oil logistics, specifically the upstream logistics and the production logistics itself, adding to the current downturn in oil prices, are becoming increasingly relevant considering the major economic impacts caused by eventual failure in logistics processes. In this context, a linear programming model was developed. It provides the optimization of offloading platforms operation coupled to the service window of various vessels, so there is no need to interrupt the production of any of those platforms, allowing that all demands are met. In any case, this method seeks to minimize operational costs by reducing the distances traveled and the number of chartered vessels. The mathematical model was applied in a case study consisting of three different scenarios. The result obtained allows effective decision making that will define the number of shuttle tankers to be chartered for a certain period of time.

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Al-Samara, Mohammad Ahmad. "Elastoplastic dynamics of skeletal structures by mathematical programming". Thesis, Imperial College London, 1986. http://hdl.handle.net/10044/1/37390.

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The thesis is concerned with investigating the role of mathematical programming in expressing the general theory of and facilitating effective computation for elasto-plastic skeletal structures subjected to deterministic sources of dynamic excitations, Static-kinematic duality, a common feature in the static analysis of structures, is extended to dynamic systems through the adoption of d'Alembert's principle. This allows the full use of graph theoretic methods for describing the fundamental structural relations in both mesh and nodal forms. For structures whose dynamic characteristics can be effectively described by a rigid-plastic constitutive law, mathematical programming formulations are presented. They are compared and contrasted with existing formulations, especially those associated with impact loading. Elasto-plastic structures are studied and their dynamic response is shown to be given by the solution of a differential linear complementarity problem. Four equivalent formulations are presented and are solved numerically through the use of direct integration methods. The effects of change of geometry may also be important in the dynamic analysis of structures. Firstly, for relatively small displacements, the method of fictitious forces is shown to lead to alternative mesh and nodal formulations. For large displacements, only the nodal method proves to be effective. An incremental differential linear complementarity problem is obtained and a suitable numerical solution procedure is proposed. Finally, a perturbation technique is established for solving the resulting differential equations and differential linear complementarity problems. It is proved that this technique is more general and flexible than the direct integration methods.

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Clemence, Robert D. "A type calculus for mathematical programming modeling languages". Thesis, Monterey, California : Naval Postgraduate School, 1990. http://handle.dtic.mil/100.2/ADA238160.

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Dissertation (Ph.D. in Operations Research)--Naval Postgraduate School, September 1990.
Dissertation supervisor: Bradley, Gordon H. "September 1990." Description based on title screen viewed on December 17, 2009. DTIC Descriptor(s): Mathematical models, sizes (dimensions), validation, models, programming languages, drug addiction, algebra, mathematical programming, language, junctions, calculus, homogeneity, integrated systems, mathematical logic. DTIC Identifier(s): Programming languages, mathematical models, calculus, linear programming. Author(s) subject terms: Data types, integrated modeling, linear programming, model validation, mathematical programming software, special purpose languages. Includes bibliographical references (p. 129-132). Also available in print.

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Vielma, Centeno Juan Pablo. "Mixed integer programming approaches for nonlinear and stochastic programming". Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29624.

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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010.
Committee Chair: Nemhauser, George; Committee Co-Chair: Ahmed, Shabbir; Committee Member: Bill Cook; Committee Member: Gu, Zonghao; Committee Member: Johnson, Ellis. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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Loucopoulos, Constantine. "Mathematical Programming Approaches to the Three-Group Classification Problem". Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc279363/.

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In the last twelve years there has been considerable research interest in mathematical programming approaches to the statistical classification problem, primarily because they are not based on the assumptions of the parametric methods (Fisher's linear discriminant function, Smith's quadratic discriminant function) for optimality. This dissertation focuses on the development of mathematical programming models for the three-group classification problem and examines the computational efficiency and classificatory performance of proposed and existing models. The classificatory performance of these models is compared with that of Fisher's linear discriminant function and Smith's quadratic discriminant function. Additionally, this dissertation investigates theoretical characteristics of mathematical programming models for the classification problem with three or more groups. A computationally efficient model for the three-group classification problem is developed. This model minimizes directly the number of misclassifications in the training sample. Furthermore, the classificatory performance of the proposed model is enhanced by the introduction of a two-phase algorithm. The same algorithm can be used to improve the classificatory performance of any interval-based mathematical programming model for the classification problem with three or more groups. A modification to improve the computational efficiency of an existing model is also proposed. In addition, a multiple-group extension of a mathematical programming model for the two-group classification problem is introduced. A simulation study on classificatory performance reveals that the proposed models yield lower misclassification rates than Fisher's linear discriminant function and Smith's quadratic discriminant function under certain data configurations. Data configurations, where the parametric methods outperform the proposed models, are also identified. A number of theoretical characteristics of mathematical programming models for the classification problem are identified. These include conditions for the existence of feasible solutions, as well as conditions for the avoidance of degenerate solutions. Additionally, conditions are identified that guarantee the classificatory non-inferiority of one model over another in the training sample.

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Shen, Yijiang. "Binary image restoration by positive semidefinite programming and signomial programming". Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/HKUTO/record/B39557431.

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Cregger, Michael L. "The general mixed-integer linear programming problem an empirical analysis /". Instructions for remote access. Click here to access this electronic resource. Access available to Kutztown University faculty, staff, and students only, 1993. http://www.kutztown.edu/library/services/remote_access.asp.

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Zhu, Yuntao. "Semidefinite programming under uncertainty". Online access for everyone, 2006. http://www.dissertations.wsu.edu/Dissertations/summer2006/y%5Fzhu%5F073106.pdf.

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Coetzee, Carla. "Mathematical thinking skills needed by first year programming students". Diss., University of Pretoria, 2016. http://hdl.handle.net/2263/60991.

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The aim of this qualitative study is to explore and describe the mathematical thinking skills that students require for a first level programming subject that forms part of the National Diploma in Information Communication Technology (ICT) at a University of Technology (UoT). Mathematics is an entry requirement for many tertiary programmes, including ICT courses, unfortunately the poor quality of schooling in South Africa limits learners' access to higher education. From the literature it is evident that students lack fluency in fundamental mathematical and problem-solving skills when they enter higher education. In this study, the concept of programming thinking skills is explored, described and linked to mathematical thinking skills. An instrument (Mathematical and Programming Thinking Skills Matrix for the Analysis of Programming Assessment) has been developed and used to analyse examination papers of a first-year programming subject (at TUT) in order to identify mathematical skills as these appear in programming assessments. Semi-structures interviews were conducted with first-year programming lecturers, examiners and moderators. The literature as well and the results of the analysed data indicated and confirmed that mathematical thinking skills are extremely important when learning to program. The results of the study indicate a strong relationship between mathematical thinking skills and programming thinking skills. The outcome of this study is therefore a set of mathematical thinking skills that needs to be developed when compiling a mathematics curriculum for first level programming students studying towards a National Diploma in ICT.
Dissertation (MEd)--University of Pretoria, 2016.
Science, Mathematics and Technology Education
MEd
Unrestricted

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Antipova, Ekaterina. "Advanced mathematical programming tools for alternative energy systems design". Doctoral thesis, Universitat Rovira i Virgili, 2013. http://hdl.handle.net/10803/124102.

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The goal of this thesis is to provide a systematic mathematical decision-support tool for the design of energy systems. Nowadays the society is becoming increasingly conscious about ecological problems originated by anthropogenic factors. In response to this situation, the authorities are taking measures with the purpose to restrict the actual and further environmental load related to human activity. Here, energy efficiency and renewable energies play an important role. Particularly, one of the measures with considerable potential is the retrofit of standard industrial processes through the incorporation of renewable energies in order to reduce the environmental impact related to the use of natural fossil fuels. The general problem we aim to solve in this thesis is the design of environmentally friendly energy systems with the lowest possible cost. To illustrate the capabilities of our approach, we consider a case study: a desalination plant located in the Tarragona region. Our methodology is general enough to be applied to other energy systems, and aims to guide decisions-makers towards the adoption of alternatives with less environmental impact.

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Que, Norbert S. Civil &amp Environmental Engineering Faculty of Engineering UNSW. "Identification of cohesive crack fracture parameters using mathematical programming". Awarded by:University of New South Wales. School of Civil and Environmental Engineering, 2003. http://handle.unsw.edu.au/1959.4/19189.

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This thesis is concerned with the characterisation of the parameters governing the tension-softening relations of the cohesive crack model. Parameter identification is an important area in fracture mechanics as it enables the use of a fracture model for the simulation of fracture processes in structures. Research, however, has shown that such a task is not trivial and continues to pose challenging problems to experimentalists and analysts alike. This dissertation presents general and efficient indirect methods for the characterisation of mode I fracture parameters defining the cohesive crack model. The identification problem is formulated as a special type of inverse problem. The formulation is in the form of a constrained optimisation problem known as a mathematical program with equilibrium constraints characterised, in the present instance, by complementarity conditions involving the orthogonality of two-sign constrained vectors. The solution of such a mathematical program is computationally challenging as it is disjunctive and nonconvex by nature. A number of nonlinear programming based approaches are proposed, after appropriate reformulation of the mathematical program as an equivalent nonlinear programming problem. Actual experimental data are used to validate and determine the most suitable algorithm for parameter identification. It was found that the smoothing-based method is by far superior than other schemes. As the problem is nonconvex and the nonlinear program can only guarantee a local or stationary point, global optimisation procedures are introduced in order to verify the accuracy of the solutions obtained by the algorithm. Two evolutionary search methods capable of finding the global optimum are implemented for parameter identification. The results generated by the evolutionary search techniques confirm the reliability of the solutions identified by the best nonlinear programming algorithm. All computations carried out in the thesis suggest the suitability and robustness of the selected algorithm for parameter identification.

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36

Ferris, Michael Charles. "Weak sharp minima and penalty functions in mathematical programming". Thesis, University of Cambridge, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.292969.

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37

Buelga, Ana Sanchez. "Mathematical programming studies of short run oil refinery rents". Thesis, Queen Mary, University of London, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.416439.

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SANTOS, DEBORA ANDREA DE OLIVEIRA. "DECOMPOSITION IN MATHEMATICAL PROGRAMMING APPLIED TO COMPUTATIONAL GREEN NETWORKS". PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=25702@1.

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O crescente consumo de energia já se tornou uma preocupação mundial e atualmente mais de quarenta países estão envolvidos em pesquisas e programas para criar mecanismos para economizá-la. No presente trabalho é tratado o problema de Engenharia de Tráfego com base na energia (em inglês, energy-aware Traffic Engineering) aplicado ao backbone de uma rede IP que utiliza como protocolo de roteamento um SPF (Shortest Path First), como o OSPF (Open Shortest Path First), por exemplo. Na abordagem proposta são considerados os problemas de desligamento de nós (roteadores) e circuitos, para a economia de energia; e da garantia de um nível de máxima utilização dos circuitos, para assegurar os requisitos de QoS. Para a resolução do problema de otimização, em lugar de adotarem-se métodos heurísticos, propõe-se o tratamento direto por meio de decomposição de Benders, segmentando um problema complicado e de elevada carga computacional em vários menores cuja resolução é mais simples e cuja convergência é mais rápida.
The growing energy consumption has already become a global concern and currently more than forty countries are involved in researches and programs in order to create mechanisms to save it. This work deals with the energy-aware Traffic Engineering problem applied to the backbone of an IP network in which the used routing protocol is a SPF (Shortest Path First) one, such as OSPF (Open Shortest Path First), for example. The proposed approach considers the problem of switching-off nodes (routers) and circuits, for energy saving; and it also considers the problem of ensuring a maximum utilization level by the circuits, towards to assure QoS requirements. In order to solve the optimization problem, rather than adopting heuristic methods, we propose the direct processing by means of Benders decomposition, crumbling a complicated and hard to solve problem into several smaller ones whose resolution is more simple and whose convergence is faster.

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39

Gu, D. W. "Design of non-linear control systems via mathematical programming". Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/37714.

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Singh, Navneet. "Efficiency and performance of some algorithms in mathematical programming". Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/38133.

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Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.
Includes bibliographical references (leaves 39-40).
by Navneet Singh.
M.Eng.

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41

Qiang, Feng. "Parallel problem generation for structured problems in mathematical programming". Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/11688.

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The aim of this research is to investigate parallel problem generation for structured optimization problems. The result of this research has produced a novel parallel model generator tool, namely the Parallel Structured Model Generator (PSMG). PSMG adopts the model syntax from SML to attain backward compatibility for the models already written in SML [1]. Unlike the proof-of-concept implementation for SML in [2], PSMG does not depend on AMPL [3]. In this thesis, we firstly explain what a structured problem is using concrete real-world problems modelled in SML. Presenting those example models allows us to exhibit PSMG’s modelling syntax and techniques in detail. PSMG provides an easy to use framework for modelling large scale nested structured problems including multi-stage stochastic problems. PSMG can be used for modelling linear programming (LP), quadratic programming (QP), and nonlinear programming (NLP) problems. The second part of this thesis describes considerable thoughts on logical calling sequence and dependencies in parallel operation and algorithms in PSMG. We explain the design concept for PSMG’s solver interface. The interface follows a solver driven work assignment approach that allows the solver to decide how to distribute problem parts to processors in order to obtain better data locality and load balancing for solving problems in parallel. PSMG adopts a delayed constraint expansion design. This allows the memory allocation for computed entities to only happen on a process when it is necessary. The computed entities can be the set expansions of the indexing expressions associated with the variable, parameter and constraint declarations, or temporary values used for set and parameter constructions. We also illustrate algorithms that are important for delivering efficient implementation of PSMG, such as routines for partitioning constraints according to blocks and automatic differentiation algorithms for evaluating Jacobian and Hessian matrices and their corresponding sparsity partterns. Furthermore, PSMG implements a generic solver interface which can be linked with different structure exploiting optimization solvers such as decomposition or interior point based solvers. The work required for linking with PSMG’s solver interface is also discussed. Finally, we evaluate PSMG’s run-time performance and memory usage by generating structured problems with various sizes. The results from both serial and parallel executions are discussed. The benchmark results show that PSMG achieve good parallel efficiency on up to 96 processes. PSMG distributes memory usage among parallel processors which enables the generation of problems that are too large to be processed on a single node due to memory restriction.

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42

Dias, da Silva Gustavo. "Symmetries and Distances : two intriguing challenges in Mathematical Programming". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX008/document.

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Cette thèse est consacrée à l’étude et à la discussion de deux questions importantes qui se posent dans le domaine de la Programmation Mathématique: les symétries et les distances. En arrière-plan, nous examinons la Programmation Semidéfinie (PSD) et sa pertinence comme l’un des principaux outils employés aujourd’hui pour résoudre les Programmes Mathématiques (PM) durs. Après le chapitre introductif, nous discutons des symétries au Chapitre 2 et des distances au Chapitre 5. Entre ces deux chapitres, nous présentons deux courts chapitres que nous préférons en fait appeler entr’actes: leur contenu ne mérite pas d’être publié pour le moment, mais ils fournissent un lien entre les deux Chapitres 2 et 5 apparemment distincts, qui contiennent les principales contributions de cette thèse. Il est bien connu que les PMs symétriques sont plus difficiles à résoudre pour l’optimalité globale en utilisant des algorithmes du type Branch-and-Bound (B&B). Il est également bien connu que certaines des symétries de solution sont évidentes dans la formulation, ce qui permet d’essayer de traiter les symétries en tant qu’étape de prétraitement. L’une des approches les plus simples consiste à rompre les symétries en associant les Contraintes de Rupture de Symétrie (CRS) à la formulation, en supprimant ainsi des optima globaux symétriques, puis à résoudre la reformulation avec un solveur générique. Ces contraintes peuvent être générés à partir de chaque orbite de l’action des symétries sur l’ensemble des indices des variables. Cependant, il est difficile de savoir si et comment il est possible de choisir deux ou plus orbites distinctes pour générer des CRSs qui sont compatibles les unes avec les autres (elles ne rendent pas tous les optima globaux infaisables). Dans le Chapitre 2, nous discutons et testons un nouveau concept d’Indépendance Orbitale (IO) qui clarifie cette question. Les expériences numériques réalisées à l’aide de PLMEs et de PNLMEs soulignent l’exactitude et l’utilité de la théorie de l’IO. Programmation Quadratique Binaire (PQB) est utilisée pour étudier les symétries et SDP dans Entr'acte 3. Programmes quadratiques binaires symétriques ayant une certaine structure de symétrie sont générés et utilisés pour illustrer les conditions dans lesquelles l'utilisation de CRSs est avantageuse. Une discussion préliminaire sur l'impact des symétries et des CRSs dans la performance des solveurs PSD est également réalisée. Le Problème Euclidien de l'Arbre de Steiner est étudié dans Entr'acte 4. Deux modèles sont dérivés, ainsi que des relaxations SDP. Un algorithme heuristique basé à la fois sur les modèles mathématiques et sur les principes d'IO présentés au Chapitre 2 est également proposé. Concernant ces méthodes, des résultats préliminaires sur un petit ensemble d'exemples bien connus sont fournis. Finalement, dans le Chapitre 5, nous abordons le problème fondamental qui se pose dans le domaine de la Géométrie de Distance: il s’agit de trouver une réalisation d’un graphe pondéré non orienté dans RK pour un certain K donné, de sorte que les positions pour les sommets adjacents respectent la distance donnée par le poids de l’arête correspondante. Le Problème de la Géométrie de Distance Euclidienne (PGDE) est d’une grande importance car il a de nombreuses applications en science et en ingénierie. Il est difficile de calculer numériquement des solutions, et la plupart des méthodes proposées jusqu’à présent ne sont pas adaptées à des tailles utiles ou sont peu susceptibles d’identifier de bonnes solutions. La nécessité de contraindre le rang de la matrice représentant des solutions réalisables du PGDE rend le problème si difficile. Nous proposons un algorithme heuristique en deux étapes basé sur la PSD (en fait basé sur le paradigme de la PDD) et la modélisation explicite de Contraintes de Rang. Nous fournissons tests informatiques comprenant des instances générées de façon aléatoire ainsi que des exemples réalistes de conformation de protéines
This thesis is mostly dedicated to study and discuss two important challenges existing not only in the field of Mathematical Programming: symmetries and distances. In the background we take a look into Semidefinite Programming (SDP) and its pertinency as one of the major tools employed nowadays to solve hard Mathematical Programs (MP). After the introductory Chapter 1, we discuss about symmetries in Chapter 2 and about distances in Chapter 5. In between them we present two short chapters that we actually prefer to call as entr’actes: their content is not necessarily worthy of publication yet, but they do provide a connection between the two seemingly separate Chapters 2 and 5, which are the ones containing the main contributions of this thesis. It is widely known that symmetric MPs are harder to solve to global optimality using Branch-and-Bound (B&B) type algorithms, given that the solution symmetry is reflected in the size of the B&B tree. It is also well-known that some of the solution symmetries are usually evident in the formulation, which makes it possible to attempt to deal with symmetries as a preprocessing step. Implementation-wise, one of the simplest approaches is to break symmetries by adjoining Symmetry-Breaking Constraints (SBC) to the formulation, thereby removing some symmetric global optima, then solve the reformulation with a generic solver. Sets of such constraints can be generated from each orbit of the action of the symmetries on the variable index set. It is unclear, however, whether and how it is possible to choose two or more separate orbits to generate SBCs which are compatible with each other (in the sense that they do not make all global optima infeasible). In Chapter 2 we discuss and test a new concept of Orbital Independence (OI) that clarifies this issue. The numerical experiences conducted using public MILPs and MINLPs emphasize the correctness and usefulness of the OI theory. Binary Quadratic Programming (BQP) is used to investigate symmetries and SDP in Entr'acte 3. Symmetric Binary Quadratic Programs having a certain symmetry structure are generated and used to exemplify the conditions under which the usage of SBCs is majoritarily advantageous. A preliminary discussion about the impact of symmetries and SBCs in the performance of SDP solvers is also carried out. The Euclidean Steiner Tree Problem is studied in Entr'acte 4. Two models (which are exact reformulations of an existing formulation) are derived, as well as SDP relaxations. A heuristic algorithm based on both the mathematical models and the OI principles presented in Chapter 2 is also proposed. As concerns these methods, preliminary results on a small set of well-known instances are provided. Finally and following up the Distance Geometry subject, in Chapter 5 we cope with the most fundamental problem arising in the field of Distance Geometry, the one of realizing graphs in Euclidean spaces: it asks to find a realization of an edge-weighted undirected graph in RK for some given K such that the positions for adjacent vertices respect the distance given by the corresponding edge weight. The Euclidean Distance Geometry Problem (EDGP) is of great importance since it has many applications to science and engineering. It is notoriously difficult to solve computationally, and most of the methods proposed so far either do not scale up to useful sizes, or unlikely identify good solutions. In fact, the need to constrain the rank of the matrix representing feasible solutions of the EDGP is what makes the problem so hard. Intending to overcome these issues, we propose a two-steps heuristic algorithm based on SDP (or more precisely based on the very recent Diagonally Dominant Programming paradigm) and the explicitly modeling of Rank Constraints. We provide extensive computational testing against randomly generated instances as well as against feasible realistic protein conformation instances taken from the Protein Data Bank to analyze our method

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43

Zhou, Fangjun. "Nonmonotone methods in optimization and DC optimization of location problems". Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/21777.

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沈逸江 i Yijiang Shen. "Binary image restoration by positive semidefinite programming and signomial programming". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B39557431.

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45

Kostin, Andrey. "Development of advanced mathematical programming methods for supply chain management". Doctoral thesis, Universitat Rovira i Virgili, 2013. http://hdl.handle.net/10803/108957.

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El objetivo es desarrollar una herramienta de apoyo a la toma de decisiones para la planificación estratégica de cadenas de suministro (CS). La tarea consiste en determinar el número, ubicación y capacidad de todos los nodos de la CS, su política de expansión, el transporte y la producción entre todos los nodos de la red. El problema se formula como un modelo de programación lineal entera mixta (MILP) que se resuelve utilizando diferentes herramientas. En primer lugar se desarrolló una estrategia de descomposición para acelerar el proceso de resolución En segundo, se utilizó el algoritmo de aproximación para resolver el problema MILP estocástico. Por último, el modelo multi-objetivo incorpora las soluciones de compromiso entre los aspectos económicos y ambientales. Todas las formulaciones se aplicaron al caso real de la industria de caña de azúcar en Argentina. El objetivo de las herramientas es ayudar a los responsables de planificación estratégica de las infraestructuras para la producción de productos químicos.
The aim of this thesis is to provide a decision-support tool for the strategic planning of supply chains (SCs). The task consists of determining the number, location and capacities of all SC facilities, their expansion policy, the transportation links that need to be established, and the production rates and flows of all materials involved in the network. The problem is formulated as a mixed-integer linear programming (MILP) model, which is solved using several mathematical programming tools. First, a decomposition strategy was developed to expedite the solving procedure. Second, the approximation algorithm was utilized to solve the stochastic version of the MILP. Finally, the multi-objective model was developed to incorporate the trade-off between economical and ecological issues. All formulations were applied to a real case based on the Argentinean sugarcane industry. The tools presented are intended to help policy-makers in the strategic planning of infrastructures for chemicals production.

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46

Sahlit, Carmen Lucia de Mesquita. "Mathematical programming methods for dynamically loaded rigid-plastic framed structures". Thesis, Imperial College London, 1992. http://hdl.handle.net/10044/1/7819.

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Grodal, Evert Olaus. "Designing primary hydrocarbon production separation systems : a mathematical programming formulation". Thesis, Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/12084.

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Ali, Syed Zahid. "A mathematical programming approach to cellular mobile radio network design". Thesis, Imperial College London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.269005.

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Ulker, Ozgur. "Office space allocation by using mathematical programming and meta-heuristics". Thesis, University of Nottingham, 2013. http://eprints.nottingham.ac.uk/13604/.

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Office Space Allocation (OSA) is the task of efficient usage of spatial resources of an organisation. A common goal in a typical OSA problem is to minimise the wastage of space either by limiting the overuse or underuse of the facilities. The problem also contains a myriad of hard and soft constraints based on the preferences of respective organisations. In this thesis, the OSA variant usually encountered in academic institutions is investigated. Previous research in this area is rather sparse. This thesis provides a definition, extension, and literature review for the problem as well as a new parametrised data instance generator. In this thesis, two main algorithmic approaches for tackling the OSA are proposed: The first one is integer linear programming. Based on the definition of several constraints and some additional variables, two different mathematical models are proposed. These two models are not strictly alternatives to each other. While one of them provides more performance for the types of instances it is applicable, it lacks generality. The other approach provides less performance; however, it is easier to apply this model to different OSA problems. The second algorithmic approach is based on metaheuristics. A three step process in heuristic development is followed. In the first step, general local search techniques (descent methods, threshold acceptance, simulated annealing, great deluge) traverse within the neighbourhood via random relocation and swap moves. The second step of heuristic development aims to investigate large sections of the whole neighbourhood greedily via very fast cost calculation, cost update, and search for best move procedures within an evolutionary local search framework. The final step involves refinements and hybridisation of best performing (in terms of solution quality) mathematical programming and meta-heuristic techniques developed in prior steps. This thesis aims to be one of the pioneering works in the research area of OSA. The major contributions are: the analysis of the problem, a new parametrised data instance generator, mathematical programming models, and meta-heuristic approaches in order to extend the state-of-the art in this area.

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Rosa, Joao Miguel Feu. "Mathematical programming applied to diet problems in a Brazilian region". Thesis, Lancaster University, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.332375.

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