Relevant bibliographies by topics / Mathematical programming formulation

Academic literature on the topic 'Mathematical programming formulation'

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Published: 10 December 2022
Last updated: 19 February 2023

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Journal articles on the topic "Mathematical programming formulation"

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Lee, Jae Sik, Christopher V. Jones, and Monique Guignard. "MAPNOS: Mathematical programming formulation normalization system." Expert Systems with Applications 1, no. 4 (January 1990): 367–81. http://dx.doi.org/10.1016/0957-4174(90)90046-w.

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Bonatsos, Nikolaos, Endrit Dheskali, Denise M. G. Freire, Aline Machado de Castro, Apostolis A. Koutinas, and Ioannis K. Kookos. "A mathematical programming formulation for biorefineries technology selection." Biochemical Engineering Journal 116 (December 2016): 135–45. http://dx.doi.org/10.1016/j.bej.2016.05.001.

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Adi, Vincentius Surya Kurnia, and Chuei-Tin Chang. "A mathematical programming formulation for temporal flexibility analysis." Computers & Chemical Engineering 57 (October 2013): 151–58. http://dx.doi.org/10.1016/j.compchemeng.2013.04.001.

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Gringauz, M. "On mathematical programming formulation for contact crack problems." International Journal of Fracture 60, no. 1 (March 1993): R3—R7. http://dx.doi.org/10.1007/bf00034516.

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Urahama, Kiichi. "Mathematical programming formulation for neural combinatorial optimization algorithms." Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 78, no. 9 (September 1995): 67–75. http://dx.doi.org/10.1002/ecjc.4430780907.

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Chen, Zeng Hai, Bin Gang Xu, Zhe Ru Chi, and Da Gan Feng. "Mathematical formulation of knitted fabric spirality using genetic programming." Textile Research Journal 82, no. 7 (January 25, 2012): 667–76. http://dx.doi.org/10.1177/0040517511435011.

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This paper proposes the use of genetic programming for the mathematical formulation of knitted fabric spirality. Both dry relaxed and wash-and-dry relaxed states of fabric spirality are studied. In total, six parameters are investigated, in which three parameters are derived from yarn and fabric, and the other three parameters are from the knitted condition. The three yarn and fabric parameters used are yarn twist liveliness, tightness factor and dyeing method, and the three knitting parameters are the number of feeders, rotational direction and gauge. Genetic programming is adopted to formulize the mathematical relationships between above the six parameters and two states of fabric spirality, respectively. For a comparison, a multiple linear regression approach is studied as well. The formulas generated by genetic programming and multiple regression for two states of spirality are comprehensively investigated and compared. Experimental results show that genetic programming, which can model non-linear mathematical relationships, obtains more accurate expressions than multiple regression for both dry relaxed and wash-and-dry relaxed states of spirality, demonstrating that genetic programming is a promising alternative for the mathematical formulation of fabric spirality.
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Patil, Vishal, Radha Gupta, Rajendran D, and Ravinder Singh Kuntal. "COMPARATIVE STUDY ON FEED FORMULATION SOFTWARE- A SHORT REVIEW." International Journal of Research -GRANTHAALAYAH 5, no. 4RAST (April 30, 2017): 105–15. http://dx.doi.org/10.29121/granthaalayah.v5.i4rast.2017.3311.

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The paper highlightsthe different feed formulation software’s for least cost formulation of livestock and animals, where the comparison of techniques is donebased on different aspectslike data collection, software used, price, scope and limitations. Feed formulation requires large amount of data about the composition of feeds, environment conditions,and availability of feeds.Development of Software’sfor feed formulations is changing with change in computer. With advancement of technology, the feed formulation can be calculated for ‘n’ number of feed stuff but still Linear Programming is used as base for mathematical modelling, where uses of non-linear programming is very less. Maximum number of feed formulation software’s is developed to select the feeds for formulation within budget of the farmers or dairy industry.
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Zhao, LiJin, and Liang Huang. "A Mathematical Programming Formulation of Disjoint Dominating Sets Problem." Journal of Computational and Theoretical Nanoscience 13, no. 11 (November 1, 2016): 8760–64. http://dx.doi.org/10.1166/jctn.2016.6037.

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Olhoff, N. "Multicriterion structural optimization via bound formulation and mathematical programming." Structural Optimization 1, no. 1 (March 1989): 11–17. http://dx.doi.org/10.1007/bf01743805.

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Chwatal, Andreas M., and Günther R. Raidl. "Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques." Advances in Operations Research 2011 (2011): 1–38. http://dx.doi.org/10.1155/2011/143732.

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We present exact mixed integer programming approaches including branch-and-cut and branch-and-cut-and-price for the minimum label spanning tree problem as well as a variant of it having multiple labels assigned to each edge. We compare formulations based on network flows and directed connectivity cuts. Further, we show how to use odd-hole inequalities and additional inequalities to strengthen the formulation. Label variables can be added dynamically to the model in the pricing step. Primal heuristics are incorporated into the framework to speed up the overall solution process. After a polyhedral comparison of the involved formulations, comprehensive computational experiments are presented in order to compare and evaluate the underlying formulations and the particular algorithmic building blocks of the overall branch-and-cut- (and-price) framework.
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Dissertations / Theses on the topic "Mathematical programming formulation"

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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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Brooks, J. Paul. "Solving a mixed-integer programming formulation of a classification model with misclassification limits." Diss., Available online, Georgia Institute of Technology, 2005, 2005. http://etd.gatech.edu/theses/available/etd-08232005-133023/.

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Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2006.
Prausnitz, Mark, Committee Member ; Vidakovic, Brani, Committee Member ; Lee, Eva, Committee Chair ; Nemhauser, George, Committee Member ; Johnson, Ellis, Committee Member. Includes bibliographical references.
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Abdullah, Ali H. "The weighted maximal planar graph : mathematical formulations and solutions." Thesis, University of Kent, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.250315.

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Melo, Márcio Daniel Tavares de. "Network virtualisation from an operator perspective." Doctoral thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/12876.

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Doutoramento em Engenharia Eletrotécnica
Network virtualisation is seen as a promising approach to overcome the so-called “Internet impasse” and bring innovation back into the Internet, by allowing easier migration towards novel networking approaches as well as the coexistence of complementary network architectures on a shared infrastructure in a commercial context. Recently, the interest from the operators and mainstream industry in network virtualisation has grown quite significantly, as the potential benefits of virtualisation became clearer, both from an economical and an operational point of view. In the beginning, the concept has been mainly a research topic and has been materialized in small-scale testbeds and research network environments. This PhD Thesis aims to provide the network operator with a set of mechanisms and algorithms capable of managing and controlling virtual networks. To this end, we propose a framework that aims to allocate, monitor and control virtual resources in a centralized and efficient manner. In order to analyse the performance of the framework, we performed the implementation and evaluation on a small-scale testbed. To enable the operator to make an efficient allocation, in real-time, and on-demand, of virtual networks onto the substrate network, it is proposed a heuristic algorithm to perform the virtual network mapping. For the network operator to obtain the highest profit of the physical network, it is also proposed a mathematical formulation that aims to maximize the number of allocated virtual networks onto the physical network. Since the power consumption of the physical network is very significant in the operating costs, it is important to make the allocation of virtual networks in fewer physical resources and onto physical resources already active. To address this challenge, we propose a mathematical formulation that aims to minimize the energy consumption of the physical network without affecting the efficiency of the allocation of virtual networks. To minimize fragmentation of the physical network while increasing the revenue of the operator, it is extended the initial formulation to contemplate the re-optimization of previously mapped virtual networks, so that the operator has a better use of its physical infrastructure. It is also necessary to address the migration of virtual networks, either for reasons of load balancing or for reasons of imminent failure of physical resources, without affecting the proper functioning of the virtual network. To this end, we propose a method based on cloning techniques to perform the migration of virtual networks across the physical infrastructure, transparently, and without affecting the virtual network. In order to assess the resilience of virtual networks to physical network failures, while obtaining the optimal solution for the migration of virtual networks in case of imminent failure of physical resources, the mathematical formulation is extended to minimize the number of nodes migrated and the relocation of virtual links. In comparison with our optimization proposals, we found out that existing heuristics for mapping virtual networks have a poor performance. We also found that it is possible to minimize the energy consumption without penalizing the efficient allocation. By applying the re-optimization on the virtual networks, it has been shown that it is possible to obtain more free resources as well as having the physical resources better balanced. Finally, it was shown that virtual networks are quite resilient to failures on the physical network.
A virtualização de rede é vista como uma abordagem promissora para ultrapassar o “Impasse da Internet” e permitir inovação na Internet, possibilitando assim uma migração fácil para novas abordagens de redes, bem como a coexistência de arquiteturas de redes complementares numa infraestrutura compartilhada e em ambiente comercial. Recentemente tem crescido de forma bastante significativa o interesse pela virtualização de rede por parte dos operadores e dos grandes fabricantes, desde que os potenciais benefícios da virtualização se tornaram claros, tanto de ponto de vista económico como operacional. No início, o conceito foi versado pelo meio académico, onde foram realizadas provas de conceito de pequena escala, e em que a virtualização de rede foi considerada como forma de investigação de novos protocolos. Esta Tese de Doutoramento tem como objetivo geral dotar uma rede de operador de um conjunto de mecanismos e algoritmos capazes de gerir e controlar redes virtuais. Para este fim, é proposta uma framework que visa alocar, monitorizar e controlar recursos virtuais de uma forma centralizada e eficiente. De forma a analisar o desempenho da framework, procedeu-se à sua implementação e avaliação numa rede de pequena dimensão. De forma a permitir que se possa efetuar uma alocação eficiente, em tempo real, e a pedido, de redes virtuais numa rede física, é proposta uma heurística para efetuar o mapeamento na rede física. Para que o operador de rede possa rentabilizar ao máximo a sua infraestrutura de rede, é ainda proposta uma formulação matemática que, através de programação linear, visa maximizar o número de redes alocadas na infraestrutura de rede. Dado que o consumo energético de uma infraestrutura de rede começa a ter significância nos custos de operação, é importante que se faça a alocação das redes virtuais no menor número de recursos físicos e também em recursos físicos ativos. Para endereçar este desafio é proposta uma formulação matemática que visa minimizar o consumo energético da rede física sem afetar a eficiência da alocação de redes virtuais. Para minimizar a fragmentação da infraestrutura de rede e ao mesmo tempo aumentar as receitas do operador, é também estendida a formulação inicial para contemplar a re-otimização de redes virtuais previamente mapeadas, fazendo com que o operador tenha um melhor aproveitamento da sua infraestrutura física. Será ainda necessário endereçar a migração de redes virtuais, quer por motivos de balanceamento de carga, quer por motivos de falha iminente de recursos físicos, sem afetar o bom funcionamento da rede virtual. Para este fim, é proposto um método baseado em técnicas de clonagem, para efetuar a migração de redes virtuais entre recursos da infraestrutura física de forma transparente e sem impacto para a rede virtual. De forma a avaliar a resiliência das redes virtuais a falhas na rede física, e ao mesmo tempo obter a solução ótima de migração de redes virtuais em caso de falha iminente dos recursos físicos, a formulação matemática é estendida para minimizar o número de nós migrados em simultâneo com a realocação de ligações virtuais. Em comparação com as nossas propostas de otimização verificou-se que as heurísticas existentes para mapeamento de redes virtuais têm um desempenho muito baixo. Verificou-se ainda que é possível efetuar a redução do consumo energético sem a penalização da alocação eficiente. Com a re-otimização das redes virtuais mostrou-se que é possível obter mais recursos livres, assim como obter uma melhor distribuição dos recursos. Por último, demonstrou-se que as redes virtuais são bastante resilientes a falhas na rede física.
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Dietert, Grant. "An integer linear programming formulation for tiling large rectangles using 4 x 6 and 5 x 7 tiles /." Online version of thesis, 2010. http://hdl.handle.net/1850/12275.

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Figueiredo, Tatiane Fernandes. "The socio-technical teams formation problem: Complexity, Mathematical Formulations and Computational Results." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=15392.

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Using concepts of the socio-technical systems theory, this dissertation defines mathematically the problems of cooperative teams formation considering social and technical constraints separately, and then presents their computational complexity. Mainly, it is defined and studied the central problem in this work, which jointly considers social and technical requirements for creating teams of cooperative work, to be called FEST (Socio-Technical Teams Formation Problem). Two mathematical formulations and a meta-heuristic are proposed for FEST. One formulation uses a cubic number of variables and constraints, whereas the second one has a quadratic number of variables but an exponential number of constraints. The proposed heuristic is based on the Non-monotonic Simulated Annealing meta-heuristic with local search using swap-like operators. The correctness of both formulations is proved. A polynomial algorithm to separate the constraints of the second formulation is presented. It is proved that the two formulations provide the same linear programming bound, and valid inequalities to strengthen it are proposed. For the compact formulation, some classes of valid inequalities are shown to be facet-inducing under suitable hypotheses. Finally, it is statistically analyzed the performance of the presented formulations and meta-heuristic. Real and random generated instances are used in the computational experiments.
Utilizando conceitos da Teoria dos Sistemas SociotÃcnicos, este trabalho define matematicamente os problemas de formaÃÃo de equipes cooperativas considerando separadamente restriÃÃes sociais e tÃcnicas e apresenta a complexidade computacional dos mesmos. Sobretudo, à definido e estudado o problema central deste trabalho, que considera conjuntamente requisitos sociais e tÃcnicos para criaÃÃo de equipes de trabalho cooperativo, denominado FEST (Problema de FormaÃÃo de Equipes SociotÃcnicas). Duas formulaÃÃes matemÃticas e uma meta-heurÃstica para o FEST sÃo propostas. Uma formulaÃÃo utiliza um nÃmero cÃbico de variÃveis e restriÃÃes, enquanto a segunda formulaÃÃo possui um nÃmero quadrÃtico de variÃveis, mas um nÃmero exponencial de restriÃÃes. A meta-heurÃstica proposta à baseada no Simulated Annealing NÃo-MonotÃnico com busca local que usa operadores tipo swap. A corretude de ambas as formulaÃÃes à provada. Um algoritmo polinomial para separar as restriÃÃes da segunda formulaÃÃo à apresentado. Mostra-se que as duas formulaÃÃes fornecem o mesmo limite de programaÃÃo linear, e desigualdades vÃlidas para fortalecÃ-lo sÃo propostas. Para a formulaÃÃo compacta, algumas classes de desigualdades vÃlidas sÃo demonstradas indutoras de facetas sob hipÃteses apropriadas. Por fim, foi analisado estatisticamente o desempenho das formulaÃÃes e da meta-heurÃstica apresentadas. InstÃncias reais e geradas aleatoriamente sÃo usadas nos experimentos computacionais.
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Solak, Senay. "Efficient Solution Procedures for Multistage Stochastic Formulations of Two Problem Classes." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19812.

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We consider two classes of stochastic programming models which are motivated by two applications related to the field of aviation. The first problem we consider is the network capacity planning problem, which arises in capacity planning of systems with network structures, such as transportation terminals, roadways and telecommunication networks. We study this problem in the context of airport terminal capacity planning. In this problem, the objective is to determine the optimal design and expansion capacities for different areas of the terminal in the presence of uncertainty in future demand levels and expansion costs, such that overall passenger delay is minimized. We model this problem as a nonlinear multistage stochastic integer program with a multicommodity network flow structure. The formulation requires the use of time functions for maximum delays in passageways and processing stations, for which we derive approximations that account for the transient behavior of flow. The deterministic equivalent of the developed model is solved via a branch and bound procedure, in which a bounding heuristic is used at the nodes of the branch and bound tree to obtain integer solutions. In the second study, we consider the project portfolio optimization problem. This problem falls in the class of stochastic programs in which times of uncertainty realizations are dependent on the decisions made. The project portfolio optimization problem deals with the selection of research and development (R&D) projects and determination of optimal resource allocations for the current planning period such that the expected total discounted return or a function of this expectation for all projects over an infinite time horizon is maximized, given the uncertainties and resource limitations over a planning horizon. Accounting for endogeneity in some parameters, we propose efficient modeling and solution approaches for the resulting multistage stochastic integer programming model. We first develop a formulation that is amenable to scenario decomposition, and is applicable to the general class of stochastic problems with endogenous uncertainty. We then demonstrate the use of the sample average approximation method in solving large scale problems of this class, where the sample problems are solved through Lagrangian relaxation and lower bounding heuristics.
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Smith, Jonathan Cole. "Tight Discrete Formulations to Enhance Solvability with Applications to Production, Telecommunications, and Air Transportation Problems." Diss., Virginia Tech, 2000. http://hdl.handle.net/10919/26710.

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In formulating discrete optimization problems, it is not only important to have a correct mathematical model, but to have a well structured model that can be solved effectively. Two important characteristics of a general integer or mixed-integer program are its size (the number of constraints and variables in the problem), and its strength or tightness (a measure of how well it approximates the convex hull of feasible solutions). In designing model formulations, it is critical to ensure a proper balance between compactness of the representation and the tightness of its linear relaxation, in order to enhance its solvability. In this dissertation, we consider these issues pertaining to the modeling of mixed-integer 0-1 programming problems in general, as well as in the context of several specific real-world applications, including a telecommunications network design problem and an airspace management problem. We first consider the Reformulation-Linearization Technique (RLT) of Sherali and Adams and explore the generation of reduced first-level representations for mixed-integer 0-1 programs that tend to retain the strength of the full first-level linear programming relaxation. The motivation for this study is provided by the computational success of the first-level RLT representation (in full or partial form) experienced by several researchers working on various classes of problems. We show that there exists a first-level representation having only about half the RLT constraints that yields the same lower bound value via its relaxation. Accordingly, we attempt to a priori predict the form of this representation and identify many special cases for which this prediction is accurate. However, using various counter-examples, we show that this prediction as well as several variants of it are not accurate in general, even for the case of a single binary variable. Since the full first-level relaxation produces the convex hull representation for the case of a single binary variable, we investigate whether this is the case with respect to the reduced first-level relaxation as well, and show similarly that it holds true only for some special cases. Empirical results on the prediction capability of the reduced, versus the full, first-level representation demonstrate a high level of prediction accuracy on a set of random as well as practical, standard test problems. Next, we focus on a useful modeling concept that is frequently ignored while formulating discrete optimization problems. Very often, there exists a natural symmetry inherent in the problem itself that, if propagated to the model, can hopelessly mire a branch-and-bound solver by burdening it to explore and eliminate such alternative symmetric solutions. We discuss three applications where such a symmetry arises. For each case, we identify the indistinguishable objects in the model which create the problem symmetry, and show how imposing certain decision hierarchies within the model significantly enhances its solvability. These hierarchies render an otherwise virtually intractable formulation computationally viable using commercial software. For the first problem, we consider a problem of minimizing the maximum dosage of noise to which workers are exposed while working on a set of machines. We next examine a problem of minimizing the cost of acquiring and utilizing machines designed to cool large facilities or buildings, subject to minimum operational requirements. For each of these applications, we generate realistic test beds of problems. The decision hierarchies allow all previously intractable problems to be solved relatively quickly, and dramatically decrease the required computational time for all other problems. For the third problem, we investigate a network design problem arising in the context of deploying synchronous optical networks (SONET) using a unidirectional path switched ring architecture, a standard of transmission using optical fiber technology. Given several rings of this type, the problem is to find a placement of nodes to possibly multiple rings, and to determine what portion of demand traffic between node pairs spanned by each ring should be allocated to that ring. The constraints require that the demand traffic between each node pair should be satisfiable given the ring capacities, and that no more than a specified maximum number of nodes should be assigned to each ring. The objective function is to minimize the total number of node-to-ring assignments, and hence, the capital investment in add-drop multiplexer equipments. We formulate the problem as a mixed-integer programming model, and propose several alternative modeling techniques designed to improve the mathematical representation of this problem. We then develop various classes of valid inequalities for the problem along with suitable separation procedures for tightening the representation of the model, and accordingly, prescribe an algorithmic approach that coordinates tailored routines with a commercial solver (CPLEX). We also propose a heuristic procedure which enhances the solvability of the problem and provides bounds within 5-13% of the optimal solution. Promising computational results that exhibit the viability of the overall approach and that lend insights into various modeling and algorithmic constructs are presented. Following this we turn our attention to the modeling and analysis of several issues related to airspace management. Currently, commercial aircraft are routed along certain defined airspace corridors, where safe minimum separation distances between aircraft may be routinely enforced. However, this mode of operation does not fully utilize the available airspace resources, and may prove to be inadequate under future National Airspace (NAS) scenarios involving new concepts such as Free-Flight. This mode of operation is further compounded by the projected significant increase in commercial air traffic. (Free-Flight is a paradigm of aircraft operations which permits the selection of more cost-effective routes for flights rather than simple traversals between designated way-points, from various origins to different destinations.) We begin our study of Air Traffic Management (ATM) by first developing an Airspace Sector Occupancy Model (AOM) that identifies the occupancies of flights within three dimensional (possibly nonconvex) regions of space called sectors. The proposed iterative procedure effectively traces each flight's progress through nonconvex sector modules which comprise the sectors. Next, we develop an Aircraft Encounter Model (AEM), which uses the information obtained from AOM to efficiently characterize the number and nature of blind-conflicts (i.e., conflicts under no avoidance or resolution maneuvers) resulting from a selected mix of flight-plans. Besides identifying the existence of a conflict, AEM also provides useful information on the severity of the conflict, and its geometry, such as the faces across which an intruder enters and exits the protective shell or envelope of another aircraft, the duration of intrusion, its relative heading, and the point of closest approach. For purposes of evaluation and assessment, we also develop an aggregate metric that provides an overall assessment of the conflicts in terms of their individual severity and resolution difficulty. We apply these models to real data provided by the Federal Aviation Administration (FAA) for evaluating several Free-Flight scenarios under wind-optimized and cruise-climb conditions. We digress at this point to consider a more general collision detection problem that frequently arises in the field of robotics. Given a set of bodies with their initial positions and trajectories, we wish to identify the first collision that occurs between any two bodies, or to determine that none exists. For the case of bodies having linear trajectories, we construct a convex hull representation of the integer programming model of Selim and Almohamad, and exhibit the relative effectiveness of solving this problem via the resultant linear program. We also extend this analysis to model a situation in which bodies move along piecewise linear trajectories, possibly rotating at the end of each linear translation. For this case, we again compare an integer programming approach with its linear programming convex hull representation, and exhibit the relative effectiveness of solving a sequence of problems based on applying the latter construct to each time segment. Returning to Air Traffic Management, another future difficulty in airspace resource utilization stems from a projected increase in commercial space traffic, due to the advent of Reusable Launch Vehicle (RLV) technology. Currently, each shuttle launch cordons off a large region of Special Use Airspace (SUA) in which no commercial aircraft are permitted to enter for the specified duration. Of concern to airspace planners is the expense of routinely disrupting air traffic, resulting in circuitous diversions and delays, while enforcing such SUA restrictions. To provide a tool for tactical and planning purposes in such a context within the framework of a coordinated decision making process between the FAA and commercial airlines, we develop an Airspace Planning Model (APM). Given a set of flights for a particular time horizon, along with (possibly several) alternative flight-plans for each flight that are based on delays and diversions due to special-use airspace (SUA) restrictions prompted by launches at spaceports or weather considerations, this model prescribes a set of flight-plans to be implemented. The model formulation seeks to minimize a delay and fuel cost based objective function, subject to the constraints that each flight is assigned one of the designated flight-plans, and that the resulting set of flight-plans satisfies certain specified workload, safety, and equity criteria. These requirements ensure that the workload for air-traffic controllers in each sector is held under a permissible limit, that any potential conflicts which may occur are routinely resolvable, and that the various airlines involved derive equitable levels of benefits from the overall implemented schedule. In order to solve the resulting 0-1 mixed-integer programming problem more effectively using commercial software (CPLEX-MIP), we explore the use of various facetial cutting planes and reformulation techniques designed to more closely approximate the convex hull of feasible solutions to the problem. We also prescribe a heuristic procedure which is demonstrated to provide solutions to the problem that are either optimal or are within 0.01% of optimality. Computational results are reported on several scenarios based on actual flight data obtained from the Federal Aviation Administration (FAA) in order to demonstrate the efficacy of the proposed approach for air traffic management (ATM) purposes. In addition to the evaluation of these various models, we exhibit the usefulness of this airspace planning model as a strategic planning tool for the FAA by exploring the sensitivity of the solution provided by the model to changes both in the radius of the SUA formulated around the spaceport, and in the duration of the launch-window during which the SUA is activated.
Ph. D.
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Boberg, Jessika. "A comparison of sequencing formulations in a constraint generation procedure for avionics scheduling." Thesis, Linköpings universitet, Optimeringslära, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-143274.

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This thesis compares different mixed integer programming (MIP) formulations for sequencing of tasks in the context of avionics scheduling. Sequencing is a key concern in many discrete optimisation problems, and there are numerous ways of accomplishing sequencing with different MIP formulations. A scheduling tool for avionic systems has previously been developed in a collaboration between Saab and Linköping University. This tool includes a MIP formulation of the scheduling problem where one of the model components has the purpose to sequence tasks. In this thesis, this sequencing component is replaced with other MIP formulations in order to study whether the computational performance of the scheduling tool can be improved. Different scheduling instances and objective functions have been used when performing the tests aiming to evaluate the performances, with the computational times of the entire avionic scheduling model determining the success of the different MIP formulations for sequencing. The results show that the choice of MIP formulation makes a considerable impact on the computational performance and that a significant improvement can be achieved by choosing the most suitable one.
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Taeihagh, Araz. "A novel approach for the development of policies for socio-technical systems." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:0183f800-51bf-4e4d-abba-cd91b7bf48f0.

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The growth in the interdependence and complexity of socio-technical systems requires the development of tools and techniques to aid in the formulation of better policies. The efforts of this research focus towards developing methodologies and support tools for better policy design and formulation. In this thesis, a new framework and a systematic approach for the formulation of policies are proposed. Focus has been directed to the interactions between policy measures, inspired by concepts in process design and network analysis. Furthermore, we have developed an agent-based approach to create a virtual environment for the exploration and analysis of different configurations of policy measures in order to build policy packages and test the effects of changes and uncertainties while formulating policies. By developing systematic approaches for the formulation and analysis of policies it is possible to analyse different configuration alternatives in greater depth, examine more alternatives and decrease the time required for the overall analysis. Moreover, it is possible to provide real-time assessment and feedback to the domain experts on the effect of changes in the configurations. These efforts ultimately help in forming more effective policies with synergistic and reinforcing attributes while avoiding internal contradictions. This research constitutes the first step towards the development of a general family of computer-based systems that support the design of policies. The results from this research also demonstrate the usefulness of computational approaches in addressing the complexity inherent in the formulation of policies. As a proof of concept, the proposed framework and methodologies have been applied to the formulation of policies that deal with transportation issues and emission reduction, but can be extended to other domains.
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Books on the topic "Mathematical programming formulation"

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Diaby, Moustapha. Advances in combinatorial optimization: Linear programming formulation of the traveling salesman and other hard combinatorial optimization problems. New Jersey: World Scientific, 2015.

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1956-, Wallace Stein W., and North Atlantic Treaty Organization. Scientific Affairs Division., eds. Algorithms and model formulations in mathematical programming. Berlin: Springer-Verlag, 1989.

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Wallace, Stein W. Algorithms and Model Formulations in Mathematical Programming. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989.

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Wallace, Stein W., ed. Algorithms and Model Formulations in Mathematical Programming. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83724-1.

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Bhargava, H. K. Reasoning with assumptions, defeasibly, in model formulation. Monterey, Calif: Dept. of Administrative Sciences, Naval Postgraduate School, 1991.

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Rimrott, F. P. J. 1927-, ed. Variational methods and complementary formulations in dynamics. Dordrecht: Kluwer Academic Publishers, 1994.

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Small, John T. Optimal Process Design of 2- and 3-Phase Horizontal Production Separators for Oil and Gas Installations: A Mathematical Programming Formulation in Excel 2016. Independently Published, 2019.

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Alternative mathematical programming formulations for FSS synthesis. Columbus, Ohio: Ohio State University ElectroScience Laboratory, Dept. of Electrical Engineering, 1986.

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Wallace, Stein W. Algorithms and Model Formulations in Mathematical Programming. Springer, 2012.

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Bowker, Geoffrey C., and Florian Jaton. The Constitution of Algorithms: Ground-Truthing, Programming, Formulating. The MIT Press, 2021.

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Book chapters on the topic "Mathematical programming formulation"

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Manne, Alan S. "On the formulation and solution of economic equilibrium models." In Mathematical Programming Studies, 1–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0121023.

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Kallrath, Josef. "From the Problem to its Mathematical Formulation." In Business Optimization Using Mathematical Programming, 33–70. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73237-0_2.

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Lucertini, M., and G. Paletta. "A class of network design problems with multiple demand: Model formulation and an algorithmic approach." In Mathematical Programming Studies, 225–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0121101.

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Kingsford, Carl, Elena Zaslavsky, and Mona Singh. "A Compact Mathematical Programming Formulation for DNA Motif Finding." In Combinatorial Pattern Matching, 233–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11780441_22.

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Olhoff, Niels. "Optimal Structural Design via Bound Formulation and Mathematical Programming." In Discretization Methods and Structural Optimization — Procedures and Applications, 255–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83707-4_32.

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Olhoff, Niels. "Solution of Max-Min Problems via Bound Formulation and Mathematical Programming." In Structural Optimization, 397. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-1413-1_52.

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Saxena, Pratiksha, and Neha Khanna. "Formulation and Computation of Animal Feed Mix: Optimization by Combination of Mathematical Programming." In Advances in Intelligent Systems and Computing, 621–29. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-13728-5_70.

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Iommazzo, Gabriele, Claudia D’Ambrosio, Antonio Frangioni, and Leo Liberti. "A Learning-Based Mathematical Programming Formulation for the Automatic Configuration of Optimization Solvers." In Machine Learning, Optimization, and Data Science, 700–712. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-64583-0_61.

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Lara, Pablo. "Linking Production Theory and Multiobjective Fractional Programming as a Support Tool for Animal Diet Formulation." In Lecture Notes in Economics and Mathematical Systems, 301–9. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-46854-4_33.

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Mitrovic-Minic, Snezana, Darren Thomson, Jean Berger, and Jeff Secker. "Collection Planning and Scheduling for Multiple Heterogeneous Satellite Missions: Survey, Optimization Problem, and Mathematical Programming Formulation." In Springer Optimization and Its Applications, 271–305. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10501-3_11.

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Conference papers on the topic "Mathematical programming formulation"

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Kerzhner, Aleksandr A., and Christiaan J. J. Paredis. "A Mathematical Programming-Based Approach for Architecture Selection." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-71025.

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Modern systems are difficult to design because there are a significant number of potential alternatives to consider. The specification of an alternative includes an architecture (which describes the components and connections of the system) and component sizings (the sizing parameter for each component). In current practice, designers rely mainly on their experience and intuition to select a desired architecture without much computational support and then spend most of their effort on optimizing component sizings. In this paper, an approach for representing an architecture selection as a mixed-integer linear programming optimization is presented; existing solvers are then used to identify promising candidate architectures at early stages of the design process. Mathematical programming is a common optimization technique, but it is rarely used for architecture selection because of the difficulty of manually formulating an architecture selection as a mathematical program. In this paper, the formulation is presented in a modular fashion so that model transformations can be applied to transform a problem formulation that is convenient for designers into the mathematical programming optimization. A modular superstructure representation is used to model the design space; in a superstructure a union of all potential architectures is represented as a set of discrete and continuous variables. Algebraic constraints are added to describe both acceptable variable combinations and system behavior to allow the solver to eliminate clearly poor alternatives and identify promising alternatives. The framework is demonstrated on the selection of an actuation subsystem for a hydraulic excavator, although the solution approach would be similar for most mechanical systems.
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Lijie Su, Lixin Tang, and Jianyou Xu. "Mathematical programming formulation for campaign planning of multi-product batch process." In 2008 Chinese Control and Decision Conference (CCDC). IEEE, 2008. http://dx.doi.org/10.1109/ccdc.2008.4597428.

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Luan, Shi-chao, Guo-zhu Jia, and Wen Kong. "A mathematical programming formulation approach to the number of POLCA cards." In 2012 International Conference on Management Science and Engineering (ICMSE). IEEE, 2012. http://dx.doi.org/10.1109/icmse.2012.6414186.

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Pierce, Robert Scott, and David Rosen. "Simulation of Mating Between Non-Analytic Surfaces Using a Mathematical Programming Formulation." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84232.

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In this paper we describe a new method for simulating mechanical assembly between components that are composed of surfaces that do not have perfect geometric form. Mating between these imperfect form surfaces is formulated as a constrained optimization problem of the form “minimize the distance from perfect fit, subject to non-interference between components.” We explore the characteristics of this mating problem and investigate the applicability of several potential solution algorithms. The problem can be solved by converting the constrained optimization formulation into an unconstrained problem using a penalty-function approach. We describe the characteristics of this unconstrained formulation and test the use of two different solution methods: a randomized search technique and a gradient-based method. We test the algorithm by simulating mating between component models that exhibit form errors typically generated in end-milling processes. These typical component variants are used as validation problems throughout our work. Results of two different validation problems are presented. Using these results, we evaluate the applicability of the mating algorithm to the problem of mechanical tolerance analysis for assemblies and mechanisms.
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Rodríguez-Bocca, Pablo, and Héctor Cancela. "A mathematical programming formulation of optimal cache expiration dates in content networks." In the 3rd international IFIP/ACM Latin American conference. New York, New York, USA: ACM Press, 2005. http://dx.doi.org/10.1145/1168117.1168130.

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Grødal, Evert O., and Matthew J. Realff. "Optimal Design of Two- and Three- Phase Separators: A Mathematical Programming Formulation." In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers, 1999. http://dx.doi.org/10.2118/56645-ms.

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Sadat, Sayed A., and Lingling Fan. "Mixed integer linear programming formulation for chance constrained mathematical programs with equilibrium constraints." In 2017 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2017. http://dx.doi.org/10.1109/pesgm.2017.8273875.

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Shah, Aditya A., Christiaan J. J. Paredis, Roger Burkhart, and Dirk Schaefer. "Combining Mathematical Programming and SysML for Automated Component Sizing of Hydraulic Systems." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28960.

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In this paper, we present a framework that improves a designer’s capability to determine near-optimal sizes of components for a given system architecture. Component sizing is a hard problem to solve because of competing objectives, requirements from multiple disciplines, and the need for finding a solution quickly for the architecture being considered. In current approaches, designers rely on heuristics and iterate over the multiple objectives and requirements until a satisfactory solution is found. To improve on this state of practice, we introduce advances in the following two areas: a) Formulating a component sizing problem in a manner that is convenient to designers and b) Solving the problem efficiently so that all of the imposed requirements are satisfied simultaneously and the solution obtained is mathematically optimal. An acausal, algebraic, equation-based, declarative modeling approach using mathematical programming (GAMS) is taken to solve these problems more efficiently. In addition the Systems Modeling Language (OMG SysML™) is used to formulate component sizing problems to facilitate problem formulation, model reuse and the automatic generation of low-level code that can be solved using GAMS and its solvers (BARON). This framework is demonstrated by applying it to an example of a hydraulic log splitter.
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Dhingra, A. K., and S. S. Rao. "Integrated Optimal Design of Planar Mechanisms Using Fuzzy Theories." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0086.

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Abstract A new integrated approach to the design of high speed planar mechanisms is presented. The resulting nonlinear programming formulation combines both the kinematic and dynamic synthesis aspects of mechanism design. The multiobjective optimization techniques presented in this work facilitate the design of a linkage to meet several kinematic and dynamic design criteria. The method can be used for motion, path, and function generation problems. The nonlinear programming formulation also permits the imposition of constraints to eliminate solutions which possess undesirable kinematic and motion characteristics. To model the vague and imprecise information in the problem formulation, the tools of fuzzy set theory have been used. A method of solving the resulting fuzzy multiobjective problem using mathematical programming techniques is presented. The outlined procedure is expected to be useful in situations where doubt arises about the exactness of permissible values, degree of credibility, and correctness of statements and judgements.
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Ota, Matheus J., Flávio K. Miyazawa, and Phablo F. S. Moura. "The Balanced Connected k-Partition Problem: Polyhedra and Algorithms." In Concurso de Teses e Dissertações da SBC. Sociedade Brasileira de Computação, 2021. http://dx.doi.org/10.5753/ctd.2021.15763.

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The balanced connected k-partition (BCPk) problem consists in partitioning a connected graph into connected subgraphs with similar weights. This problem arises in multiple practical applications, such as police patrolling, image processing, data base and operating systems. In this work, we address the BCPk using mathematical programming. We propose a compact formulation based on flows and a formulation based on separators. We introduce classes of valid inequalities and design polynomial-time separation routines. Moreover, to the best of our knowledge, we present the first polyhedral study for BCPk in the literature. Finally, we report on computational experiments showing that the proposed algorithms significantly outperform the state of the art for BCPk.
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Reports on the topic "Mathematical programming formulation"

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Ratmanski, Kiril, and Sergey Vecherin. Resilience in distributed sensor networks. Engineer Research and Development Center (U.S.), October 2022. http://dx.doi.org/10.21079/11681/45680.

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With the advent of cheap and available sensors, there is a need for intelligent sensor selection and placement for various purposes. While previous research was focused on the most efficient sensor networks, we present a new mathematical framework for efficient and resilient sensor network installation. Specifically, in this work we formulate and solve a sensor selection and placement problem when network resilience is also a factor in the optimization problem. Our approach is based on the binary linear programming problem. The generic formulation is probabilistic and applicable to any sensor types, line-of-site and non-line-of-site, and any sensor modality. It also incorporates several realistic constraints including finite sensor supply, cost, energy consumption, as well as specified redundancy in coverage areas that require resilience. While the exact solution is computationally prohibitive, we present a fast algorithm that produces a near-optimal solution that can be used in practice. We show how such formulation works on 2D examples, applied to infrared (IR) sensor networks designed to detect and track human presence and movements in a specified coverage area. Analysis of coverage and comparison of sensor placement with and without resilience considerations is also performed.
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Macal, C. M., and A. P. Hurter. Solution of mathematical programming formulations of subgame perfect equilibrium problems. Office of Scientific and Technical Information (OSTI), February 1992. http://dx.doi.org/10.2172/10134527.

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