Teachers’ everyday practices are embedded in school contexts in which their teaching autonomy is constrained by rules, moral obligations, physical settings,and official directives. When a curricular revision mandated that programming was to be a part of mathematics in upper secondary education, teachers’ conditions changed. How teachers adapted to the new curriculum and how they navigated the tensions and contradictions that they encountered is in this thesis analyzed in terms of teachers’ tactics and policy strategies. The overall goal of the investigation is to contribute to a critical understanding of how mathematics teachers integrate programming in their professional practice and how this integration aligns and diverges from the intentions behind the reform. The empirical material is drawn from nine individual interviews with mathematics teachers that were already proficient in programming. The teachers’ unit plans and other lesson materials featuring programming activities served as a trigger point to delve into further reflections upon their own professional practices. To complete the scene, the policy documents were also examined. These included the mathematics curriculum, as well as related official documents and a collection of institutionally sanctioned programming exercises and demonstrations. Two tactical approaches were made apparent when mathematics teachers began to integrate computer programming in their subject: Dual teaching and Interspersed programming. The teacher’s use of dual teaching practices or interspersed programming are tactics shaped by and in response to the conditions of the new curriculum and their own preferences and views on student learning. These two tactics disclose different ontological commitments in relation to the strategies dictated by the curriculum and reflect a cardinal distinction between planning mathematics activities with elements of programming and planning programming activities with elements of mathematics. Of relevance for teachers and curriculum designers is the understanding of (a) how the notion of programming and mathematics as separate subjects oversimplifies teachers’ actual integration practices, and (b) how the curricular choices made by policy can shape the teaching tactics adopted by educators.

Indiana University-Purdue University Indianapolis (IUPUI) / This thesis proposed an algorithm that can find optimized Petri nets from given observation sequences according to some rules of optimization. The basic idea of this algorithm is that although the length of the observation sequences can keep growing, we can think of the growing as periodic and algorithm deals with fixed observations at different time. And the algorithm developed has polynomial complexity. A segment of example code programed according to this algorithm has also been shown. Furthermore, we modify this algorithm and it can check whether a Petri net could fit the observation sequences after several steps. The modified algorithm could work in constant time. These algorithms could be used in optimization of the control systems and communication networks to simplify their structures.

This thesis describes the development and implementation of an Interleaving Warehouse Layout Model. Traditionally, the space allocated to items in a warehouse is determined on the basis of inventory cost considerations. With space requirements taken as given, the actual assignment of items to locations in the warehouse is carried out independently. Assuming an interleaving ("dual command") order picking method and the simple economic order quantity inventory model, it is demonstrated that the quantity and location problems must be considered simultaneously in order to achieve a minimum total cost (order picking cost plus inventory cost). A heuristic optimization technique is developed and applied to a set of realistic, hypothetical problems. This model allows warehouse management to assess the tradeoffs in handling costs among various stock arrangements and reorder quantities to achieve a minimum total cost. / Master of Science

Many concrete problems, ranging from Portfolio selection to Water resource management, may be cast into a multiobjective programming framework. The simplistic way of superseding blindly conflictual goals by one objective function let no chance to the model but to churn out meaningless outcomes. Hence interest of discussing ways for tackling Multiobjective Programming Problems. More than this, in many real-life situations, uncertainty and imprecision are in the state of affairs. In this dissertation we discuss ways for solving Multiobjective Programming Problems with fixed and fuzzy coefficients. No preference, a priori, a posteriori, interactive and metaheuristic methods are discussed for the deterministic case. As far as the fuzzy case is concerned, two approaches based respectively on possibility measures and on Embedding Theorem for fuzzy numbers are described. A case study is also carried out for the sake of illustration. We end up with some concluding remarks along with lines for further development, in this field. / Operations Research / M. Sc. (Operations Research)

Approved for public release, distribution is unlimited / Many potential adversaries seek, or already have theater ballistic missiles capable of threatening targets of interest to the United States. The U.S. Missile Defense Agency and armed forces are developing and fielding missile interceptors carried by many different platforms, including ships, aircraft, and ground units. Given some exigent threat, the U.S. must decide where to position defensive platforms and how they should engage potential belligerent missile attacks. To plan such defenses, the Navy uses its Area Air Defense Commander (AADC) system afloat and ashore, the Air Force has its Theater Battle Management Core Systems (TBMCS) used in air operations centers, and the Missile Defense Agency uses the Commander's Analysis and Planning Simulation (CAPS). AADC uses a server farm to exhaustively enumerate potential enemy launch points, missiles, threatened targets, and interceptor platform positions. TBMCS automates a heuristic cookie-cutter overlay of potential launch fans by defensive interceptor envelopes. Given a complete missile attack plan and a responding defense, CAPS assesses the engagement geometry and resulting coverage against manually prepared attack scenarios and defense designs. We express the enemy courses of action as a mathematical optimization to maximize expected damage, and then show how to optimize our defensive interceptor pre-positioning to minimize the maximum achievable expected damage. We can evaluate exchanges where each of our defending platform locations and interceptor commitments are hidden from, or known in advance by the attacker. Using a laptop computer we can produce a provably optimal defensive plan in minutes. / Lieutenant, United States Navy

Orientador: Antonio Roberto Balbo / Banca: Edilaine Martins Soler / Banca: Leonardo Nepomuceno / Resumo: Neste trabalho apresentamos o método previsor-corretor primal-dual de pontos interiores, com barreira logarítmica modificada e estratégia de ajuste cúbico (MPIBLM-EX) e o método previsor-corretor primal-dual de pontos interiores, com barreira logarítmica modificada, com estratégias de ajuste cúbico e de convergência global (MPIBLMCG-EX). Na definição do algoritmo proposto, a função barreira logarítmica modificada auxilia o método em sua inicialização com pontos inviáveis. Porém, a inviabilidade pode ocorrer em pontos tais que o logaritmo não está definido, consequentemente, isso implica na não existência de função barreira logarítmica modificada. Para suprir essa dificuldade um polinômio cúbico ajustado ao logaritmo, que preserva as derivadas de primeira e segunda do mestre definido a partir de um ponto da região ampliada ao método previsor-corretor primal-dual de pontos interiores com barreira logarítmica modificada (MPIBML); no processo previsor são realizadas atualizações do parâmetro de barreira nos resíduos das restrições de complementaridade, considerando aproximações de primeira ordem do sistema de direções de busca, enquanto que no procedimento corretor, incluímos os termos quadráticos não-lineares dos resíduos citados, que foram desprezados no procedimento previsor. Considerando também a estratégia de convergência global para o MPIBLM-EX, a qual utiliza uma variante do método de Levenberg-Marquardt para ajustar a matriz dual normal da função lagrangiana, caso esta não seja definida positiva. A matriz dual normal é redefinida para as restrições primais de igualdade, de desigualdade e para as variáveis canalizadas, incorporando variáveis duais e matrizes diagonais relativas às restrições de complementariade. Desse estudo, o MPIBLM-EX é transformado no MPIBLMCG-EX e mostramos... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This work presents a predictor primal-dual interior point method with modified log-barrier and third order extrapolation strategy (IPMLBM-EX) and also and extension of this method with the inclusion of the global convergence strategy (IPMLBGCM-EX). In the definition of the proposed algorithm, the modified log-barrier function helps the method initialize with infeasible points. However, infeasibility may occur for some point where the logarithm is not defined. The implicates in non-existence of the modified log-barrier function. To cope with such as problem, a cubic polynomial function is adjusted to the logarithmic function. Sucha polynomial function preserves first and second order derivatives in certain point defined in the extended region. This function is applied to the predictor-corretor primal-dual interior point method with modified log-barrier function. In the predictor procedure, the barrier parameter is updated in the complementarity conditions considering first-order approximations of the search direction, while the corrector procedure includes the nonlinear quadratic terms of the mentioned residuals, which were neglected in the predictor procedure. We also consider the global convergence strategy for the method, which uses a variant of the Levenberg-Marquardt method to update the normal dual matrix of the Langrangian function, should it fail to be positively defined. In this case, this matrix is redefined for equality primal constraints, bounded inequality primal constraints and bounded variables, incorporating dual variables and diagonal matrices of the complementarity constraints. From such studies, the IPMLBM-EX method is extended to include the global convergence strategy (IPMLBGCM-EX). We have show that both methods are projected gradient methods. An implementation performed with Matlab 6.1 has shown the... (Complete abstract click electronic access below) / Mestre

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.

Integer Programming (IP) is a powerful and widely-used formulation for combinatorial problems. The study of IP over the past several decades has led to fascinating theoretical developments, and has improved our ability to solve discrete optimization problems arising in practice. This thesis makes progress on algorithmic solutions for IP by building on combinatorial, geometric and Linear Programming (LP) approaches. We use a combinatorial approach to give an approximation algorithm for the feedback vertex set problem (FVS) in a recently developed Implicit Hitting Set framework. Our algorithm is a simple online algorithm which finds a nearly optimal FVS in random graphs. We also propose a planted model for FVS and show that an optimal hitting set for a polynomial number of subsets is sufficient to recover the planted subset. Next, we present an unexplored geometric connection between integer feasibility and the classical notion of discrepancy of matrices. We exploit this connection to show a phase transition from infeasibility to feasibility in random IP instances. A recent algorithm for small discrepancy solutions leads to an efficient algorithm to find an integer point for random IP instances that are feasible with high probability. Finally, we give a provably efficient implementation of a cutting-plane algorithm for perfect matchings. In our algorithm, cuts separating the current optimum are easy to derive while a small LP is solved to identify the cuts that are to be retained for later iterations. Our result gives a rigorous theoretical explanation for the practical efficiency of the cutting plane approach for perfect matching evident from implementations. In summary, this thesis contributes to new models and connections, new algorithms and rigorous analysis of well-known approaches for IP.

Thesis--University of Amsterdam. / Includes bibliographical references.

Many concrete problems, ranging from Portfolio selection to Water resource management, may be cast into a multiobjective programming framework. The simplistic way of superseding blindly conflictual goals by one objective function let no chance to the model but to churn out meaningless outcomes. Hence interest of discussing ways for tackling Multiobjective Programming Problems. More than this, in many real-life situations, uncertainty and imprecision are in the state of affairs. In this dissertation we discuss ways for solving Multiobjective Programming Problems with fixed and fuzzy coefficients. No preference, a priori, a posteriori, interactive and metaheuristic methods are discussed for the deterministic case. As far as the fuzzy case is concerned, two approaches based respectively on possibility measures and on Embedding Theorem for fuzzy numbers are described. A case study is also carried out for the sake of illustration. We end up with some concluding remarks along with lines for further development, in this field. / Operations Research / M. Sc. (Operations Research)