Tesi: "Mixed integer nonlinear programming"

1

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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Wiese, Sven <1985&gt. "On the interplay of Mixed Integer Linear, Mixed Integer Nonlinear and Constraint Programming". Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amsdottorato.unibo.it/7612/.

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In this thesis we study selected topics in the field of Mixed Integer Programming (MIP), in particular Mixed Integer Linear and Nonlinear Programming (MI(N)LP). We set a focus on the influences of Constraint Programming (CP). First, we analyze Mathematical Programming approaches to water network optimization, a set of challenging optimization problems frequently modeled as non-convex MINLPs. We give detailed descriptions of many variants and survey solution approaches from the literature. We are particularly interested in MILP approximations and present a respective computational study for water network design problems. We analyze this approach by algorithmic considerations and highlight the importance of certain convex substructures in these non-convex MINLPs. We further derive valid inequalities for water network design problems exploiting these substructures. Then, we treat Mathematical Programming problems with indicator constraints, recalling their most popular reformulation techniques in MIP, leading to either big-M constraints or disjunctive programming techniques. The latter give rise to reformulations in higher-dimensional spaces, and we review special cases from the literature that allow to describe the projection on the original space of variables explicitly. We theoretically extend the respective results in two directions and conduct computational experiments. We then present an algorithm for MILPs with indicator constraints that incorporates elements of CP into MIP techniques, including computational results for the JobShopScheduling problem. Finally, we introduce an extension of the class of MILPs so that linear expressions are allowed to have non-contiguous domains. Inspired by CP, this permits to model holes in the domains of variables as a special case. For such problems, we extend the theory of split cuts and show two ways of separating them, namely as intersection and lift-and-project cuts, and present computational results. We further experiment with an exact algorithm for such problems, applied to the Traveling Salesman Problem with multiple time windows.

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Akrotirianakis, Ioannis. "Interior point methods for nonlinear programming and application to mixed integer nonlinear programming". Thesis, Imperial College London, 2011. http://hdl.handle.net/10044/1/7923.

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The main objectives of this thesis are (i) to develop primal-dual interior point algorithms for solving Nonlinear Programming (NLP) problems (ii) to develop a branch and cut algorithm for solving 0-1 Mixed Integer Nonlinear Programming (MINLP) problems and (iii) the application of the interior point algorithms to solve the NLP problems arising during the solution process of a 0-1 MINLP problem. Two primal-dual interior point algorithms are developed for solving NLP problems with both equality and inequality constraints. In the first algorithm the perturbed optimality conditions of the initial problem are solved by using a quasi- Newton method. The descent property of the search direction is established for a penalty-barrier merit function, based on an approximation of Fletcher's exact and differentiable penalty function. In the second algorithm, an equivalent problem is formulated with the equality constraints incorporated into the objective by means of the quadratic penalty function. The inequality constraints are also included into the objective by means of the logarithmic barrier function. The optimality conditions of the transformed problem are solved by using a quasi-Newton method. The descent property of the search direction is ensured for a merit function, using an adaptive strategy to determine the penalty parameter. Global convergence of both interior point algorithms is achieved through line search procedures that ensure the monotonic decrease of the corresponding merit function. Numerical results demonstrate the efficient performance of both algorithms for a variety of test problems. A branch and cut algorithm is also developed for solving 0-1 MINLP problems. The algorithm integrates Branch and Bound, Outer Approximation and Gomory Cutting Planes. Only the initial Mixed Integer Linear Programming (MILP) master problem is considered. At integer solutions NLP problems are solved, using the primal-dual interior point algorithms mentioned above. The objective and constraints are linearized at the optimum solution of those NLP problems and the linearizations are added to all the unsolved nodes of the enumerations tree. Also, Gomory cutting planes, which are valid throughout the tree, are generated at selected nodes. These cuts help the algorithm to locate integer solutions quickly and consequently improve the linear approximation of the objective and constraints, held at the unsolved nodes of the tree. Numerical results show that the addition of Gomory cuts can reduce the number of nodes in the enumeration tree.

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Vigerske, Stefan. "Decomposition in multistage stochastic programming and a constraint integer programming approach to mixed-integer nonlinear programming". Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://dx.doi.org/10.18452/16704.

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Diese Arbeit leistet Beiträge zu zwei Gebieten der mathematischen Programmierung: stochastische Optimierung und gemischt-ganzzahlige nichtlineare Optimierung (MINLP). Im ersten Teil erweitern wir quantitative Stetigkeitsresultate für zweistufige stochastische gemischt-ganzzahlige lineare Programme auf Situationen in denen Unsicherheit gleichzeitig in den Kosten und der rechten Seite auftritt, geben eine ausführliche Übersicht zu Dekompositionsverfahren für zwei- und mehrstufige stochastische lineare und gemischt-ganzzahlig lineare Programme, und diskutieren Erweiterungen und Kombinationen des Nested Benders Dekompositionsverfahrens und des Nested Column Generationsverfahrens für mehrstufige stochastische lineare Programme die es erlauben die Vorteile sogenannter rekombinierender Szenariobäume auszunutzen. Als eine Anwendung dieses Verfahrens betrachten wir die optimale Zeit- und Investitionsplanung für ein regionales Energiesystem unter Einbeziehung von Windenergie und Energiespeichern. Im zweiten Teil geben wir eine ausführliche Übersicht zum Stand der Technik bzgl. Algorithmen und Lösern für MINLPs und zeigen dass einige dieser Algorithmen innerhalb des constraint integer programming Softwaresystems SCIP angewendet werden können. Letzteres erlaubt uns die Verwendung schon existierender Technologien für gemischt-ganzzahlige linear Programme und constraint Programme für den linearen und diskreten Teil des Problems. Folglich konzentrieren wir uns hauptsächlich auf die Behandlung der konvexen und nichtkonvexen nichtlinearen Nebenbedingungen mittels Variablenschrankenpropagierung, äußerer Approximation und Reformulierung. In einer ausführlichen numerischen Studie untersuchen wir die Leistung unseres Ansatzes anhand von Anwendungen aus der Tagebauplanung und des Aufbaus eines Wasserverteilungssystems und mittels verschiedener Vergleichstests. Die Ergebnisse zeigen, dass SCIP ein konkurrenzfähiger Löser für MINLPs geworden ist.
This thesis contributes to two topics in mathematical programming: stochastic optimization and mixed-integer nonlinear programming (MINLP). In the first part, we extend quantitative continuity results for two-stage stochastic mixed-integer linear programs to include situations with simultaneous uncertainty in costs and right-hand side, give an extended review on decomposition algorithm for two- and multistage stochastic linear and mixed-integer linear programs, and discuss extensions and combinations of the Nested Benders Decomposition and Nested Column Generation methods for multistage stochastic linear programs to exploit the advantages of so-called recombining scenario trees. As an application of the latter, we consider the optimal scheduling and investment planning for a regional energy system including wind power and energy storages. In the second part, we give a comprehensive overview about the state-of-the-art in algorithms and solver technology for MINLPs and show that some of these algorithm can be applied within the constraint integer programming framework SCIP. The availability of the latter allows us to utilize the power of already existing mixed integer linear and constraint programming technologies to handle the linear and discrete parts of the problem. Thus, we focus mainly on the domain propagation, outer-approximation, and reformulation techniques to handle convex and nonconvex nonlinear constraints. In an extensive computational study, we investigate the performance of our approach on applications from open pit mine production scheduling and water distribution network design and on various benchmarks sets. The results show that SCIP has become a competitive solver for MINLPs.

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5

Nowak, Ivo. "Relaxation and decomposition methods for mixed integer nonlinear programming". [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=974403326.

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Nowak, Ivo. "Relaxation and decomposition methods for mixed integer nonlinear programming". Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2005. http://dx.doi.org/10.18452/13962.

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Die Habilitationsschrift beschäftigt sich mit Theorie, Algorithmen und Software zur Lösung von nichtkonvexen, gemischt-ganzzahligen, nichtlinearen Optimierungsproblemen (MINLP). Sie besteht aus 14 Kapiteln, die in zwei Teile gegliedert sind. Im ersten Teil werden grundlegende Optimierungswerkzeuge beschrieben und im zweiten Teil werden Lösungsalgorithmen vorgestellt. Fast alle vorgeschlagenen Algorithmen wurden als Teil der objektorientierten C++ Bibliothek LaGO implementiert. Numerische Experimente mit verschiedenen MINLP-Problemen zeigen die Möglichkeiten und Grenzen dieser Verfahren.
This book is concerned with theory, algorithms and software for solving nonconvex mixed integer nonlinear programs. It consists of two parts. The first part describes basic optimization tools, such as block-separable reformulations, convex and Lagrangian relaxations, decomposition methods and global optimality criteria. The second part is devoted to algorithms. Starting with a short overview on existing methods, we present deformation, rounding, partitioning and Lagrangian heuristics, and a branch-cut-and-price algorithm. The algorithms are implemented as part of an object-oriented library, called LaGO. We report numerical results on several mixed integer nonlinear programs to show abilities and limits of the proposed solution methods.

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Philipp, Anne [Verfasser]. "Mixed-Integer Nonlinear Programming with Application to Wireless Communication Systems / Anne Philipp". München : Verlag Dr. Hut, 2015. http://d-nb.info/1077403984/34.

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8

Schilling, Gordian Hansjoerg. "Algorithms for short-term and periodic process scheduling and rescheduling". Thesis, Imperial College London, 1998. http://hdl.handle.net/10044/1/7696.

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9

Handley-Schachler, Sybille H. "Applications of parallel processing to optimization". Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240512.

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10

Vigerske, Stefan [Verfasser], Werner [Akademischer Betreuer] Römisch, Rüdiger [Akademischer Betreuer] Schultz e Pierre [Akademischer Betreuer] Bonami. "Decomposition in multistage stochastic programming and a constraint integer programming approach to mixed-integer nonlinear programming / Stefan Vigerske. Gutachter: Werner Römisch ; Rüdiger Schultz ; Pierre Bonami". Berlin : Humboldt Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://d-nb.info/1033586579/34.

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11

Mesquita, Luis Clemente. "Structural optimization for control of stiffened laminated composite plates using nonlinear mixed integer programming". Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/52309.

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The effect of structural optimization on control of stiffened laminated composite structures is considered. The structural optimization considered here, is the maximization of structural frequencies of the structure subject to maximum weight and frequency separation constraints and an upper bound on weight. The number of plies with a given orientation and the stiffener areas form the two sets of design variables. As the number of plies is restricted to integer values, the optimization problem considered belongs to the class of nonlinear mixed integer problems (NMIP). Several efficiency measures are proposed to reduce the computational cost for solution of the optimization problem. Savings in computer time due to each of the measures is discussed. The control problem is solved using the independent modal space control technique. This technique greatly simplifies the evaluation of the sensitivity of the performance index with respect to the individual frequencies. The effect of different optimization schemes on the control performance is considered. To reduce the probability, that conclusions drawn from numerical results, are purely coincidental, a large number of cases has been studied. It has been concluded that sufficient improvement in control performance can be achieved through structural optimization.
Ph. D.

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Huang, Wei. "Optimal Operation of Water Supply Networks by Mixed Integer Nonlinear Programming and Algebraic Methods". Phd thesis, tuprints, 2019. http://tuprints.ulb.tu-darmstadt.de/8657/1/Dissertation_Wei_Huang.pdf.

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In this thesis we are dealing with the operative planning of water supply networks. The task of an operative planning is to create a pump and valve configuration such that the water requirement from consumers is fulfilled with necessary quality. An optimal operation corresponds to a configuration that minimizes the operation cost as well as potential water procurement cost. There are different ways to handle this problem. We solve it as an optimization problem using mathematical programming. On the one hand, the network problem contains some discrete variables, for example, the pump or valve status; on the other hand, nonlinearities and nonconvexities from physical behaviors make the mathematical model extremely difficult. We model the optimization problem as a mixed-integer nonlinear program (MINLP). We choose MINLP solver SCIP, developed mainly at Zuse Insitute Berlin. We use two real-world instances provided by industrial partner Siemens and a further real-world instance obtained from the Department of Hydraulic Engineering of Tsinghua University. In this thesis, we first show that our solver SCIP is able to solve the optimal operation problem to global optimality in a fixed point of time. However, for a daily operation which contains 24 coupled time periods (hours), "good" solutions are usually found rapidly, but the dual gap cannot verify the solution quality. In a further chapter we show that a class of subnetworks which only contains pipes and consumers, can be simplified and the original nonlinear constraints can be replaced by few (or single) nonlinear constraints, without changing the feasible region. Computation shows that this simplification makes the MINLP easier to solve. The algorithm which solves our nonconvex MINLP generates at every iteration a convex relaxation of the feasible region. A lot of theories and experiments showed that tighter convex relaxation is quite relevant for the branch-and-bound approach. In the objective of our model, we have bivariate polynomial term with degree 3. Based on the default construction of convex relaxation, we want to find additional linear constrains ("valid cuts") to make the relaxation tighter. We investigate the graph of general polynomial functions over a polytope in general dimension and develop theory to describe the convex hull of the graph and to find halfspaces which contain the convex hull. After that we define "tight" halfspaces which denote the "efficient" halfspaces when forming the convex hull. For bivariate polynomial functions with degree 3, algorithms are designed to find such tight halfspaces. After adding these halfspaces (linear constraints) into the MINLP, computation shows that both primal and dual bound are definitively improved within the same time limit.

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Mencarelli, Luca. "The Multiplicative Weights Update Algorithm for Mixed Integer NonLinear Programming : Theory, Applications, and Limitations". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX099/document.

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L'objectif de cette thèse consiste à présenter un nouvel algorithme pour la programmation non linéaire en nombres entiers, inspirée par la méthode Multiplicative Weights Update et qui compte sur une nouvelle classe de reformulations, appelées les reformulations ponctuelles.La programmation non linéaire en nombres entiers est un sujet très difficile et fascinant dans le domaine de l'optimisation mathématique à la fois d'un point de vue théorique et computationnel. Il est possible de formuler de nombreux problèmes dans ce schéma général et, habituellement, ils posent de réels défis en termes d'efficacité et de précision de la solution obtenue quant aux procédures de résolution.La thèse est divisée en trois parties principales : une introduction composée par le Chapitre 1, une définition théorique du nouvel algorithme dans le Chapitre 2 et l'application de cette nouvelle méthodologie à deux problèmes concrets d'optimisation, tels que la sélection optimale du portefeuille avec le critère moyenne-variance dans le Chapitre 3 et le problème du sac à dos non linéaire dans le Chapitre 4. Conclusions et questions ouvertes sont présentées dans le Chapitre 5
This thesis presents a new algorithm for Mixed Integer NonLinear Programming, inspired by the Multiplicative Weights Update framework and relying on a new class of reformulations, called the pointwise reformulations.Mixed Integer NonLinear Programming is a hard and fascinating topic in Mathematical Optimization both from a theoretical and a computational viewpoint. Many real-word problems can be cast this general scheme and, usually, are quite challenging in terms of efficiency and solution accuracy with respect to the solving procedures.The thesis is divided in three main parts: a foreword consisting in Chapter 1, a theoretical foundation of the new algorithm in Chapter 2, and the application of this new methodology to two real-world optimization problems, namely the Mean-Variance Portfolio Selection in Chapter 3, and the Multiple NonLinear Separable Knapsack Problem in Chapter 4. Conclusions and open questions are drawn in Chapter 5

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Sadat, Sayed Abdullah. "Optimal Bidding Strategy for a Strategic Power Producer Using Mixed Integer Programming". Scholar Commons, 2017. http://scholarcommons.usf.edu/etd/6631.

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The thesis focuses on a mixed integer linear programming (MILP) formulation for a bi-level mathematical program with equilibrium constraints (MPEC) considering chance constraints. The particular MPEC problem relates to a power producer’s bidding strategy: maximize its total benefit through determining bidding price and bidding power output while considering an electricity pool’s operation and guessing the rival producer’s bidding price. The entire decision-making process can be described by a bi-level optimization problem. The contribution of our thesis is the MILP formulation of this problem considering the use of chance constrained mathematical program for handling the uncertainties. First, the lower-level poor operation problem is replaced by Karush-Kuhn-Tucker (KKT) optimality condition, which is further converted to an MILP formulation except a bilinear item in the objective function. Secondly, duality theory is implemented to replace the bilinear item by linear items. Finally, two types of chance constraints are examined and modeled in MILP formulation. With the MILP formulation, the entire MPEC problem considering randomness in price guessing can be solved using off-shelf MIP solvers, e.g., Gurobi. A few examples and a case study are given to illustrate the formulation and show the case study results.

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Andreas, April Kramer. "Mathematical Programming Algorithms for Reliable Routing and Robust Evacuation Problems". Diss., The University of Arizona, 2006. http://hdl.handle.net/10150/195737.

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Most traditional routing problems assume perfect operability of all arcs and nodes. However, when independent arc failure probabilities exist, a secondary objective must be present to retain some measure of expected functionality. We first briefly consider the reliability-constrained single-path problem, where we look for the lowest cost path that meets a reliability side constraint. This analysis enables us to then examine the reliability-constrained two-path problem, which seeks to establish two minimum-cost paths between a source and destination node wherein at least one path must remain fully operable with some threshold probability. We consider the case in which both paths must be arc-disjoint and the case in which arcs can be shared between the paths. We prove both problems to be NP-hard. We examine strategies for solving the resulting nonlinear integer program, including pruning, coefficient tightening, lifting, and branch-and-bound partitioning schemes. Next, we consider the reliable h-path routing problem, which seeks a minimum-cost set of h ≥ 2 arc-independent paths between a source and destination node, such that the probability that at least one path remains operational is sufficiently large. Our prior arc-based models and algorithms tailored for the case in which h = 2 do not extend well to the general h-path problem. Thus, we propose two alternative integer programming formulations for the h-path problem in which the variables correspond to origin-destination paths. We propose two branch-and-price-and-cut algorithms for solving these new formulations, and provide computational results to demonstrate the efficiency of these algorithms. Finally, we examine the robust design of an evacuation tree, in which evacuation is subject to capacity restrictions on arcs. Given a discrete set of disaster scenarios with varying network populations, arc capacities, transit times, and time-dependent penalty functions, we seek to establish an optimal a priori evacuation tree that minimizes the expected evacuation penalty. The solution strategy is based on Benders decomposition, and we provide effcient methods for obtaining primal and dual sub-problem solutions. We analyze techniques for strengthening the master problem formulation, thus reducing the number of master problem solutions required for the algorithm's convergence.

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Trieu, Long [Verfasser], Christoph [Akademischer Betreuer] Buchheim e Christian [Gutachter] Meyer. "Continuous optimization methods for onvex mixed-integer nonlinear programming / Long Trieu. Betreuer: Christoph Buchheim. Gutachter: Christian Meyer". Dortmund : Universitätsbibliothek Dortmund, 2015. http://d-nb.info/1110892640/34.

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Uebbing, Jennifer Verfasser], Sebastian [Gutachter] [Sager e Kai [Gutachter] Sundmacher. "Power-to-methane process synthesis via mixed integer nonlinear programming / Jennifer Uebbing ; Gutachter: Sebastian Sager, Kai Sundmacher". Magdeburg : Universitätsbibliothek Otto-von-Guericke-Universität, 2021. http://d-nb.info/1236341007/34.

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Al, Ismaili Riham. "Optimisation of heat exchanger network maintenance scheduling problems". Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/280281.

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This thesis focuses on the challenges that arise from the scheduling of heat exchanger network maintenance problems which undergo fouling and run continuously over time. The original contributions of the current research consist of the development of novel optimisation methodologies for the scheduling of cleaning actions in heat exchanger network problems, the application of the novel solution methodology developed to other general maintenance scheduling problems, the development of a stochastic programming formulation using this optimisation technique and its application to these scheduling problems with parametric uncertainty. The work presented in this thesis can be divided into three areas. To efficiently solve this non-convex heat exchanger network maintenance scheduling problem, new optimisation strategies are developed. The resulting contributions are outlined below. In the first area, a novel methodology is developed for the solution of the heat exchanger network maintenance scheduling problems, which is attributed towards a key discovery in which it is observed that these problems exhibit bang-bang behaviour. This indicates that when integrality on the binary decision variables is relaxed, the solution will tend to either the lower or the upper bound specified, obviating the need for integer programming solution techniques. Therefore, these problems are in ac- tuality optimal control problems. To suitably solve these problems, a feasible path sequential mixed integer optimal control approach is proposed. This methodology is coupled with a simple heuristic approach and applied to a range of heat exchanger network case studies from crude oil refinery preheat trains. The demonstrated meth- odology is shown to be robust, reliable and efficient. In the second area of this thesis, the aforementioned novel technique is applied to the scheduling of the regeneration of membranes in reverse osmosis networks which undergo fouling and are located in desalination plants. The results show that the developed solution methodology can be generalised to other maintenance scheduling problems with decaying performance characteristics. In the third and final area of this thesis, a stochastic programming version of the feasible path mixed integer optimal control problem technique is established. This is based upon a multiple scenario approach and is applied to two heat exchanger network case studies of varying size and complexity. Results show that this methodology runs automatically with ease without any failures in convergence. More importantly due to the significant impact on economics, it is vital that uncertainty in data is taken into account in the heat exchanger network maintenance scheduling problem, as well as other general maintenance scheduling problems when there is a level of uncertainty in parameter values.

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Theußl, Stefan, Florian Schwendinger e Kurt Hornik. "ROI: An extensible R Optimization Infrastructure". WU Vienna University of Economics and Business, 2019. http://epub.wu.ac.at/5858/1/ROI_StatReport.pdf.

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Optimization plays an important role in many methods routinely used in statistics, machine learning and data science. Often, implementations of these methods rely on highly specialized optimization algorithms, designed to be only applicable within a specific application. However, in many instances recent advances, in particular in the field of convex optimization, make it possible to conveniently and straightforwardly use modern solvers instead with the advantage of enabling broader usage scenarios and thus promoting reusability. This paper introduces the R Optimization Infrastructure which provides an extensible infrastructure to model linear, quadratic, conic and general nonlinear optimization problems in a consistent way. Furthermore, the infrastructure administers many different solvers, reformulations, problem collections and functions to read and write optimization problems in various formats.
Series: Research Report Series / Department of Statistics and Mathematics

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Müller, Benjamin [Verfasser], Thorsten [Akademischer Betreuer] Koch, Thorsten [Gutachter] Koch, Andrea [Gutachter] Lodi e Marc [Gutachter] Pfetsch. "Tighter relaxations in mixed-integer nonlinear programming / Benjamin Müller ; Gutachter: Thorsten Koch, Andrea Lodi, Marc Pfetsch ; Betreuer: Thorsten Koch". Berlin : Technische Universität Berlin, 2020. http://d-nb.info/1210027194/34.

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Gleixner, Ambros M. [Verfasser], Martin [Akademischer Betreuer] Grötschel, Thorsten [Gutachter] Koch e Andrea [Gutachter] Lodi. "Exact and fast algorithms for mixed-integer nonlinear programming / Ambros M. Gleixner ; Gutachter: Thorsten Koch, Andrea Lodi ; Betreuer: Martin Grötschel". Berlin : Technische Universität Berlin, 2015. http://d-nb.info/1156015839/34.

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Serrano, Musalem Felipe [Verfasser], Thorsten [Akademischer Betreuer] Koch, Thorsten [Gutachter] Koch e Juan Pablo [Gutachter] Vielma. "On cutting planes for mixed-integer nonlinear programming / Felipe Serrano Musalem ; Gutachter: Thorsten Koch, Juan Pablo Vielma ; Betreuer: Thorsten Koch". Berlin : Technische Universität Berlin, 2021. http://d-nb.info/1239177151/34.

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Lobato, Rafael Durbano. "Algoritmos para problemas de programação não-linear com variáveis inteiras e contínuas". Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/45/45134/tde-06072009-130912/.

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Muitos problemas de otimização envolvem tanto variáveis inteiras quanto contínuas e podem ser modelados como problemas de programação não-linear inteira mista. Problemas dessa natureza aparecem com freqüência em engenharia química e incluem, por exemplo, síntese de processos, projeto de colunas de destilação, síntese de rede de trocadores de calor e produção de óleo e gás. Neste trabalho, apresentamos algoritmos baseados em Lagrangianos Aumentados e branch and bound para resolver problemas de programação não-linear inteira mista. Duas abordagens são consideradas. Na primeira delas, um algoritmo do tipo Lagrangianos Aumentados é usado como método para resolver os problemas de programação não-linear que aparecem em cada um dos nós do método branch and bound. Na segunda abordagem, usamos o branch and bound para resolver os problemas de minimização em caixas com variáveis inteiras que aparecem como subproblemas do método de Lagrangianos Aumentados. Ambos os algoritmos garantem encontrar a solução ótima de problemas convexos e oferecem recursos apropriados para serem usados na resolução de problemas não convexos, apesar de não haver garantia de otimalidade nesse caso. Apresentamos um problema de empacotamento de retângulos em regiões convexas arbitrárias e propomos modelos para esse problema que resultam em programas não-lineares com variáveis inteiras e contínuas. Realizamos alguns experimentos numéricos e comparamos os resultados obtidos pelo método descrito neste trabalho com os resultados alcançados por outros métodos. Também realizamos experimentos com problemas de programação não-linear inteira mista encontrados na literatura e comparamos o desempenho do nosso método ao de outro disponível publicamente.
Many optimization problems contain both integer and continuous variables and can be modeled as mixed-integer nonlinear programming problems. Problems of this nature appear frequently in chemical engineering and include, for instance, process synthesis, design of distillation columns, heat exchanger network synthesis and oil and gas production. In this work, we present algorithms based on Augmented Lagrangians and branch and bound for solving mixed-integer nonlinear programming problems. Two approaches are considered. In the first one, an Augmented Lagrangian algorithm is used for solving nonlinear programming problems that appear at each node in the branch and bound method. In the second approach, we use a branch and bound method for solving box-constrained problems with integer variables that appear as subproblems of the Augmented Lagrangian algorithm. Both algorithms guarantee to find an optimal solution for convex problems and have appropriate strategies to deal with non-convex problems, although there is no guarantee of optimality in this case. We present a problem of packing rectangles within an arbitrary convex region and propose models for this problem that result in nonlinear programs with integer and continuous variables. We have performed some numerical experiments and compared the results reached by the method described in this work and the results obtained by other methods. We have also performed experiments with mixed-integer nonlinear programming problems found in the literature and compared the performance of our method to that of other method publicly available.

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Huang, Wei [Verfasser], Marc E. [Akademischer Betreuer] Pfetsch e Raymond [Akademischer Betreuer] Hemmecke. "Optimal Operation of Water Supply Networks by Mixed Integer Nonlinear Programming and Algebraic Methods / Wei Huang ; Marc E. Pfetsch, Raymond Hemmecke". Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2019. http://d-nb.info/1187919799/34.

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Vinel, Alexander. "Mathematical programming techniques for solving stochastic optimization problems with certainty equivalent measures of risk". Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1786.

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The problem of risk-averse decision making under uncertainties is studied from both modeling and computational perspectives. First, we consider a framework for constructing coherent and convex measures of risk which is inspired by infimal convolution operator, and prove that the proposed approach constitutes a new general representation of these classes. We then discuss how this scheme may be effectively employed to obtain a class of certainty equivalent measures of risk that can directly incorporate decision maker's preferences as expressed by utility functions. This approach is consequently utilized to introduce a new family of measures, the log-exponential convex measures of risk. Conducted numerical experiments show that this family can be a useful tool when modeling risk-averse decision preferences under heavy-tailed distributions of uncertainties. Next, numerical methods for solving the rising optimization problems are developed. A special attention is devoted to the class p-order cone programming problems and mixed-integer models. Solution approaches proposed include approximation schemes for $p$-order cone and more general nonlinear programming problems, lifted conic and nonlinear valid inequalities, mixed-integer rounding conic cuts and new linear disjunctive cuts.

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26

Hannisdal, Erik Lundegaard. "Optimal Voltage Control of the Southern Norwegian Power Grid : Mixed Integer Nonlinear Programming (MINLP) for Control and Optimization of the High Voltage Southern Norwegian Power Grid". Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for teknisk kybernetikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-13180.

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This thesis contains the synthesis, analysis and simulation results of an automatic optimal voltage controller for the Southern Norwegian power grid. Currently the high voltage power grid is controlled manually by operators switching control components. The optimal controller handles the voltage control of the system, as well as keeping the number of control actions to a minimum.The system model is derived from power system analysis. Due to a highy nonlinear system model and integer decission variables in on/off control components, the controller is based on mixed integer nonlinear programming (MINLP). The MINLP uses BONMIN as a solver, and is implemented with the AMPL programming language.It was found that a MINLP controller is good choice for voltage control in transmission systems. The controller handles voltage limits, as well as reducing the number of control actions.The thesis also contains comparison between different solution methods for applying the optimal voltage controller, as well as other approaches to the automatic voltage control problem.

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Maragno, Donato. "Optimization with machine learning-based modeling: an application to humanitarian food aid". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21621/.

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In this thesis, we propose a machine learning-based optimization methodology to build (part of) optimization models with a data-driven approach. This approach is useful whenever we have to model one or more relations between the decisions and their impact on the system. This kind of relationship can be challenging to model manually, and so machine learning is used to learn it through the use of data. We demonstrate the potential of this method through a case study in which a predictive model is used to approximate the palatability scoring function in a typical diet problem formulation. First, the performance of this approach is analyzed by embedding a Linear Regression model and then by embedding a Fully Connected Neural Network.

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Jitprapaikulsarn, Suradet. "An Optimization-Based Treatment Planner for Gamma Knife Radiosurgery". Case Western Reserve University School of Graduate Studies / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=case1109959500.

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Spratt, Belinda G. "Reactive operating theatre scheduling". Thesis, Queensland University of Technology, 2018. https://eprints.qut.edu.au/116885/1/Belinda_Spratt_Thesis.pdf.

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This project considers the planning and scheduling of an operating theatre at a large Australian public hospital, with the aim of reducing the length of elective surgery waiting lists. Operating theatre planning and scheduling is performed using an integrated approach, where specialties, surgeons, and patients are scheduled simultaneously. Hyper and hybrid metaheuristic techniques are presented, as the case study instances are too difficult for commercial solvers. Results indicate that these methods can be implemented in real-life to improve surgical departments at public hospitals by reducing surgical overtime, increasing patient throughput, and increasing operating theatre utilisation.

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Defterli, Ozlem. "Modern Mathematical Methods In Modeling And Dynamics Ofregulatory Systems Of Gene-environment Networks". Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613592/index.pdf.

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Inferring and anticipation of genetic networks based on experimental data and environmental measurements is a challenging research problem of mathematical modeling. In this thesis, we discuss gene-environment network models whose dynamics are represented by a class of time-continuous systems of ordinary differential equations containing unknown parameters to be optimized. Accordingly, time-discrete version of that model class is studied and improved by using different numerical methods. In this aspect, 3rd-order Heun&rsquo
s method and 4th-order classical Runge-Kutta method are newly introduced, iteration formulas are derived and corresponding matrix algebras are newly obtained. We use nonlinear mixed-integer programming for the parameter estimation and present the solution of a constrained and regularized given mixed-integer problem. By using this solution and applying the 3rd-order Heun&rsquo
s and 4th-order classical Runge-Kutta methods in the timediscretized model, we generate corresponding time-series of gene-expressions by this thesis. Two illustrative numerical examples are studied newly with an artificial data set and a realworld data set which expresses a real phenomenon. All the obtained approximate results are compared to see the goodness of the new schemes. Different step-size analysis and sensitivity tests are also investigated to obtain more accurate and stable predictions of time-series results for a better service in the real-world application areas. The presented time-continuous and time-discrete dynamical models are identified based on given data, and studied by means of an analytical theory and stability theories of rarefication, regularization and robustification.

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Pontes, Ricardo de Freitas Fernandes. "Modelagem e síntese ótima de rede de reatores de processos oxidativos avançados para o tratamento de efluentes". Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/3/3137/tde-18122009-131117/.

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Substâncias tóxicas como o fenol e outros compostos aromáticos dificultam o tratamento de efluentes via digestores biológicos. Estes compostos tóxicos em altas concentrações são nocivos aos lodos biológicos, podendo inviabilizar por completo o tratamento. Nas últimas décadas, os Processos Oxidativos Avançados (POAs), como os processos Fenton e foto- Fenton, surgiram como alternativa para o tratamento de compostos tóxicos. Os POAs degradam os compostos orgânicos pela geração de compostos oxidantes fortes, como o radical hidroxila, a partir de reagentes como peróxido de hidrogênio. Os processos Fenton e foto-Fenton fazem uso de ferro (II), um catalisador relativamente barato, para catalisar a decomposição do peróxido de hidrogênio, reação denominada como reação de Fenton. Em virtude dos complexos mecanismos presentes nos processos Fenton e foto-Fenton, torna-se necessária uma compreensão da cinética do processo, que envolve reações térmicas e fotoquímicas, por meio de sua modelagem matemática fenomenológica. A modelagem da degradação do fenol via processos Fenton e foto-Fenton proposta por este trabalho começa pela estequiometria dos dois processos, que descreve as reações químicas, térmicas e fotoquímicas existentes. A partir destas, é possível desenvolver o modelo cinético dos processos Fenton e foto-Fenton, no qual se determina a velocidade com que estas reações ocorrem. O passo seguinte é o da modelagem hidráulica (ou de escoamento) dos reatores de processo Fenton e foto-Fenton, sendo que para o segundo processo, o modelo deve levar em conta a propagação da radiação por dentro de reator. Foram realizados 3 experimentos de degradação de fenol via processo Fenton para análise das variações das concentrações de fenol, catecol e hidroquinona. Os dados experimentais são comparados com resultados simulados com intuito do ajuste das constantes cinéticas do modelo. Com as constantes ajustadas, são realizadas comparações entre os processos Fenton e foto-Fenton para análise de suas eficiências. A partir dos modelos matemáticos dos reatores de processos Fenton e foto-Fenton, é desenvolvido um modelo de otimização baseado em superestrutura de redes de reatores para a síntese de uma planta de tratamento de efluentes contaminados com fenol. Objetivou-se a redução dos custos de capital, operação e depreciação desta planta, sujeitos às restrições de projeto e ao modelo da superestrutura, resultando em modelos de programação não-linear inteira mista. Foram geradas soluções ótimas para o tratamento de efluentes contaminados com fenol em redes de um, dois e três reatores de POAs.
Toxic substances such as phenol and other aromatic compounds make the wastewater treatment by biological (aerobic or anaerobic) digestors more difficult. These toxic compounds in high concentrations are harmful for the biological sludge and they may render the treatment impractical. In recent decades, Advanced Oxidative Processes (AOPs) appeared as an alternative for the treatment of toxic compounds. AOPs degrade the organic compounds by generating strong oxidizing compounds, such as the hydroxyl radical, from reactants such as hydrogen peroxide. The Fenton and photo-Fenton processes make use of iron (II), a relatively inexpensive catalyst, to catalyze the hydrogen peroxide decomposition, reaction known as the Fenton reaction. Because of the complex nature of the mechanisms that take place in the Fenton and photo-Fenton processes, the understanding of the process kinetics, which involves thermal and photochemical reactions, becomes necessary through its first-principle mathematical modeling. The modeling of phenol degradation by the Fenton and photo-Fenton processes proposed in this work starts with the stoichiometry of the two processes that enumerates the existing thermal and photochemical reactions. Furthermore, it is possible to develop the Fenton and photo- Fenton kinetic model, which determines the reaction rates. The next step is to model the hydraulic (or flow) behavior of the Fenton and photo-Fenton process reactor, whereas the model for the latter must consider how the radiation propagates inside the reactor. Three experiments of the phenol degradation by the Fenton process were carried out to analyze the concentration variation for phenol, catechol and hydroquinone. The experimental data are compared with simulated results aiming the estimation of the kinetic constants of the model. Using the adjusted constants, the Fenton and photo-Fenton processes were compared to analyze their efficiencies. From the mathematical models of the Fenton and photo-Fenton process reactors, an optimization model based on reactor network superstructure is developed for the synthesis of a phenol contaminated wastewater treatment plant. The objective is to minimize the plant capital, operation and depreciation costs, subject to design constraints and to the superstructure model, thus resulting in mixed integer nonlinear programming models. Optimal solutions were generated for the phenol contaminated wastewater treatment in networks with one, two and three AOP reactors.

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Omer, Jérémy Jean Guy. "Modèles déterministes et stochastiques pour la résolution numérique du problème de maintien de séparation entre aéronefs". Thesis, Toulouse, ISAE, 2013. http://www.theses.fr/2013ESAE0007/document.

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Cette thèse s’inscrit dans le domaine de la programmation mathématique appliquée à la séparation d’aéronefs stabilisés en altitude. L’objectif est le développement d’algorithmes de résolution de conflits aériens ; l’enjeu étant d’augmenter la capacité de l’espace aérien afin de diminuer les retards et d’autoriser un plus grand nombre d’aéronefs à suivre leur trajectoire optimale. En outre, du fait de l’imprécision des prédictions relatives à la météo ou à l’état des aéronefs, l’incertitude sur les données est une caractéristique importante du problème. La démarche suivie dans ce mémoire s’attache d’abord au problème déterministe dont l’étude est nettement plus simple. Pour cela, quatre modèles basés sur la programmation non linéaire et sur la programmation linéaire à variables mixtes sont développés en intégrant notamment un critère reflétant la consommation de carburant et la durée de vol. Leur comparaison sur un ensemble de scénarios de test met en évidence l’intérêt d’utiliser un modèle linéaire approché pour l’étude du problème avec incertitudes. Un champ de vent aléatoire, corrélé en temps et en espace, ainsi qu’une erreur gaussienne sur la mesure de la vitesse sont ensuite pris en compte.Dans un premier temps, le problème déterministe est adapté en ajoutant une marge sur la norme de séparation grâce au calcul d’une approximation des probabilités de conflits. Finalement, une formulation stochastique avec recours est développée. Ainsi, les erreurs aléatoires sont explicitement incluses dans le modèle afin de tenir compte de la possibilité d’ordonner des manoeuvres de recours lorsque les erreurs observées engendrent de nouveaux conflits
This thesis belongs to the field of mathematical programming, applied to the separation of aircraft stabilised on the same altitude. The primary objective is to develop algorithms for the resolution of air conflicts. The expected benefit of such algorithm is to increase the capacity of the airspace in order to reduce the number of late flights and let more aircraft follow their optimal trajectory. Moreover, meteorological forecast and trajectory predictions being inexact,the uncertainty on the data is an important issue. The approach that is followed focuses on the deterministic problem in the first place because it is much simpler. To do this, four nonlinear and mixed integer linear programming models, including a criterion based on fuel consumption and flight duration, are developed. Their comparison on a benchmark of scenarios shows the relevance of using an approximate linear model for the study of the problem with uncertainties.A random wind field, correlated in space and time, as well as speed measures with Gaussianerrors are then taken into account. As a first step, the deterministic problem is adapted by computinga margin from an approximate calculation of conflict probabilities and by adding it tothe reference separation distance. Finally, a stochastic formulation with recourse is developed.In this model, the random errors are explicitly included in order to consider the possibility of ordering recourse actions if the observed errors cause new conflicts

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33

Swart, Marinda. "A Scheduling model for a coal handling facility [electronic resource] /". Diss., Pretoria : [s.n.], 2004. http://hdl.handle.net/2263/25388.

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The objective of this project is to develop an operational scheduling model for Sasol Mining’s coal handling facility, Sasol Coal Supply (referred to as SCS), to optimise daily operations. In this document, the specific scheduling problem at SCS is presented and solved using Mixed Integer Non-Linear Programming (MINLP) continuous time representation techniques. The most recent MINLP scheduling techniques are presented and applied to an example problem. The assumption is made that the results from the example problem will display trends which will apply to the SCS scheduling problem as well. Based on this assumption, the unit-specific event based continuous time formulation is chosen to apply to the SCS scheduling problem. The detail mathematical formulation of the SCS scheduling problem, based on the chosen technique, is discussed and the necessary changes presented to customise the formulation for the SCS situation. The results presented show that the first phase model does not solve within 72 hours. A solution time of more than three days is not acceptable for an operational scheduling model in a dynamic system like SCS. Various improvement approaches are applied during the second phase of the model development. Special Ordered Sets of Type 1 (SOS1) variables are successfully applied in the model to reduce the amount of binary variables. The time and duration constraints are restructured to simplify the structure of the model. A specific linearization and solution technique is applied to the non-linear equations to ensure reduced model solution times and reliable results. The improved model for one period solves to optimality within two minutes. This dramatic improvement ensures that the model will be used operationally at SCS to optimise daily operations. The scheduling model is currently being implemented at SCS. Examples of the input variables and output results are presented. It is concluded that the unit-specific event based MINLP continuous time formulation method, as presented in the literature, is not robust enough to be applied to an operational industrial-sized scheduling problem such as the SCS problem. Customised modifications to the formulation are necessary to ensure that the model solves in a time acceptable for operational use. However, it is proved that Mixed Integer Non-linear Programming (MINLP) can successfully be applied to optimise the scheduling of an industrial-sized plant such as SCS. Although more research is required to derive robust formulation techniques, the principle of using mathematical methods to optimise operational scheduling in industry can dramatically impact the way plants are operated. The optimisation of daily schedules at SCS by applying the MINLP continuous time scheduling technique, has made a significant contribution to the coal handling industry. Finally, it can be concluded that the SCS scheduling problem was successfully modelled and the operational scheduling model will add significant value to the Sasol Group.
Dissertation (MEng (Industrial Engineering))--University of Pretoria, 2006.
Industrial and Systems Engineering
unrestricted

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34

Mefo, Kue Floriane. "Mixed integer bilevel programming problems". Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2017. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-230335.

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This thesis presents the mixed integer bilevel programming problems where some optimality conditions and solution algorithms are derived. Bilevel programming problems are optimization problems which are partly constrained by another optimization problem. The theoretical part of this dissertation is mainly based on the investigation of optimality conditions of mixed integer bilevel program. Taking into account both approaches (optimistic and pessimistic) which have been developed in the literature to deal with this type of problem, we derive some conditions for the existence of solutions. After that, we are able to discuss local optimality conditions using tools of variational analysis for each different approach. Moreover, bilevel optimization problems with semidefinite programming in the lower level are considered in order to formulate more optimality conditions for the mixed integer bilevel program. We end the thesis by developing some algorithms based on the theory presented

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35

Connard, Peter. "Mixed Integer Programming on transputers". Thesis, University of Warwick, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.359933.

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Campo, Sergio Daniel Martinez. "Alocação de dispositivos de proteção e manobras para otimização da confiabilidade de sistemas elátricos de distribuição de energia com restrições de restabelecimento". reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2014. http://hdl.handle.net/10183/105020.

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Uma das principais metas das empresas concessionárias é fornecer energia a seus clientes de forma continua, confiável e com baixo custo. A qualidade do serviço de distribuição de energia é fiscalizada por órgãos reguladores do setor elétrico, sendo quantificada por métricas como o indicador de confiabilidade SAIDI (System Average Interruption Duration Index). A melhoria da confiabilidade dos sistemas de distribuição de energia elétrica é um assunto em destaque atualmente, tendo em vista a necessidade de um suprimento de energia cada vez mais confiável, para evitar as perdas econômicas que ocorrem com as interrupções. Neste contexto, este trabalho apresenta uma contribuição para a solução do problema de restabelecimento de sistemas de distribuição. A abordagem consiste no desenvolvimento de um modelo analítico de otimização, cujo objetivo principal é determinar a localização das chaves de manobras na rede que possibilite o restabelecimento efetivo da carga no período pós-falta. A viabilidade do restabelecimento é considerada através de restrições que garantem níveis adequados das tensões nas cargas, bem como a limitação da sobrecarga das linhas e as capacidades de reserva dos alimentadores adjacentes. A modelagem destas restrições é efetuada através de uma versão linear do fluxo de potência em termos das injeções nodais de correntes. As equações que descrevem o fluxo de potência são formuladas como funções das localizações das chaves de manobras no alimentador. A confiabilidade é caracterizada em termos da duração média das interrupções sustentadas, mensurada pelo indicador SAIDI. Visando à maior precisão na representação do efeito das faltas sobre a confiabilidade do alimentador, a metodologia agrega um modelo existente na literatura para alocação dos dispositivos de proteção de forma simultânea às chaves de manobras. A alocação dos dispositivos de proteção e manobras é sujeita a restrições técnicas e econômicas. Para resolver o modelo de otimização não-linear inteira mista, é usada uma técnica de otimização de uso geral, baseada no algoritmo Branch-and-Bound. Assim, metodologia permite a otimização determinística da confiabilidade do alimentador, garantindo o nível ótimo de confiabilidade e a racionalização dos investimentos por parte das concessionárias. Um estudo de caso é apresentado para avaliar a efetividade da metodologia na otimização da confiabilidade de um alimentador de distribuição real.
One of the main goals of utility companies is to provide energy to its customers continuously, reliably and cost effectively. The quality of power distribution service is supervised by regulators of the electricity sector, being quantified by metrics such as the reliability index SAIDI (System Average Interruption Duration Index). Improving the reliability of electricity distribution systems is a key issue nowadays, in view of the need for an increasingly reliable power supply in order to avoid the economic losses due to interruptions. In this context, this work presents a contribution to solve the distribution systems restoration problem. An analytical model is developed to determine locations of the sectionalizing switches in order to restore the system loads in the post-fault period. Restoration feasibility is considered by constraints that ensure adequate voltage levels on the system loads, emergency capacity of support feeders as well as line overloads. Constraints modeling is performed by a linear power flow based on current injection approach. Power flow equations are formulated as functions of switches locations. Reliability is considered in terms of average interruption durations measured by the SAIDI index. Aiming to a greater precision in representing the reliability impact of faults, the methodology aggregates a model from the literature for simultaneous allocation of protective devices and switches. Protective devices and switches allocation is subject to technical and economical constraints. The proposed model is solved by a general-use optimization technique, based on the branch-and-bound method. The proposed methodology makes possible the deterministic optimization of distribution reliability, as well as to rationalize investments of electric utilities. A case study is presented to evaluate the effectiveness of reliability optimization of a real distribution feeder.

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37

Yildiz, Sercan. "Valid Inequalities for Mixed-Integer Linear and Mixed-Integer Conic Programs". Research Showcase @ CMU, 2016. http://repository.cmu.edu/dissertations/777.

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Mixed-integer programming provides a natural framework for modeling optimization problems which require discrete decisions. Valid inequalities, used as cutting-planes and cuttingsurfaces in integer programming solvers, are an essential part of today’s integer programming technology. They enable the solution of mixed-integer programs of greater scale and complexity by providing tighter mathematical descriptions of the feasible solution set. This dissertation presents new structural results on general-purpose valid inequalities for mixedinteger linear and mixed-integer conic programs. Cut-generating functions are a priori formulas for generating a cutting-plane from the data of a mixed-integer linear program. This concept has its roots in the work of Balas, Gomory, and Johnson from the 1970s. It has received renewed attention in the past few years. Gomory and Johnson studied cut-generating functions for the corner relaxation of a mixedinteger linear program, which ignores the nonnegativity constraints on the basic variables in a tableau formulation. We consider models where these constraints are not ignored. In our first contribution, we generalize a classical result of Gomory and Johnson characterizing minimal cut-generating functions in terms of subadditivity, symmetry, and periodicity. Our analysis also exposes shortcomings in the usual definition of minimality in our general setting. To remedy this, we consider stronger notions of minimality and show that these impose additional structure on cut-generating functions. A stronger notion than the minimality of a cut-generating function is its extremality. While extreme cut-generating functions produce powerful cutting-planes, their structure can be very complicated. For the corner relaxation of a one-row integer linear program, Gomory and Johnson identified continuous, piecewise linear, minimal cut-generating functions with only two distinct slope values as a “simple” class of extreme cut-generating functions. In our second contribution, we establish a similar result for a one-row problem which takes the nonnegativity constraint on the basic variable into account. In our third contribution, we consider a multi-row model where only continuous nonbasic variables are present. Conforti, Cornuéjols, Daniilidis, Lemaréchal, and Malick recently showed that not all cutting-planes can be obtained from cut-generating functions in this framework. They also conjectured a natural condition under which cut-generating functions might be sufficient. In our third contribution, we prove that this conjecture is true. This justifies the recent research interest in cut-generating functions for this model. Despite the power of mixed-integer linear programming, many optimization problems of practical and theoretical interest cannot be modeled using a linear objective function and constraints alone. Next, we turn to a natural generalization of mixed-integer linear programming which allows nonlinear convex constraints: mixed-integer conic programming. Disjunctive inequalities, introduced by Balas in the context of mixed-integer linear programming in the 1970s, have been a principal ingredient in the practical success of mixed-integer programming in the last two decades. In order to extend our understanding of disjunctive inequalities to mixed-integer conic programming, we pursue a principled study of two-term disjunctions on conic sets. In our fourth contribution, we consider two-term disjunctions on a general regular cone. A result of Kılınç-Karzan indicates that conic minimal valid linear inequalities are all that is needed for a closed convex hull description of such sets. First we characterize the structure of conic minimal and tight valid linear inequalities for the disjunction. Then we develop structured nonlinear valid inequalities for the disjunction by grouping subsets of valid linear inequalities. We analyze the structure of these inequalities and identify conditions which guarantee that a single such inequality characterizes the closed convex hull of the disjunction. In our fifth and sixth contributions, we extend our earlier results to the cases where the regular cone under consideration is a direct product of second order cones and nonnegative rays and where it is the positive semidefinite cone. Disjunctions on these cones deserve special attention because they provide fundamental relaxations for mixed-integer second-order cone and mixed-integer semidefinite programs. We identify conditions under which our valid convex inequalities can be expressed in computationally tractable forms and present techniques to generate low-complexity relaxations when these conditions are not satisfied. In our final contribution, we provide closed convex hull descriptions for homogeneous two-term disjunctions on the second-order cone and general two-term disjunctions on affine cross-sections of the second-order cone. Our results yield strong convex disjunctive inequalities which can be used as cutting-surfaces in generic mixed-integer conic programming solvers.

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D'Ambrosio, Claudia <1980&gt. "Application-oriented Mixed Integer Non-Linear Programming". Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2009. http://amsdottorato.unibo.it/1634/.

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In the most recent years there is a renovate interest for Mixed Integer Non-Linear Programming (MINLP) problems. This can be explained for different reasons: (i) the performance of solvers handling non-linear constraints was largely improved; (ii) the awareness that most of the applications from the real-world can be modeled as an MINLP problem; (iii) the challenging nature of this very general class of problems. It is well-known that MINLP problems are NP-hard because they are the generalization of MILP problems, which are NP-hard themselves. However, MINLPs are, in general, also hard to solve in practice. We address to non-convex MINLPs, i.e. having non-convex continuous relaxations: the presence of non-convexities in the model makes these problems usually even harder to solve. The aim of this Ph.D. thesis is to give a flavor of different possible approaches that one can study to attack MINLP problems with non-convexities, with a special attention to real-world problems. In Part 1 of the thesis we introduce the problem and present three special cases of general MINLPs and the most common methods used to solve them. These techniques play a fundamental role in the resolution of general MINLP problems. Then we describe algorithms addressing general MINLPs. Parts 2 and 3 contain the main contributions of the Ph.D. thesis. In particular, in Part 2 four different methods aimed at solving different classes of MINLP problems are presented. Part 3 of the thesis is devoted to real-world applications: two different problems and approaches to MINLPs are presented, namely Scheduling and Unit Commitment for Hydro-Plants and Water Network Design problems. The results show that each of these different methods has advantages and disadvantages. Thus, typically the method to be adopted to solve a real-world problem should be tailored on the characteristics, structure and size of the problem. Part 4 of the thesis consists of a brief review on tools commonly used for general MINLP problems, constituted an integral part of the development of this Ph.D. thesis (especially the use and development of open-source software). We present the main characteristics of solvers for each special case of MINLP.

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39

Richards, Arthur George 1977. "Trajectory optimization using mixed-integer linear programming". Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/16873.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2002.
Includes bibliographical references (p. 121-129).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
This thesis presents methods for finding optimal trajectories for vehicles subjected to avoidance and assignment requirements. The former include avoidance of collisions with obstacles or other vehicles and avoidance of thruster plumes from spacecraft. Assignment refers to the inclusion of decisions about terminal constraints in the optimization, such as assignment of waypoints to UAVs and the assignment of spacecraft to positions in a formation. These requirements lead to non-convex constraints and difficult optimizations. However, they can be formulated as mixed-integer linear programs (MILP) that can be solved for global optimality using powerful, commercial software. This thesis provides several extensions to previous work using MILP. The constraints for avoidance are extended to prevent plume impingement, which occurs when one spacecraft fire thrusters towards another. Methods are presented for efficient simplifications to complex problems, allowing solutions to be obtained in practical computation times. An approximation is developed to enable the inclusion of aircraft dynamics in a linear optimization, and also to include a general form of waypoint assignment suitable for UAV problems. Finally, these optimizations are used in model predictive control, running in real-time to incorporate feedback and compensate for uncertainty. Two major application areas are considered: spacecraft and aircraft. Spacecraft problems involve minimum fuel optimizations, and include ISS rendezvous and satellite cluster configuration. Aircraft problems are solved for minimum flight-time, or in the case of UAV problems with assignment, waypoint values and vehicle capabilities are included. Aircraft applications include air traffic management and coordination of autonomous UAVs. The results in this thesis provide a direct route to globally-optimal solutions of these non-convex trajectory optimizations.
by Arthur George Richards.
S.M.

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Rider, Flores Marcos Julio 1975. "Planejamento da expansão de sistemas de transmissão usando os modelos CC - CA e tecnicas de programação não-linear". [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260508.

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Orientador: Ariovaldo Verandio Garcia, Ruben Augusto Romero Lazaro
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
Made available in DSpace on 2018-08-06T06:56:43Z (GMT). No. of bitstreams: 1 RiderFlores_MarcosJulio_D.pdf: 1021887 bytes, checksum: 6000961c2f5457b410ac691912476270 (MD5) Previous issue date: 2006
Resumo: Neste trabalho são propostos modelos matemáticos e técnicas de solução para resolver o problema de planejamento da expansão de sistemas de transmissão através de três enfoques. a) Usando o modelo de corrente alternada do sistema de transmissão e um algoritmo heurístico construtivo especializado para resolver o problema de planejamento, e, ainda, realiza-se uma primeira tentativa de alocação de fontes de potência reativas; b) Usando o modelo de corrente contínua e técnicas de programação não-linear especializadas. Nesse caso emprega-se uma versão relaxada do problema de planejamento da expansão de sistemas de transmissão usando o modelo de corrente contínua, onde a integralidade das variáveis de investimento é desprezada. Resolve-se o problema de programação não-linear, modelado de forma matricial com um algoritmo de otimização especializado e, além disso, um algoritmo heurístico construtivo especializado é utilizado para resolver o problema de planejamento. c) Usando o modelo de corrente contínua e um algoritmo Branch and Bound (B&B) sem empregar técnicas de decomposição. Para isso foram redefinidos os chamados testes de sondagem no algoritmo B&B e em cada nó da árvore de B&B tem-se um problema de programação não-linear que são resolvidos usando a metodologia desenvolvida no item (b). Os ítens (a), (b) e (c) requerem a solução de problemas de programação não-linear diferenciados. Uma revisão das características principais da resolução iterativa dos métodos de pontos interiores é apresentada. Foi desenvolvida uma técnica baseada em uma combinação de métodos de pontos interiores de alta ordem (MPI-AO) para resolver os problemas de programação não-linear de forma rápida, eficiente e robusta. Essa combinação dos MPI-AO tem como objetivo colocar num único método as características particulares de cada um dos MPI-AO e melhorar o desempenho computacional comparado com os MPI-AO de forma individual
Abstract: In this work mathematical models and solution techniques are proposed to solve the power system transmission expansion planning problem through three approaches: a) Using the nonlinear model ofthe transmission system (AC model) and a specialized constructive heuristic algorithm to solve the problem and, yet, a first attempt to allocate reactive power sources is also considered; b) Using the direct-current (DC) model and specialized techniques of nonlinear programming. In this case a version of the power system transmission expansion planning problem using the DC model where the integrality of the investment variables is relaxed is used. The nonlinear programming problem is solved with a specialized optimization algorithm and, moreover, a constructive heuristic algorithm is employed to solve the planning problem. c) Using the DC model and Branch and Bound (B&B) algorithm without the use of decomposition techniques. The so called fathoming tests of the B&B were redefined and at each node of the tree a nonlinear programming problem is solved using the method developed in b). Items a), b) and c) require the solution of distinct problems of nonlinear programming. A revision of the main characteristics of the iterative solution of the interior points methods is presented. An optimization technique based on a combination of the higher order interior point methods (HO-IPM) had been developed to solve the nonlinear programming problems in a fast, efficient and robust way. This combination of the HO-IPM has as objective to explore the particular characteristics of each method in a single one and to improve the comparative computational performance with the HO-IPM of individual form
Doutorado
Energia Eletrica
Doutor em Engenharia Elétrica

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41

Wang, Guanglei. "Relaxations in mixed-integer quadratically constrained programming and robust programming". Thesis, Evry, Institut national des télécommunications, 2016. http://www.theses.fr/2016TELE0026/document.

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De nombreux problèmes de la vie réelle sont exprimés sous la forme de décisions à prendre à l’aide de l’information accessible dans le but d’atteindre certains objectifs. La programmation numérique a prouvé être un outil efficace pour modéliser et résoudre une grande variété de problèmes de ce type. Cependant, de nombreux problèmes en apparence faciles sont encore durs à résoudre. Et même des problèmes faciles de programmation linéaire deviennent durs avec l’incertitude de l’information disponible. Motivés par un problème de télécommunication où l’on doit associer des machines virtuelles à des serveurs tout en minimisant les coûts, nous avons employé plusieurs outils de programmation mathématique dans le but de résoudre efficacement le problème, et développé de nouveaux outils pour des problèmes plus généraux. Dans l’ensemble, résumons les principaux résultats de cette thèse comme suit. Une formulation exacte et plusieurs reformulations pour le problème d’affectation de machines virtuelles dans le cloud sont données. Nous utilisons plusieurs inégalités valides pour renforcer la formulation exacte, accélérant ainsi l’algorithme de résolution de manière significative. Nous donnons en outre un résultat géométrique sur la qualité de la borne lagrangienne montrant qu’elle est généralement beaucoup plus forte que la borne de la relaxation continue. Une hiérarchie de relaxation est également proposée en considérant une séquence de couverture de l’ensemble de la demande. Ensuite, nous introduisons une nouvelle formulation induite par les symétries du problème. Cette formulation permet de réduire considérablement le nombre de termes bilinéaires dans le modèle, et comme prévu, semble plus efficace que les modèles précédents. Deux approches sont développées pour la construction d’enveloppes convexes et concaves pour l’optimisation bilinéaire sur un hypercube. Nous établissons plusieurs connexions théoriques entre différentes techniques et nous discutons d’autres extensions possibles. Nous montrons que deux variantes de formulations pour approcher l’enveloppe convexe des fonctions bilinéaires sont équivalentes. Nous introduisons un nouveau paradigme sur les problèmes linéaires généraux avec des paramètres incertains. Nous proposons une hiérarchie convergente de problèmes d’optimisation robuste – approche robuste multipolaire, qui généralise les notions de robustesse statique, de robustesse d’affinement ajustable, et de robustesse entièrement ajustable. En outre, nous montrons que l’approche multipolaire peut générer une séquence de bornes supérieures et une séquence de bornes inférieures en même temps et les deux séquences convergent vers la valeur robuste des FARC sous certaines hypothèses modérées
Many real life problems are characterized by making decisions with current information to achieve certain objectives. Mathematical programming has been developed as a successful tool to model and solve a wide range of such problems. However, many seemingly easy problems remain challenging. And some easy problems such as linear programs can be difficult in the face of uncertainty. Motivated by a telecommunication problem where assignment decisions have to be made such that the cloud virtual machines are assigned to servers in a minimum-cost way, we employ several mathematical programming tools to solve the problem efficiently and develop new tools for general theoretical problems. In brief, our work can be summarized as follows. We provide an exact formulation and several reformulations on the cloud virtual machine assignment problem. Then several valid inequalities are used to strengthen the exact formulation, thereby accelerating the solution procedure significantly. In addition, an effective Lagrangian decomposition is proposed. We show that, the bounds providedby the proposed Lagrangian decomposition is strong, both theoretically and numerically. Finally, a symmetry-induced model is proposed which may reduce a large number of bilinear terms in some special cases. Motivated by the virtual machine assignment problem, we also investigate a couple of general methods on the approximation of convex and concave envelopes for bilinear optimization over a hypercube. We establish several theoretical connections between different techniques and prove the equivalence of two seeming different relaxed formulations. An interesting research direction is also discussed. To address issues of uncertainty, a novel paradigm on general linear problems with uncertain parameters are proposed. This paradigm, termed as multipolar robust optimization, generalizes notions of static robustness, affinely adjustable robustness, fully adjustable robustness and fills the gaps in-between. As consequences of this new paradigms, several known results are implied. Further, we prove that the multipolar approach can generate a sequence of upper bounds and a sequence of lower bounds at the same time and both sequences converge to the robust value of fully adjustable robust counterpart under some mild assumptions

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42

Goycoolea, Marcos G. "Cutting Planes for Large Mixed Integer Programming Models". Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/13956.

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In this thesis I focus on cutting planes for large Mixed Integer Programming (MIP) problems. More specifically, I focus on two independent cutting planes studies. The first of these deals with cutting planes for the Traveling Salesman Problem (TSP), and the second with cutting planes for general MIPs. In the first study I introduce a new class of cutting planes which I call the Generalized Domino Parity (GDP) inequalities. My main achievements with regard to these are: (1) I show that these are valid for the TSP and for the graphical TSP. (2) I show that they generalize most well-known TSP inequalities (including combs, domino-parity constraints, clique-trees, bipartitions, paths and stars). (3) I show that a sub-class of these (which contains all clique-tree inequalities w/ a fixed number of handles) can be separated in polynomial time, on planar graphs. My second study can be subdivided in two parts. In the first of these I study the Mixed Integer Knapsack Problem (MIKP) and develop a branch-and-bound based algorithm for solving it. The novelty of the approach is that it exploits the notion of "dominance" in order to effectively prune solutions in the branch-and-bound tree. In the second part, I develop a Mixed Integer Rounding (MIR) cut separation heuristic, and embed the MIKP solver in a column generation algorithm in order to assess the performance of said heuristic. The goal of this study is to understand why no other class of inequalities derived from single-row systems has been able to outperform the MIR. Computational results are presented.

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Pogiatzis, Thomas. "Application of mixed-integer programming in chemical engineering". Thesis, University of Cambridge, 2013. https://www.repository.cam.ac.uk/handle/1810/245023.

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Mixed-Integer Programming has been a vital tool for the chemical engineer in the recent decades and is employed extensively in process design and control. This dissertation presents some new Mixed-Integer Programming formulations developed for two well-studied problems, one with a central role in the area of Optimisation, the other of great interest to the chemical industry. These are the Travelling Salesman Problem and the problem of scheduling cleaning actions for heat exchanger networks subject to fouling. The Travelling Salesman Problem finds a plethora of applications in many scientific disciplines, Chemical Engineering included. None of the mathematical programming formulations proposed for solving the problem considers fewer than O(n^2) binary degrees of freedom. The first part of this dissertation introduces a novel mathematical description of the Travelling Salesman Problem that succeeds in reducing the binary degrees of freedom to O(nlog2(n)). Three Mixed-Integer Linear Programming formulations are developed and the computational performance of these is tested through computational studies. Sophisticated methods are now available for scheduling the cleaning actions for networks of heat exchangers subject to fouling. In the majority of these, only one form of cleaning is used, which restores the performance of the exchanger back to its clean level. A recent study revised the scheduling problem for the case where there are several cleaning methods available. The second part of this dissertation extends their approach, developed for individual units, to heat exchanger networks and explores the concept of selection of cleaning techniques further. Mixed-Integer Programming formulations are proposed for the scheduling task, for two fouling scenarios: (i) chemical reaction fouling and (ii) biological fouling. A series of results are presented for the implementation of the scheduling formulations to networks of different sizes.

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Richard, Jean-Philippe P. "Lifted inequalities for 0-1 mixed integer programming". Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/24590.

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Tramontani, Andrea <1978&gt. "Enhanced Mixed Integer Programming Techniques and Routing Problems". Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2009. http://amsdottorato.unibo.it/1754/.

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Mixed integer programming is up today one of the most widely used techniques for dealing with hard optimization problems. On the one side, many practical optimization problems arising from real-world applications (such as, e.g., scheduling, project planning, transportation, telecommunications, economics and finance, timetabling, etc) can be easily and effectively formulated as Mixed Integer linear Programs (MIPs). On the other hand, 50 and more years of intensive research has dramatically improved on the capability of the current generation of MIP solvers to tackle hard problems in practice. However, many questions are still open and not fully understood, and the mixed integer programming community is still more than active in trying to answer some of these questions. As a consequence, a huge number of papers are continuously developed and new intriguing questions arise every year. When dealing with MIPs, we have to distinguish between two different scenarios. The first one happens when we are asked to handle a general MIP and we cannot assume any special structure for the given problem. In this case, a Linear Programming (LP) relaxation and some integrality requirements are all we have for tackling the problem, and we are ``forced" to use some general purpose techniques. The second one happens when mixed integer programming is used to address a somehow structured problem. In this context, polyhedral analysis and other theoretical and practical considerations are typically exploited to devise some special purpose techniques. This thesis tries to give some insights in both the above mentioned situations. The first part of the work is focused on general purpose cutting planes, which are probably the key ingredient behind the success of the current generation of MIP solvers. Chapter 1 presents a quick overview of the main ingredients of a branch-and-cut algorithm, while Chapter 2 recalls some results from the literature in the context of disjunctive cuts and their connections with Gomory mixed integer cuts. Chapter 3 presents a theoretical and computational investigation of disjunctive cuts. In particular, we analyze the connections between different normalization conditions (i.e., conditions to truncate the cone associated with disjunctive cutting planes) and other crucial aspects as cut rank, cut density and cut strength. We give a theoretical characterization of weak rays of the disjunctive cone that lead to dominated cuts, and propose a practical method to possibly strengthen those cuts arising from such weak extremal solution. Further, we point out how redundant constraints can affect the quality of the generated disjunctive cuts, and discuss possible ways to cope with them. Finally, Chapter 4 presents some preliminary ideas in the context of multiple-row cuts. Very recently, a series of papers have brought the attention to the possibility of generating cuts using more than one row of the simplex tableau at a time. Several interesting theoretical results have been presented in this direction, often revisiting and recalling other important results discovered more than 40 years ago. However, is not clear at all how these results can be exploited in practice. As stated, the chapter is a still work-in-progress and simply presents a possible way for generating two-row cuts from the simplex tableau arising from lattice-free triangles and some preliminary computational results. The second part of the thesis is instead focused on the heuristic and exact exploitation of integer programming techniques for hard combinatorial optimization problems in the context of routing applications. Chapters 5 and 6 present an integer linear programming local search algorithm for Vehicle Routing Problems (VRPs). The overall procedure follows a general destroy-and-repair paradigm (i.e., the current solution is first randomly destroyed and then repaired in the attempt of finding a new improved solution) where a class of exponential neighborhoods are iteratively explored by heuristically solving an integer programming formulation through a general purpose MIP solver. Chapters 7 and 8 deal with exact branch-and-cut methods. Chapter 7 presents an extended formulation for the Traveling Salesman Problem with Time Windows (TSPTW), a generalization of the well known TSP where each node must be visited within a given time window. The polyhedral approaches proposed for this problem in the literature typically follow the one which has been proven to be extremely effective in the classical TSP context. Here we present an overall (quite) general idea which is based on a relaxed discretization of time windows. Such an idea leads to a stronger formulation and to stronger valid inequalities which are then separated within the classical branch-and-cut framework. Finally, Chapter 8 addresses the branch-and-cut in the context of Generalized Minimum Spanning Tree Problems (GMSTPs) (i.e., a class of NP-hard generalizations of the classical minimum spanning tree problem). In this chapter, we show how some basic ideas (and, in particular, the usage of general purpose cutting planes) can be useful to improve on branch-and-cut methods proposed in the literature.

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Drouven, Markus G. "Mixed Integer Programming Models for Shale Gas Development". Research Showcase @ CMU, 2017. http://repository.cmu.edu/dissertations/874.

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Shale gas development is transforming the energy landscape in the United States. Advances in production technologies, notably the dual application of horizontal drilling and hydraulic fracturing, allow the extraction of vast deposits of trapped natural gas that, until recently, were uneconomic to produce. The objective of this work is to develop mixed-integer programming models to support upstream operators in making faster and better decisions that ensure low-cost and responsible natural gas production from shale formations. We propose a multiperiod mixed-integer nonlinear programming (MINLP) model along with a tailored solution strategy for strategic, quality-sensitive shale gas development planning. The presented model coordinates planning and design decisions to maximize the net present value of a field-wide development project. By performing a lookback analysis based on data from a shale gas producer in the Appalachian Basin, we find that return-to-pad operations are the key to cost-effective shale gas development strategies. We address impaired water management challenges in active development areas through a multiperiod mixed-integer linear programming (MILP) model. This model is designed to schedule the sequence of fracturing jobs and coordinate impaired- and freshwater deliveries to minimize water management expenses, while simultaneously maximizing revenues from gas sales. Based on the results of a real-world case study, we conclude that rigorous optimization can support upstream operators in cost-effectively reducing freshwater consumption significantly, while also achieving effective impaired water disposal rates of less than one percent. We also propose a multiperiod MINLP model and a tailor-designed solution strategy for line pressure optimization in shale gas gathering systems. The presented model determines when prospective wells should be turned in-line, and how the pressure profile within a gathering network needs to be managed to maximize the net present value of a development project. We find that backoff effects associated with turn-in line operations can be mitigated through preventive line pressure manipulations. Finally, we develop deterministic and stochastic MILP models for refracturing planning. These models are designed to determine whether or not a shale well should be restimulated, and when exactly to refracture it. The stochastic refracturing planning model explicitly considers exogenous price forecast uncertainty and endogenous well performance uncertainty. Our results suggest that refracturing is a promising strategy for combatting the characteristically steep decline curves of shale gas wells.

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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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48

Stellato, Bartolomeo. "Mixed-integer optimal control of fast dynamical systems". Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:b8a7323c-e36e-45ec-ae8d-6c9eb4350629.

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Many applications in engineering, computer science and economics involve mixed-integer optimal control problems. Solving these problems in real-time is a challenging task because of the explosion of integer combinations to evaluate. This thesis focuses on the development of new algorithms for mixed-integer programming with an emphasis on optimal control problems of fast dynamical systems with discrete controls. The first part proposes two reformulations to reduce the computational complexity. The first reformulation avoids integer variables altogether. By considering a sequence of switched dynamics, we analyze the switching time optimization problem. Even though it is a continuous smooth problem, it is non-convex and the cost function and derivatives are hard to compute. We develop a new efficient method to compute the cost function and its derivatives. Our technique brings up to two orders of magnitude speedups with respect to state-of-the-art tools. The second approach reduces the number of integer decisions. In hybrid model predictive control (MPC) the computational complexity grows exponentially with the horizon length. Using approximate dynamic programming (ADP) we reduce the horizon length while maintaining good control performance by approximating the tail cost offline. This approach allows, for the first time, the application of such control techniques to fast dynamical systems with sampling times of only a few microseconds. The second part investigates embedded branch-and-bound algorithms for mixed-integer quadratic programs (MIQPs). A core component of these methods is the solution of continuous quadratic programs (QPs). We develop OSQP, a new robust and efficient general-purpose QP solver based on the alternating direction method of multipliers (ADMM) and able, for the first time, to detect infeasible problems. We include OSQP into a custom branch-and-bound algorithm suitable for embedded systems. Our extension requires only a single matrix factorization and exploits warm-starting, thereby greatly reducing the number of ADMM iterations required. Numerical examples show that our algorithm solves small to medium scale MIQPs more quickly than commercial solvers.

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Garcés, Negrete Lina Paola. "Planejamento da expansão de sistemas de transmissão considerando análise de confiabilidade e incertezas na demanda futura /". Ilha Solteira : [s.n.], 2010. http://hdl.handle.net/11449/100328.

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Orientador: Rubén Augusto Romero Lázaro
Banca: Jose Roberto Sanches Mantovani
Banca: Anna Diva Plasencia Lotufo
Banca: Marcos Julio Rider Flores
Banca: Eduardo Nobuhiro Asada
Resumo: Nessa pesquisa tem-se por objetivo a análise teórica e a implementação computacional de duas propostas de solução ao problema de planejamento da expansão de sistemas de transmissão de energia elétrica considerando diferentes fatores relacionados com a confiabilidade do sistema e a adoção dos novos modelos de mercados elétricos. É importante notar, que no planejamento básico não são levados em conta esses importantes aspectos. Dessa forma, uma primeira aproximação considera um critério de confiabilidade para expandir o sistema, de forma que ele opere adequadamente no horizonte de planejamento satisfazendo um nível de confiabilidade pré-definido. O índice de confiabilidade utilizado para exigir esse nível de confiabilidade é o LOLE, que corresponde ao número médio de horas/dias em um período dado (normalmente um ano) no qual o pico da carga horária/diária do sistema possivelmente exceder'a a capacidade de geração disponível. O problema de planejamento considerando a confiabilidade é, portanto, formulado como um problema de otimização que minimiza o investimento sujeito ao critério de confiabilidade. O índice de confiabilidade para o sistema de transmissão é calculado para cada configuração, subtraindo o índice de confiabilidade do sistema de geração do sistema composto geração-transmissão (bulk power system ). Para calcular o índice no sistema composto geração transmissão, utiliza-se uma curva de duração de carga efetiva para este sistema. Esta curva acumulada de carga é obtida de um processo de convolução de outras duas curvas que representam a função de distribuição de probabilidade (FDP) das saídas aleatórias dos componentes do sistema e a curva de duração de carga, respectivamente. A avaliação de confiabilidade no sistema de geração é feita usando um método que calcula o índice de confiabilidade por meio dos momentos... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: This work aims to the theoretical analysis and computational implementation of two proposals for the transmission expansion planning problem considering several factors such as system reliability and new electricity market structures. It is important to observe, that the basic planning does not consider these issues. Therefore, one first approach considers a reliability criterion to expand the system, so that it operates in adequate conditions in the horizon planning while satisfying pre-defined limits in the reliability index. Transmission system reliability criterion regards to LOLE, which refers to the number of hours/days in a specified period of time (normally one year), in which the hourly/daily peak load possibly will exceed the available generation capacity. So, the planning problem considering reliability is formulated as an optimization problem that minimizes the investment subject to probabilistic reliability criterion. Reliability index for the transmission system is calculated for each configuration by subtraction of generation and bulk power reliability indexes. A composite power system effective load curve is used for reliability analysis of the bulk power system. This accumulate curve is obtained convolving two curves, one of them corresponding to a probability distribution function of the random outages of the system components, and the other one corresponding to the load duration curve. Reliability assessment in the generation system is done using a method that calculates the reliability index through the statistics moments of the frequency distribution of equivalents loads. This curve is obtained by convolving the generation units which are dispached in merit order. The proposed model is solved using the specialized genetic algorithm of Chu-Beasley (AGCB). Detailed results on two test systems are analyzed and discussed. A second approach to the transmission expansion... (Complete abstract click electronic access below)
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Märkert, Hans Jürgen Andreas. "Deviation measures in stochastic programming with mixed integer recourse". [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=971485267.

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Tesi sul tema "Mixed integer nonlinear programming"

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