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Littérature scientifique sur le sujet « Binary quadratic programming »

Auteur : Grafiati
Publié le 11 janvier 2025

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Articles de revues sur le sujet "Binary quadratic programming"

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MU, XUEWEN, SANYANG LID, and YALING ZHANG. "A SUCCESSIVE QUADRATIC PROGRAMMING ALGORITHM FOR SDP RELAXATION OF THE BINARY QUADRATIC PROGRAMMING." Bulletin of the Korean Mathematical Society 42, no. 4 (2005): 837–49. http://dx.doi.org/10.4134/bkms.2005.42.4.837.

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Mu, Xuewen, and Yaling Zhang. "A Rank-Two Feasible Direction Algorithm for the Binary Quadratic Programming." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/963563.

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Based on the semidefinite programming relaxation of the binary quadratic programming, a rank-two feasible direction algorithm is presented. The proposed algorithm restricts the rank of matrix variable to be two in the semidefinite programming relaxation and yields a quadratic objective function with simple quadratic constraints. A feasible direction algorithm is used to solve the nonlinear programming. The convergent analysis and time complexity of the method is given. Coupled with randomized algorithm, a suboptimal solution is obtained for the binary quadratic programming. At last, we report some numerical examples to compare our algorithm with randomized algorithm based on the interior point method and the feasible direction algorithm on max-cut problem. Simulation results have shown that our method is faster than the other two methods.
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Wang, Yang, Zhipeng Lü, Fred Glover, and Jin-Kao Hao. "Path relinking for unconstrained binary quadratic programming." European Journal of Operational Research 223, no. 3 (2012): 595–604. http://dx.doi.org/10.1016/j.ejor.2012.07.012.

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Sun, X. L., C. L. Liu, D. Li, and J. J. Gao. "On duality gap in binary quadratic programming." Journal of Global Optimization 53, no. 2 (2011): 255–69. http://dx.doi.org/10.1007/s10898-011-9683-4.

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Kochenberger, Gary, Jin-Kao Hao, Fred Glover, et al. "The unconstrained binary quadratic programming problem: a survey." Journal of Combinatorial Optimization 28, no. 1 (2014): 58–81. http://dx.doi.org/10.1007/s10878-014-9734-0.

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Glover, Fred, and Jin-Kao Hao. "f-Flip strategies for unconstrained binary quadratic programming." Annals of Operations Research 238, no. 1-2 (2015): 651–57. http://dx.doi.org/10.1007/s10479-015-2076-1.

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Ronagh, Pooya, Brad Woods, and Ehsan Iranmanesh. "Solving constrained quadratic binary problems via quantum adiabatic evolution." Quantum Information and Computation 16, no. 11&12 (2016): 1029–47. http://dx.doi.org/10.26421/qic16.11-12-6.

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Quantum adiabatic evolution is perceived as useful for binary quadratic programming problems that are a priori unconstrained. For constrained problems, it is a common practice to relax linear equality constraints as penalty terms in the objective function. However, there has not yet been proposed a method for efficiently dealing with inequality constraints using the quantum adiabatic approach. In this paper, we give a method for solving the Lagrangian dual of a binary quadratic programming (BQP) problem in the presence of inequality constraints and employ this procedure within a branch-and-bound framework for constrained BQP (CBQP) problems.
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Recht, Peter. "Characterization of optimal points in binary convex quadratic programming." Optimization 56, no. 1-2 (2007): 39–47. http://dx.doi.org/10.1080/02331930600815801.

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Merz, Peter, and Kengo Katayama. "Memetic algorithms for the unconstrained binary quadratic programming problem." Biosystems 78, no. 1-3 (2004): 99–118. http://dx.doi.org/10.1016/j.biosystems.2004.08.002.

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Liefooghe, Arnaud, Sébastien Verel, and Jin-Kao Hao. "A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming." Applied Soft Computing 16 (March 2014): 10–19. http://dx.doi.org/10.1016/j.asoc.2013.11.008.

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Thèses sur le sujet "Binary quadratic programming"

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Bettiol, Enrico. "Column generation methods for quadratic mixed binary programming." Thesis, Paris 13, 2019. http://www.theses.fr/2019PA131073.

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La programmation non linéaire mixte peut modéliser un grand nombre de problèmes réels. Cependant, ces problèmes peuvent contenir de nombreuses variables ou contraintes, il convient donc de proposer des méthodes de décomposition afin de les résoudre efficacement. Parmi ces techniques on peut citer la génération de colonnes et notamment la décomposition de Dantzig-Wolfe. Il s’agit d’une reformulation du problème original, qui permet de générer une séquence de sous-problèmes plus simples, appelés maître etpricing, pour obtenir la valeur optimale. Développée d’abord pour les problèmes linéaires, la décomposition de Dantzig-Wolfe peut être généralisée à des problèmes convexes: dans ce contexte, elle est notamment connue sous le nom de décomposition simpliciale. Cette thèse présente des algorithmes de décomposition pour des problèmes quadratiques. La première partie de ce manuscrit est dédiée aux problèmes quadratiques convexes, continus et mixtes binaires. Dans la deuxième partie, des algorithmes pour résoudre des problèmes binaires avec contraintes quadratiques sont présentés. La première partie est consacrée à la résolution de problèmes convexes, quadratiques et continus. Un algorithme basé sur la décomposition simpliciale est proposé: des nouveaux éléments sont ajoutés à la fois au problème maître et au pricing; nous avons testé notre algorithme sur une grande quantité d’instances avec une structure déterminée, et nos résultats montrent que l’algorithme que nous proposons est très efficace par rapport à Cplex, un solveur générique pour ces problèmes. Ce premier travail a été soumis à un journal pour publication. Ensuite, nous étendons cet algorithme aux problèmes convexes mixtes binaires. Nous incorporons la méthode pour le cas continu dans un algorithme de branch and bound qui nous permet d’exploiter des propriétés de notre formulation. Dans ce contexte aussi, des résultats numériques sont fournis: ils montrent que, dans certains cas, les performances de notre algorithme sont efficaces par rapport à Cplex. Ce travail est en préparation pour soumission à un journal. La deuxième partie de cette thèse est dédiée à l’étude d’algorithmes pour des problèmes quadratiques avec contraintes quadratiques. On se concentre sur les problèmes binaires, dont la relaxation continue peut être non convexe. Nous considérons en premier lieu la formulation étendue avec une matrice qui représente les produits des variables. Nous proposons ensuite un algorithme basé sur la décomposition de Dantzig-Wolfe pour obtenir une relaxation dans le Boolean Quadric Polytope (BQP). Ce polytope est connu aussi comme Correlation polytope et il est strictement contenu dans le cône des matrices complètement positives et des matrices semi définies positives. Notre algorithme permet de résoudre cette relaxation, les bornes obtenues sont plus fortes que les bornes SDP et, dans certains cas, les temps de calcul sont comparables ou meilleurs que ceux de BiqCrunch, unsolveur ad-hoc. On montre aussi que la relaxation BQP est une reformulation du problème binaire original, en exploitant un résultat sur les matrices complètement positives, pour les problèmes à contraintes linéaires en égalité. Ensuite, nous considérons des problèmes où les matrices sont décomposables par blocs. On montre aussi que la relaxation BQP est une reformulation du problème binaire original, en exploitant un résultat sur les matrices complètement positives, pour les problèmes à contraintes linéaires en égalité. Ensuite, nous considérons des problèmes où les matrices sont décomposables par blocs. Une relaxation basée sur les blocs est proposée et nous prouvons que cette relaxation est valide pour la relaxation BQP. De plus, prouver l’équivalence entre les deux relaxations est un problème de complétion BQP. La relaxation décomposée par blocs est BQP complétable dans certains cas, mais n’est pas possible dans d’autres cas [....]<br>Non linear programming problems. There are several solution methods in literature for these problems, which are, however, not always efficient in general, in particular for large scale problems. Decomposition strategies such as Column Generation have been developed in order to substitute the original problem with a sequence of more tractable ones. One of the most known of these techniques is Dantzig-Wolfe Decomposition: it has been developed for linear problems and it consists in solving a sequence of subproblems, called respectively master and pricing programs, which leads to the optimum. This method can be extended to convex non linear problems and a classic example of this, which can be seen also as a generalization of the Frank-Wolfe algorithm, is Simplicial Decomposition(SD).In this thesis we discuss decomposition algorithms for solving quadratic optimization problems. In particular, we start with quadratic convex problems, both continuous and mixed binary. Then we tackle the more general class of binary quadratically constrained, quadratic problems. In the first part, we concentrate on SD based-methods for continuous, convex quadratic programming. We introduce new features in the algorithms, for both the master and the pricing problems of the decomposition, and provide results for a wide set of instances, showing that our algorithm is really efficient if compared to the state-of-the-art solver Cplex. This first work is accepted for publication in the journal Computational Optimization and Applications.We then extend the SD-based algorithm to mixed binary convex quadratic problems;we embed the continuous algorithm in a branch and bound scheme that makes us able to exploit some properties of our framework. In this context again we obtain results which show that in some sets of instances this algorithm is still more efficient than Cplex,even with a very simple branch and bound algorithm. This work is in preparation for submission to a journal. In the second part of the thesis, we deal with a more general class of problems, that is quadratically constrained, quadratic problems, where the constraints can be quadratic and both the objective function and the constraints can be non convex. For this class of problems we extend the formulation to the matrix space of the products of variables; we study an algorithm based on Dantzig-Wolfe Decomposition that exploits a relaxation on the Boolean Quadric Polytope (BQP), which is strictly contained in the Completely Positive cone and hence in the cone of positive semi definite (PSD) matrices. This is a constructive algorithm to solve the BQP relaxation of a binary problem an dwe obtain promising results for the root node bound for some quadratic problems. We compare our results with those obtained by the Semi definite relaxation of the ad-hocsolver BiqCrunch. We also show that, for linearly constrained quadratic problems, our relaxation can provide the integer optimum, under certain assumptions. We further study block decomposed matrices and provide results on the so-called BQP-completion problem ; these results are connected to those of PSD and CPP matrices. We show that, given a BQP matrix with some unspecified elements, it can be completed to a full BQP matrix under some assumptions on the positions of the specified elements. This result is related to optimization problems. We propose a BQP-relaxation based on the block structure of the problem. We prove that it provides a lower bound for the previously introduced relaxation, and that in some cases the two formulations are equivalent. We also conjecture that the equivalence result holds if and only if its so-called specification graph is chordal. We provide computational results which show the improvement in the performance of the block-based relaxation, with respect to the unstructured relaxation, and which support our conjecture. This work is in preparation for submission to a journal
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Battikh, Rabih. "La résοlutiοn de prοblème quadratique binaire par des méthοdes d'οptimisatiοn exactes et apprοchées". Electronic Thesis or Diss., Normandie, 2024. http://www.theses.fr/2024NORMLH20.

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Dans cette thèse, nous avons présenté un nouvel algorithme hybride (HA) pour la résolution du problème (UQP). Cet algorithme est basé sur la combinaison d'un bloc de cinq procédures spéciales et de la méthode du recuit simulé. Nos procédures sont très efficaces et rapides, mais malheureusement, parfois elles sont bloquées par un minimum local. Pour surmonter cet inconvénient, nous les avons combinées avec un algorithme de recuit simulé. Ensuite, nous avons répété ces procédures plusieurs fois pour obtenir la meilleure solution en utilisant notre algorithme hybride.Nous avons remarqué que l'écart entre la solution trouvée par (HA) et le logiciel CPLEX est très faible, ce résultat implique l'efficacité de notre stratégie. Par ailleurs, nous avons intégré notre méthode hybride à un problème de relaxation semi-définie du (UQP) dans le cadre d'une stratégie de branch and bound. Pour faciliter la résolution du (UQP), nous suggérons d'appliquer des critères de fixation afin de réduire la taille du problème et d'accélérer l'obtention d'une solution exacte. La qualité de la borne inférieure trouvée par notre code (QPTOSDP) est très bonne, mais le temps d'exécution augmente avec la taille du problème. Les résultats numériques prouvent l'exactitude de notre solution optimale et l'efficacité et la robustesse de notre approche.Nous avons étendu les critères de fixation pour le problème (QP), ce qui permet, dans certains cas, de réduire la dimension du problème, voire de le résoudre entièrement en appliquant une boucle de répétition fondée sur ces critères<br>In this thesis, we presented a new hybrid algorithm (HA) for solving the unconstrained quadratic programming problem (UQP). This algorithm is based on the combination of a block of five special procedures and the simulated annealing method. Our procedures are very efficient and fast, but unfortunately, they sometimes get stuck in a local minimum. To overcome this drawback, we combined them with a simulated annealing algorithm. Then, we repeated these procedures several times to obtain the best solution using our hybrid algorithm.We noticed that the gap between the solution found by (HA) and the CPLEX software is very small, which implies the efficiency of our strategy. Moreover, we integrated our hybrid method into a semi-definite relaxation problem of (UQP) within a branch and bound strategy. To facilitate the resolution of (UQP), we suggest applying fixing criteria to reduce the size of the problem and speed up the process of obtaining an exact solution. The quality of the lower bound found by our code (QPTOSDP) is very good, but the execution time increases with the size of the problem. Numerical results prove the accuracy of our optimal solution and the efficiency and robustness of our approach.We extended the fixing criteria to the quadratic programming problem (QP), which in some cases allows reducing the dimension of the problem, or even solving it entirely by applying a repetition loop based on these criteria
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Silva, Pedro Miguel Dias da. "Quantum Computing for Optimizing Power Flow in Energy Grids." Master's thesis, 2021. http://hdl.handle.net/10316/98073.

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Dissertação de Mestrado em Engenharia Informática apresentada à Faculdade de Ciências e Tecnologia<br>Quantum Computing is beginning to gather even more attention at a time where efforts are being made into familiarizing younger audiences into not only learning programming on a classical computer, but also on a quantum one.This new paradigm of computation is set to revolutionize several industries as the hardware keeps developing, with the potential to solve problems that a classical computer would consider intangible, as well as giving some specific problems a so sought after speed-up. This is done by applying the properties of quantum physics, like superposition and entanglement, for computation. These properties not only allow to process a larger amount of data simultaneously, but also allows to tackle problems in a completely different way that would not be possible in a classical computer.This thesis focuses on solving a known and relevant problem in the electrical industry and studying its application on a quantum environment. The Unit Commitment Problem, the problem in question, consists in minimizing the cost of power production, for a certain time horizon, by scheduling different generating units in order to meet a certain demand given by a valid forecast. Given that this is an NP-hard problem, it quickly becomes intractable on classical computers when considering real world scenarios on a large scale.A test scenario was also designed to study, by conducting an experimental analysis, the influences that each of the parameters have on the solution quality. To that end, the formulation of the Unit Commitment Problem was also translated to a suitable QUBO form which is then solved through a quantum annealer from D-Wave. For that test scenario, both the parameters from the problem formulation as well as the parameters related to the quantum computer were considered.The results from the experimental analysis suggest that most parameters do have an impact on the solution quality. With some having a greater impact overall such as Grids, that are representing how accurate the linearization of the problem is, as well the delta value associated with the first constraint, a value that is tied to how much of a weight the first constraint, that restricts each unit to a single production level, has. While the parameters with the overall greater impact are tied to the formulation of the problem, parameters like chain strength that affects the strength of coupling between qubits representing a single variable also have a significant impact on the solution quality. While most parameters have a statistical impact on the solution quality, the delta associated with the second constraint, that restricts power generation to equal the demand, fails to have an impact.<br>Quantum Computing is beginning to gather even more attention at a time where efforts are being made into familiarizing younger audiences into not only learning programming on a classical computer, but also on a quantum one.This new paradigm of computation is set to revolutionize several industries as the hardware keeps developing, with the potential to solve problems that a classical computer would consider intangible, as well as giving some specific problems a so sought after speed-up. This is done by applying the properties of quantum physics, like superposition and entanglement, for computation. These properties not only allow to process a larger amount of data simultaneously, but also allows to tackle problems in a completely different way that would not be possible in a classical computer.This thesis focuses on solving a known and relevant problem in the electrical industry and studying its application on a quantum environment. The Unit Commitment Problem, the problem in question, consists in minimizing the cost of power production, for a certain time horizon, by scheduling different generating units in order to meet a certain demand given by a valid forecast. Given that this is an NP-hard problem, it quickly becomes intractable on classical computers when considering real world scenarios on a large scale.A test scenario was also designed to study, by conducting an experimental analysis, the influences that each of the parameters have on the solution quality. To that end, the formulation of the Unit Commitment Problem was also translated to a suitable QUBO form which is then solved through a quantum annealer from D-Wave. For that test scenario, both the parameters from the problem formulation as well as the parameters related to the quantum computer were considered.The results from the experimental analysis suggest that most parameters do have an impact on the solution quality. With some having a greater impact overall such as Grids, that are representing how accurate the linearization of the problem is, as well the delta value associated with the first constraint, a value that is tied to how much of a weight the first constraint, that restricts each unit to a single production level, has. While the parameters with the overall greater impact are tied to the formulation of the problem, parameters like chain strength that affects the strength of coupling between qubits representing a single variable also have a significant impact on the solution quality. While most parameters have a statistical impact on the solution quality, the delta associated with the second constraint, that restricts power generation to equal the demand, fails to have an impact.
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Livres sur le sujet "Binary quadratic programming"

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Li, Jian, Antonio De Maio, Guolong Cui, and Alfonso Farina. Radar Waveform Design Based on Optimization Theory. Institution of Engineering & Technology, 2020.

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Radar Waveform Design Based on Optimization Theory. Institution of Engineering & Technology, 2020.

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Chapitres de livres sur le sujet "Binary quadratic programming"

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Punnen, Abraham P., and Renata Sotirov. "Mathematical Programming Models and Exact Algorithms." In The Quadratic Unconstrained Binary Optimization Problem. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-04520-2_6.

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Cifuentes, Diego, Santanu S. Dey, and Jingye Xu. "Sensitivity Analysis for Mixed Binary Quadratic Programming." In Integer Programming and Combinatorial Optimization. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-59835-7_33.

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Buchheim, Christoph, and Emiliano Traversi. "Separable Non-convex Underestimators for Binary Quadratic Programming." In Experimental Algorithms. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38527-8_22.

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Dong, Hongbo, and Jeff Linderoth. "On Valid Inequalities for Quadratic Programming with Continuous Variables and Binary Indicators." In Integer Programming and Combinatorial Optimization. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36694-9_15.

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Borndörfer, Ralf, and Carlos Cardonha. "A Binary Quadratic Programming Approach to the Vehicle Positioning Problem." In Modeling, Simulation and Optimization of Complex Processes. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25707-0_4.

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Wang, Yang, Zhipeng Lü, Fred Glover, and Jin-Kao Hao. "Effective Variable Fixing and Scoring Strategies for Binary Quadratic Programming." In Evolutionary Computation in Combinatorial Optimization. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20364-0_7.

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Wang, Yang, Zhipeng Lü, Fred Glover, and Jin-Kao Hao. "A Multilevel Algorithm for Large Unconstrained Binary Quadratic Optimization." In Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29828-8_26.

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Liefooghe, Arnaud, Sébastien Verel, Luís Paquete, and Jin-Kao Hao. "Experiments on Local Search for Bi-objective Unconstrained Binary Quadratic Programming." In Lecture Notes in Computer Science. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15934-8_12.

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Zhou, Ying, Lingjing Kong, Lijun Yan, Shaopeng Liu, and Jiaming Hong. "A Multiobjective Memetic Algorithm for Multiobjective Unconstrained Binary Quadratic Programming Problem." In Lecture Notes in Computer Science. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-78811-7_3.

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de Souza, Marcelo, and Marcus Ritt. "Automatic Grammar-Based Design of Heuristic Algorithms for Unconstrained Binary Quadratic Programming." In Evolutionary Computation in Combinatorial Optimization. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77449-7_5.

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Actes de conférences sur le sujet "Binary quadratic programming"

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Zanotti, Roberto, and Francesco Negro. "An Innovative Binary Quadratic Programming Approach for the Accurate Identification of Discharge Timings of Motor Units From High-Density Surface EMG Signals." In 2024 IEEE International Conference on Metrology for eXtended Reality, Artificial Intelligence and Neural Engineering (MetroXRAINE). IEEE, 2024. https://doi.org/10.1109/metroxraine62247.2024.10795886.

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De Souza, Murilo Zangari, and Aurora Trinidad Ramirez Pozo. "Multiobjective Binary ACO for Unconstrained Binary Quadratic Programming." In 2015 Brazilian Conference on Intelligent Systems (BRACIS). IEEE, 2015. http://dx.doi.org/10.1109/bracis.2015.15.

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Lin, Geng. "Solving unconstrained binary quadratic programming using binary particle swarm optimization." In 2013 International Conference of Information Technology and Industrial Engineering. WIT Press, 2013. http://dx.doi.org/10.2495/itie130311.

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Istrati, Daniela, Vasile Moraru, and Sergiu Zaporojan. "A Method for Binary Quadratic Programming with Circulant Matrix." In 12th International Conference on Electronics, Communications and Computing. Technical University of Moldova, 2022. http://dx.doi.org/10.52326/ic-ecco.2022/cs.01.

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Binary quadratic programming is a classical combinatorial optimization problem that has many real-world applications. This paper presents a method for solving the quadratic programming problem with circulant matrix by reformulating and relaxing it into a separable optimization problem. The proposed method determines local suboptimal solutions. To solve the relaxing problem, the DCA algorithm it is proposed to calculate the solutions, in the general case, only local suboptimal.
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Lee, Gim Hee. "Line Association and Vanishing Point Estimation with Binary Quadratic Programming." In 2017 International Conference on 3D Vision (3DV). IEEE, 2017. http://dx.doi.org/10.1109/3dv.2017.00072.

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Toyama, Fubito, Kenji Shoji, Hiroshi Mori, and Juichi Miyamichi. "An iterated greedy algorithm for the binary quadratic programming problem." In 2012 Joint 6th Intl. Conference on Soft Computing and Intelligent Systems (SCIS) and 13th Intl. Symposium on Advanced Intelligent Systems (ISIS). IEEE, 2012. http://dx.doi.org/10.1109/scis-isis.2012.6505143.

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Mejari, Manas, Vihangkumar V. Naik, Dario Piga, and Alberto Bemporad. "Energy Disaggregation using Piecewise Affine Regression and Binary Quadratic Programming." In 2018 IEEE Conference on Decision and Control (CDC). IEEE, 2018. http://dx.doi.org/10.1109/cdc.2018.8619175.

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Masti, Daniele, and Alberto Bemporad. "Learning binary warm starts for multiparametric mixed-integer quadratic programming." In 2019 18th European Control Conference (ECC). IEEE, 2019. http://dx.doi.org/10.23919/ecc.2019.8795808.

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Olsson, Carl, Anders P. Eriksson, and Fredrik Kahl. "Solving Large Scale Binary Quadratic Problems: Spectral Methods vs. Semidefinite Programming." In 2007 IEEE Conference on Computer Vision and Pattern Recognition. IEEE, 2007. http://dx.doi.org/10.1109/cvpr.2007.383202.

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Jialong Shi, Qingfu Zhang, Bilel Derbel, and Arnaud Liefooghe. "A Parallel Tabu Search for the Unconstrained Binary Quadratic Programming problem." In 2017 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2017. http://dx.doi.org/10.1109/cec.2017.7969360.

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Rapports d'organisations sur le sujet "Binary quadratic programming"

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Coffrin, Carleton James, Harsha Nagarajan, and Russell Whitford Bent. Challenges and Successes of Solving Binary Quadratic Programming Benchmarks on the DW2X QPU. Office of Scientific and Technical Information (OSTI), 2016. http://dx.doi.org/10.2172/1330084.

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