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Articoli di riviste sul tema "Binary quadratic programming"

Autore: Grafiati

Pubblicato: 11 gennaio 2025

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1

MU, XUEWEN, SANYANG LID e YALING ZHANG. "A SUCCESSIVE QUADRATIC PROGRAMMING ALGORITHM FOR SDP RELAXATION OF THE BINARY QUADRATIC PROGRAMMING". Bulletin of the Korean Mathematical Society 42, n. 4 (1 novembre 2005): 837–49. http://dx.doi.org/10.4134/bkms.2005.42.4.837.

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2

Mu, Xuewen, e 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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Abstract (sommario):

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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3

Wang, Yang, Zhipeng Lü, Fred Glover e Jin-Kao Hao. "Path relinking for unconstrained binary quadratic programming". European Journal of Operational Research 223, n. 3 (dicembre 2012): 595–604. http://dx.doi.org/10.1016/j.ejor.2012.07.012.

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4

Sun, X. L., C. L. Liu, D. Li e J. J. Gao. "On duality gap in binary quadratic programming". Journal of Global Optimization 53, n. 2 (18 febbraio 2011): 255–69. http://dx.doi.org/10.1007/s10898-011-9683-4.

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5

Kochenberger, Gary, Jin-Kao Hao, Fred Glover, Mark Lewis, Zhipeng Lü, Haibo Wang e Yang Wang. "The unconstrained binary quadratic programming problem: a survey". Journal of Combinatorial Optimization 28, n. 1 (18 aprile 2014): 58–81. http://dx.doi.org/10.1007/s10878-014-9734-0.

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6

Glover, Fred, e Jin-Kao Hao. "f-Flip strategies for unconstrained binary quadratic programming". Annals of Operations Research 238, n. 1-2 (11 dicembre 2015): 651–57. http://dx.doi.org/10.1007/s10479-015-2076-1.

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7

Ronagh, Pooya, Brad Woods e Ehsan Iranmanesh. "Solving constrained quadratic binary problems via quantum adiabatic evolution". Quantum Information and Computation 16, n. 11&12 (settembre 2016): 1029–47. http://dx.doi.org/10.26421/qic16.11-12-6.

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Abstract (sommario):

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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8

Recht, Peter. "Characterization of optimal points in binary convex quadratic programming". Optimization 56, n. 1-2 (febbraio 2007): 39–47. http://dx.doi.org/10.1080/02331930600815801.

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9

Merz, Peter, e Kengo Katayama. "Memetic algorithms for the unconstrained binary quadratic programming problem". Biosystems 78, n. 1-3 (dicembre 2004): 99–118. http://dx.doi.org/10.1016/j.biosystems.2004.08.002.

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10

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

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11

Mauri, Geraldo Regis, e Luiz Antonio Nogueira Lorena. "Lagrangean decompositions for the unconstrained binary quadratic programming problem". International Transactions in Operational Research 18, n. 2 (2 febbraio 2011): 257–70. http://dx.doi.org/10.1111/j.1475-3995.2009.00743.x.

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12

Xia, Yong, e Wenxun Xing. "Parametric Lagrangian dual for the binary quadratic programming problem". Journal of Global Optimization 61, n. 2 (27 febbraio 2014): 221–33. http://dx.doi.org/10.1007/s10898-014-0164-4.

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13

Gondzio, Jacek, e E. Alper Yıldırım. "Global solutions of nonconvex standard quadratic programs via mixed integer linear programming reformulations". Journal of Global Optimization 81, n. 2 (20 aprile 2021): 293–321. http://dx.doi.org/10.1007/s10898-021-01017-y.

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Abstract (sommario):

AbstractA standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We propose two alternative formulations. Our first formulation is based on casting a standard quadratic program as a linear program with complementarity constraints. We then employ binary variables to linearize the complementarity constraints. For the second formulation, we first derive an overestimating function of the objective function and establish its tightness at any global minimizer. We then linearize the overestimating function using binary variables and obtain our second formulation. For both formulations, we propose a set of valid inequalities. Our extensive computational results illustrate that the proposed mixed integer linear programming reformulations significantly outperform other global solution approaches. On larger instances, we usually observe improvements of several orders of magnitude.

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14

Zheng, Xiaojin, Yutong Pan e Xueting Cui. "Quadratic convex reformulation for nonconvex binary quadratically constrained quadratic programming via surrogate constraint". Journal of Global Optimization 70, n. 4 (26 febbraio 2018): 719–35. http://dx.doi.org/10.1007/s10898-017-0591-0.

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15

Moghadas, Foroogh Moeen, e Hossein Taghizadeh Kakhki. "Queueing Maximal Covering Location-Allocation Problem: An Extension with M/G/1 Queueing Systems". Advances in Decision Sciences 2011 (29 gennaio 2011): 1–13. http://dx.doi.org/10.1155/2011/605629.

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We consider the queueing maximal covering location-allocation problem (QM-CLAP) with an M/G/1 queueing system. We first formulate the problem as a binary quadratic programming problem and then propose a new solution procedure based on decomposition of the problem into smaller binary quadratic sub-problems. The heuristic procedure GRASP is used to solve the sub-problems, as well as the entire model. Some computational results are also presented.

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16

Murakami, Takenori, Fubito Toyama, Kenji Shoji e Jyuichi Miyamichi. "An Iterated Greedy Algorithm for the Binary Quadratic Programming Problem". IEEJ Transactions on Electronics, Information and Systems 130, n. 6 (2010): 1089–90. http://dx.doi.org/10.1541/ieejeiss.130.1089.

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17

Ren, Jianfeng, Xudong Jiang, Junsong Yuan e Gang Wang. "Optimizing LBP Structure For Visual Recognition Using Binary Quadratic Programming". IEEE Signal Processing Letters 21, n. 11 (novembre 2014): 1346–50. http://dx.doi.org/10.1109/lsp.2014.2336252.

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18

Yang, Mei-Jia, Yong Xia e Hui-Min Zou. "On linearization techniques for budget-constrained binary quadratic programming problems". Operations Research Letters 44, n. 6 (novembre 2016): 702–5. http://dx.doi.org/10.1016/j.orl.2016.09.002.

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19

Zheng, Xiaojin, Xiaoling Sun, Duan Li e Yong Xia. "Duality Gap Estimation of Linear Equality Constrained Binary Quadratic Programming". Mathematics of Operations Research 35, n. 4 (novembre 2010): 864–80. http://dx.doi.org/10.1287/moor.1100.0472.

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20

Kim, Young Han, Sang Yeul Kim e Ju Bong Kim. "Adaptive control of a binary distillation column using quadratic programming". Korean Journal of Chemical Engineering 6, n. 4 (ottobre 1989): 306–12. http://dx.doi.org/10.1007/bf02705219.

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21

Huang, Hong-Xuan, Panos M. Pardalos e Oleg A. Prokopyev. "Lower Bound Improvement and Forcing Rule for Quadratic Binary Programming". Computational Optimization and Applications 33, n. 2-3 (18 ottobre 2005): 187–208. http://dx.doi.org/10.1007/s10589-005-3062-3.

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22

Pan, Shaohua, Tao Tan e Yuxi Jiang. "A global continuation algorithm for solving binary quadratic programming problems". Computational Optimization and Applications 41, n. 3 (9 novembre 2007): 349–62. http://dx.doi.org/10.1007/s10589-007-9110-4.

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23

Jin, Weihua, Zhiying Hu e Christine W. Chan. "A Genetic-Algorithms-Based Approach for Programming Linear and Quadratic Optimization Problems with Uncertainty". Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/272491.

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This paper proposes a genetic-algorithms-based approach as an all-purpose problem-solving method for operation programming problems under uncertainty. The proposed method was applied for management of a municipal solid waste treatment system. Compared to the traditional interactive binary analysis, this approach has fewer limitations and is able to reduce the complexity in solving the inexact linear programming problems and inexact quadratic programming problems. The implementation of this approach was performed using the Genetic Algorithm Solver of MATLAB (trademark of MathWorks). The paper explains the genetic-algorithms-based method and presents details on the computation procedures for each type of inexact operation programming problems. A comparison of the results generated by the proposed method based on genetic algorithms with those produced by the traditional interactive binary analysis method is also presented.

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24

G.S L. Brandão, Fernando, Richard Kueng e Daniel Stilck França. "Faster quantum and classical SDP approximations for quadratic binary optimization". Quantum 6 (20 gennaio 2022): 625. http://dx.doi.org/10.22331/q-2022-01-20-625.

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We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. This class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine ideas from quantum Gibbs sampling and matrix exponent updates. A de-quantization of the algorithm also leads to a faster classical solver. For generic instances, our quantum solver gives a nearly quadratic speedup over state-of-the-art algorithms. Such instances include approximating the ground state of spin glasses and MaxCut on Erdös-Rényi graphs. We also provide an efficient randomized rounding procedure that converts approximately optimal SDP solutions into approximations of the original quadratic optimization problem.

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25

Lara, Hugo José, Abel Soares Siqueira e Jinyun Yuan. "A Reduced Semidefinite Programming Formulation for HA Assignment Problems in Sport Scheduling". TEMA (São Carlos) 19, n. 3 (17 dicembre 2018): 471. http://dx.doi.org/10.5540/tema.2018.019.03.471.

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Home-Away Assignment problems are naturally cast as quadraticpro gramming models in binary variables. In this work we compare alternative formulations for this kind of problems. First,write a quadratic programming formulation with linear constraints, and then a quadratically constrained version. We also propose another formulation by manipulating their special structure to obtain versions with 1/4 of the original size. The quadratic programming formulations leads to semidefinite relaxations, which allows us to approximately solve the models. We compare our SDP relaxation with the MIN-RES-CUT based formulation. Numerical experiments exhibit the characteristics of each model.

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26

Douiri, Sidi Mohamed, e Souad Elbernoussi. "An unconstrained binary quadratic programming for the maximum independent set problem". Nonlinear Analysis: Modelling and Control 17, n. 4 (25 ottobre 2012): 410–17. http://dx.doi.org/10.15388/na.17.4.14047.

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For a given graph G = (V, E) the maximum independent set problem is to find the largest subset of pairwise nonadjacent vertices. We propose a new model which is a reformulation of the maximum independent set problem as an unconstrained quadratic binary programming, and we resolve it afterward by means of a genetic algorithm. The efficiency of the approach is confirmed by results of numerical experiments on DIMACS benchmarks.

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27

Mauri, Geraldo Regis, e Luiz Antonio Nogueira Lorena. "A column generation approach for the unconstrained binary quadratic programming problem". European Journal of Operational Research 217, n. 1 (febbraio 2012): 69–74. http://dx.doi.org/10.1016/j.ejor.2011.09.016.

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28

Wang, Yang, Jin-Kao Hao, Fred Glover, Zhipeng Lü e Qinghua Wu. "Solving the maximum vertex weight clique problem via binary quadratic programming". Journal of Combinatorial Optimization 32, n. 2 (21 gennaio 2016): 531–49. http://dx.doi.org/10.1007/s10878-016-9990-2.

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29

Kochenberger, Gary A., Fred Glover, Bahram Alidaee e Cesar Rego. "An Unconstrained Quadratic Binary Programming Approach to the Vertex Coloring Problem". Annals of Operations Research 139, n. 1 (ottobre 2005): 229–41. http://dx.doi.org/10.1007/s10479-005-3449-7.

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30

Mauri, Geraldo Regis, e Luiz Antonio Nogueira Lorena. "Improving a Lagrangian decomposition for the unconstrained binary quadratic programming problem". Computers & Operations Research 39, n. 7 (luglio 2012): 1577–81. http://dx.doi.org/10.1016/j.cor.2011.09.008.

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31

Wang, Yulan, Zhixia Yang e Xiaomei Yang. "Kernel-Free Quadratic Surface Minimax Probability Machine for a Binary Classification Problem". Symmetry 13, n. 8 (28 luglio 2021): 1378. http://dx.doi.org/10.3390/sym13081378.

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Abstract (sommario):

In this paper, we propose a novel binary classification method called the kernel-free quadratic surface minimax probability machine (QSMPM), that makes use of the kernel-free techniques of the quadratic surface support vector machine (QSSVM) and inherits the advantage of the minimax probability machine (MPM) without any parameters. Specifically, it attempts to find a quadratic hypersurface that separates two classes of samples with maximum probability. However, the optimization problem derived directly was too difficult to solve. Therefore, a nonlinear transformation was introduced to change the quadratic function involved into a linear function. Through such processing, our optimization problem finally became a second-order cone programming problem, which was solved efficiently by an alternate iteration method. It should be pointed out that our method is both kernel-free and parameter-free, making it easy to use. In addition, the quadratic hypersurface obtained by our method was allowed to be any general form of quadratic hypersurface. It has better interpretability than the methods with the kernel function. Finally, in order to demonstrate the geometric interpretation of our QSMPM, five artificial datasets were implemented, including showing the ability to obtain a linear separating hyperplane. Furthermore, numerical experiments on benchmark datasets confirmed that the proposed method had better accuracy and less CPU time than corresponding methods.

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32

Vyskocil, Tomas, e Hristo Djidjev. "Embedding Equality Constraints of Optimization Problems into a Quantum Annealer". Algorithms 12, n. 4 (17 aprile 2019): 77. http://dx.doi.org/10.3390/a12040077.

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Quantum annealers such as D-Wave machines are designed to propose solutions for quadratic unconstrained binary optimization (QUBO) problems by mapping them onto the quantum processing unit, which tries to find a solution by measuring the parameters of a minimum-energy state of the quantum system. While many NP-hard problems can be easily formulated as binary quadratic optimization problems, such formulations almost always contain one or more constraints, which are not allowed in a QUBO. Embedding such constraints as quadratic penalties is the standard approach for addressing this issue, but it has drawbacks such as the introduction of large coefficients and using too many additional qubits. In this paper, we propose an alternative approach for implementing constraints based on a combinatorial design and solving mixed-integer linear programming (MILP) problems in order to find better embeddings of constraints of the type ∑ x i = k for binary variables x i. Our approach is scalable to any number of variables and uses a linear number of ancillary variables for a fixed k.

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33

Wang, Qiwei. "Support vector machine based on the quadratic unconstrained binary optimization model". Journal of Physics: Conference Series 2858, n. 1 (1 ottobre 2024): 012002. http://dx.doi.org/10.1088/1742-6596/2858/1/012002.

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Abstract Support vector machine (SVM) is a powerful supervised machine learning model that is often used in binary classification algorithms. As Moore’s Law approaches its theoretical limits and the demand for machine learning to handle large-scale, high-dimensional data analysis intensifies, the necessity of adopting non-traditional computational approaches becomes evident. Quantum computing, in particular, emerges as a vital solution for the effective training of SVM models, providing capabilities beyond those of classical computing systems. To solve the above problems, a QUBO (quadratic unconstrained binary optimization) model is proposed to transform the SVM machine learning model into a quadratic unconstrained binary optimization problem so that they can be effectively trained on the D-Wave platform using adiabatic quantum computer. The results show that the QUBO model can transform the SVM model into a simple quadratic programming problem, which makes it suitable for adiabatic quantum computer processing. When processing large-scale and high-dimensional data, this transformation shows a natural advantage and significantly improves computational efficiency. The application potential of this transformation technology is huge in the medical field.

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34

Zhang, Lu, Frans Coenen e Paul Leng. "Setting attribute weights for k-NN based binary classification via quadratic programming". Intelligent Data Analysis 7, n. 5 (17 novembre 2003): 427–41. http://dx.doi.org/10.3233/ida-2003-7504.

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35

Gui, Jihong, Zhipeng Jiang e Suixiang Gao. "PCI Planning Based on Binary Quadratic Programming in LTE/LTE-A Networks". IEEE Access 7 (2019): 203–14. http://dx.doi.org/10.1109/access.2018.2885313.

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36

Lu, Cheng, e Xiaoling Guo. "Convex reformulation for binary quadratic programming problems via average objective value maximization". Optimization Letters 9, n. 3 (17 luglio 2014): 523–35. http://dx.doi.org/10.1007/s11590-014-0768-0.

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37

Shylo, V. P., e O. V. Shylo. "Systems Analysis; Solving unconstrained binary quadratic programming problem by global equilibrium search". Cybernetics and Systems Analysis 47, n. 6 (novembre 2011): 889–97. http://dx.doi.org/10.1007/s10559-011-9368-5.

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38

LEWIS, MARK, e GARY KOCHENBERGER. "GRAPH BISECTION MODELED AS CARDINALITY CONSTRAINED BINARY QUADRATIC TASK ALLOCATION". International Journal of Information Technology & Decision Making 12, n. 02 (marzo 2013): 261–76. http://dx.doi.org/10.1142/s0219622013500119.

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In this paper, the cardinality constrained quadratic model for binary quadratic programming is used to model and solve the graph bisection problem as well as its generalization in the form of the task allocation problem with two processors (2-TAP). Balanced graph bisection is an NP-complete problem which partitions a set of nodes in the graph G = (N, E) into two sets with equal cardinality such that a minimal sum of edge weights exists between the nodes in the two separate sets. 2-TAP is graph bisection with the addition of node preference costs in the objective function. We transform the general linear k-TAP model to the cardinality constrained quadratic binary model so that it may be efficiently solved using tabu search with strategic oscillation. On a set of benchmark graph bisections, we improve the best known solution for several problems. Comparison results with the state-of-the-art graph partitioning program METIS, as well as Cplex and Gurobi are presented on a set of randomly generated graphs. This approach is shown to also work well with 2-TAP, comparing favorably to Cplex and Gurobi, providing better solutions in a much shorter time.

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39

Katayama, Kengo, e Hiroyuki Narihisa. "Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem". European Journal of Operational Research 134, n. 1 (ottobre 2001): 103–19. http://dx.doi.org/10.1016/s0377-2217(00)00242-3.

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40

Gu, Shenshen, Tao Hao e Hanmei Yao. "A pointer network based deep learning algorithm for unconstrained binary quadratic programming problem". Neurocomputing 390 (maggio 2020): 1–11. http://dx.doi.org/10.1016/j.neucom.2019.06.111.

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41

Cai, Yiqiao, Jiahai Wang, Jian Yin e Yalan Zhou. "Memetic clonal selection algorithm with EDA vaccination for unconstrained binary quadratic programming problems". Expert Systems with Applications 38, n. 6 (giugno 2011): 7817–27. http://dx.doi.org/10.1016/j.eswa.2010.12.124.

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42

Mu, Xuewen, Yaling Zhang e Sanyang Liu. "A new branch and bound method with pretreatment for the binary quadratic programming". Applied Mathematics and Computation 192, n. 1 (settembre 2007): 252–59. http://dx.doi.org/10.1016/j.amc.2007.03.006.

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43

Kratica, Jozef. "A Mixed Integer Quadratic Programming Model for the Low Autocorrelation Binary Sequence Problem". Serdica Journal of Computing 6, n. 4 (20 marzo 2013): 385–400. http://dx.doi.org/10.55630/sjc.2012.6.385-400.

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In this paper the low autocorrelation binary sequence problem (LABSP) is modeled as a mixed integer quadratic programming (MIQP) problem and proof of the model’s validity is given. Since the MIQP model is semidefinite, general optimization solvers can be used, and converge in a finite number of iterations. The experimental results show that IQP solvers, based on this MIQP formulation, are capable of optimally solving general/skew-symmetric LABSP instances of up to 30/51 elements in a moderate time. ACM Computing Classification System (1998): G.1.6, I.2.8.

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44

Lu, Cheng, Zhenbo Wang e Wenxun Xing. "An improved lower bound and approximation algorithm for binary constrained quadratic programming problem". Journal of Global Optimization 48, n. 3 (18 dicembre 2009): 497–508. http://dx.doi.org/10.1007/s10898-009-9504-1.

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45

Zhou, Ying, Lingjing Kong, Yong Liu, Yiqiao Cai e Shaopeng Liu. "A Single Deep Neural Network Model for Multiobjective Unconstrained Binary Quadratic Programming Problem". International Journal of Cognitive Informatics and Natural Intelligence 18, n. 1 (3 dicembre 2024): 1–17. https://doi.org/10.4018/ijcini.361012.

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The multiobjective unconstrained binary quadratic programming problem is an important combinatorial optimization problem with both theory and practical values. Until now, several efforts have been made to design metaheuristic methods to solve the problem. However, designing such effective methods is not trivial and heavily depends on experts' specific knowledge. Meanwhile, due to the iterative nature of metaheuristic methods, they require a long time to find high-quality solutions. From the perspective of machine learning, this paper proposes a deep reinforcement learning method to solve the problem. The method can automatically learn effective heuristics from a large amount of data, thus decreasing the need for experts' knowledge. Meanwhile, by leveraging the power of GPU, the method can quickly obtain high-quality solutions for a batch of instances. Experimental results show the proposed method outperforms two classical metaheuristic methods in terms of solution quality and running time for solving the problem.

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46

Zdunek, Rafał, Andrzej Grobelny, Jerzy Witkowski e Radosław Igor Gnot. "On–Off Scheduling for Electric Vehicle Charging in Two-Links Charging Stations Using Binary Optimization Approaches". Sensors 21, n. 21 (28 ottobre 2021): 7149. http://dx.doi.org/10.3390/s21217149.

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In this study, we deal with the problem of scheduling charging periods of electrical vehicles (EVs) to satisfy the users’ demands for energy consumption as well as to optimally utilize the available power. We assume three-phase EV charging stations, each equipped with two charging ports (links) that can serve up to two EVs in the scheduling period but not simultaneously. Considering such a specification, we propose an on–off scheduling scheme wherein control over an energy flow is achieved by flexibly switching the ports in each station on and off in a manner such as to satisfy the energy demand of each EV, flatten the high energy-consuming load on the whole farm, and to minimize the number of switching operations. To satisfy these needs, the on–off scheduling scheme is formulated in terms of a binary linear programming problem, which is then extended to a quadratic version to incorporate the smoothness constraints. Various algorithmic approaches are used for solving a binary quadratic programming problem, including the Frank–Wolfe algorithm and successive linear approximations. The numerical simulations demonstrate that the latter is scalable, efficient, and flexible in a charging procedure, and it shaves the load peak while maintaining smooth charging profiles.

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47

Moraru, Vasile, Daniela Istrati e Sergiu Zaporojan. "SOLVING THE DAYS-OFF SCHEDULING PROBLEM USING QUADRATIC PROGRAMMING WITH CIRCULANT MATRIX". Journal of Engineering Science 29, n. 4 (gennaio 2023): 97–108. http://dx.doi.org/10.52326/jes.utm.2022.29(4).05.

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The purpose of this paper is the approach of a mathematical model dedicated to planning the consecutive days off of a company’s employees. Companies must find a flexible work schedule between employees, always considering the satisfaction of work tasks as well as guaranteeing consecutive days off. The analysis is based on solving a quadratic programming problem with binary variables. The proposed method uses the properties of the circulant symmetric matrix in the researched model, which allows the transformation of the considered problems into an equivalent separable non-convex optimization problem. A practical continuous convex relaxation approach is proposed. DC Algorithm is used to solve relaxed problems. A solved numerical example is presented.

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48

Zavvar Sabegh, Mohammad Reza, e Chris Bingham. "Model Predictive Control with Binary Quadratic Programming for the Scheduled Operation of Domestic Refrigerators". Energies 12, n. 24 (7 dicembre 2019): 4649. http://dx.doi.org/10.3390/en12244649.

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Abstract (sommario):

The rapid proliferation of the ‘Internet of Things’ (IoT) now affords the opportunity to schedule the operation of widely distributed domestic refrigerator and freezers to collectively improve energy efficiency and reduce peak power consumption on the electrical grid. To accomplish this, the paper proposes the real-time estimation of the thermal mass of each refrigerator in a network using on-line parameter identification, and the co-ordinated (ON-OFF) scheduling of the refrigerator compressors to maintain their respective temperatures within specified hysteresis bands commensurate with accommodating food safety standards. A custom model predictive control (MPC) scheme is devised using binary quadratic programming to realize the scheduling methodology which is implemented through IoT hardware (based on a NodeMCU). Benefits afforded by the proposed scheme are investigated through experimental trials which show that the co-ordinated operation of domestic refrigerators can i) reduce the peak power consumption as seen from the perspective of the electrical power grid (i.e., peak load levelling), ii) can adaptively control the temperature hysteresis band of individual refrigerators to increase operational efficiency, and iii) contribute to a widely distributed aggregated load shed for demand side response purposes in order to aid grid stability. Importantly, the number of compressor starts per hour for each refrigerator is also bounded as an inherent design feature of the algorithm so as not to operationally overstress the compressors and reduce their lifetime. Experimental trials show that such co-ordinated operation of refrigerators can reduce energy consumption by ~30% whilst also providing peak load levelling, thereby affording benefits to both individual consumers as well as electrical network suppliers.

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Zhou, Ying, Lingjing Kong, Ziyan Wu, Shaopeng Liu, Yiqiao Cai e Ye Liu. "Ensemble of multi-objective metaheuristic algorithms for multi-objective unconstrained binary quadratic programming problem". Applied Soft Computing 81 (agosto 2019): 105485. http://dx.doi.org/10.1016/j.asoc.2019.105485.

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50

Wang, Jiahai. "Discrete Hopfield network combined with estimation of distribution for unconstrained binary quadratic programming problem". Expert Systems with Applications 37, n. 8 (agosto 2010): 5758–74. http://dx.doi.org/10.1016/j.eswa.2010.02.032.

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