Relevant bibliographies by topics / Multidimensional Vector Packing Problem

Academic literature on the topic 'Multidimensional Vector Packing Problem'

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Published: 6 September 2023

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Journal articles on the topic "Multidimensional Vector Packing Problem"

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Alves, Cláudio, José Valério de Carvalho, François Clautiaux, and Jürgen Rietz. "Multidimensional dual-feasible functions and fast lower bounds for the vector packing problem." European Journal of Operational Research 233, no. 1 (February 2014): 43–63. http://dx.doi.org/10.1016/j.ejor.2013.08.011.

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Chekanin, Vladislav A., and Alexander V. Chekanin. "Multilevel Linked Data Structure for the Multidimensional Orthogonal Packing Problem." Applied Mechanics and Materials 598 (July 2014): 387–91. http://dx.doi.org/10.4028/www.scientific.net/amm.598.387.

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The actual NP-completed orthogonal bin packing problem is considered in the article. In practice a solution of a large number of different practical problems, including problems in logistics and scheduling comes down to the bin packing problem. A decision of an any packing problem is represented as a placement string which contains a sequence of objects selected to pack. The article proposes a new multilevel linked data structure that improves the effectiveness of decoding of the placement string and as a consequence, increases the speed of packing generation. The new data structure is applicable for all multidimensional orthogonal bin packing problems.
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Chekanin, Alexander V., and Vladislav A. Chekanin. "Effective Data Structure for the Multidimensional Orthogonal Bin Packing Problems." Advanced Materials Research 962-965 (June 2014): 2868–71. http://dx.doi.org/10.4028/www.scientific.net/amr.962-965.2868.

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The actual in industry multidimensional orthogonal packing problem is considered in the article. Solution of a large number of different practical optimization problems, including resources saving problem, optimization problems in logistics, scheduling and planning comes down to the orthogonal packing problem which is NP-hard in strong sense. One of the indicators characterizing the efficiency of packing constructing algorithm is the efficiency of the used data structure. In the article a multilevel linked data structure that increases the speed of constructing of a packing is proposed. The carried out computational experiments show the high efficiency of the new data structure. Multilevel linked data structure is applicable for multidimensional orthogonal bin packing problems any kind.
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Chekanin, Alexander V., and Vladislav A. Chekanin. "Improved Packing Representation Model for the Orthogonal Packing Problem." Applied Mechanics and Materials 390 (August 2013): 591–95. http://dx.doi.org/10.4028/www.scientific.net/amm.390.591.

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The multidimensional NP-hard orthogonal bin packing problem is considered in the article. Usually the problem is solved using heuristic algorithms of discrete optimization which optimize a selection sequence of objects to be packed in containers. The quality and speed of getting the resulting packing for a given sequence of placing objects is determined by the used packing representation model. In the article presented a new packing representation model for constructing the orthogonal packing. The proposed model of potential containers describes all residual free spaces of containers in packing. The developed model is investigated on well-known standard benchmarks of three-dimensional orthogonal bin packing problem. The model can be used in development of applied software for the optimal allocation of orthogonal resources.
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Chekanin, Vladislav A., and Alexander V. Chekanin. "Improved Data Structure for the Orthogonal Packing Problem." Advanced Materials Research 945-949 (June 2014): 3143–46. http://dx.doi.org/10.4028/www.scientific.net/amr.945-949.3143.

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In paper is considered the actual in industry and engineering orthogonal multidimensional packing problem. This problem is NP-hard in strong sense therefore an important role is played effectiveness of the used packing representation model. To increase the speed of placement of a given set of orthogonal objects into containers is offered a new data structure – multilevel linked data structure. The carried out computational experiments demonstrate high time efficiency of the proposed data structure compared to the ordered simple linked list.
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Hu, Qian, Lijun Wei, and Andrew Lim. "The two-dimensional vector packing problem with general costs." Omega 74 (January 2018): 59–69. http://dx.doi.org/10.1016/j.omega.2017.01.006.

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Caprara, Alberto, and Paolo Toth. "Lower bounds and algorithms for the 2-dimensional vector packing problem." Discrete Applied Mathematics 111, no. 3 (August 2001): 231–62. http://dx.doi.org/10.1016/s0166-218x(00)00267-5.

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Hu, Qian, Andrew Lim, and Wenbin Zhu. "The two-dimensional vector packing problem with piecewise linear cost function." Omega 50 (January 2015): 43–53. http://dx.doi.org/10.1016/j.omega.2014.07.004.

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Billaut, Jean-Charles, Federico Della Croce, and Andrea Grosso. "A single machine scheduling problem with two-dimensional vector packing constraints." European Journal of Operational Research 243, no. 1 (May 2015): 75–81. http://dx.doi.org/10.1016/j.ejor.2014.11.036.

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Morales, Fernando. "Application and assessment of divide-and-conquer-based heuristic algorithms for some integer optimization problems." Yugoslav Journal of Operations Research, no. 00 (2022): 30. http://dx.doi.org/10.2298/yjor2111015030m.

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In this paper three heuristic algorithms using the Divide-and-Conquer paradigm are developed and assessed for three integer optimizations problems: Multidimensional Knapsack Problem (d-KP), Bin Packing Problem (BPP) and Travelling Salesman Problem (TSP). For each case, the algorithm is introduced, together with the design of numerical experiments, in order to empirically establish its performance from both points of view: its computational time and its numerical accuracy.
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Dissertations / Theses on the topic "Multidimensional Vector Packing Problem"

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Khan, Arindam. "Approximation algorithms for multidimensional bin packing." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54371.

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The bin packing problem has been the corner stone of approximation algorithms and has been extensively studied starting from the early seventies. In the classical bin packing problem, we are given a list of real numbers in the range (0, 1], the goal is to place them in a minimum number of bins so that no bin holds numbers summing to more than 1. In this thesis we study approximation algorithms for three generalizations of bin packing: geometric bin packing, vector bin packing and weighted bipartite edge coloring. In two-dimensional (2-D) geometric bin packing, we are given a collection of rectangular items to be packed into a minimum number of unit size square bins. Geometric packing has vast applications in cutting stock, vehicle loading, pallet packing, memory allocation and several other logistics and robotics related problems. We consider the widely studied orthogonal packing case, where the items must be placed in the bin such that their sides are parallel to the sides of the bin. Here two variants are usually studied, (i) where the items cannot be rotated, and (ii) they can be rotated by 90 degrees. We give a polynomial time algorithm with an asymptotic approximation ratio of $\ln(1.5) + 1 \approx 1.405$ for the versions with and without rotations. We have also shown the limitations of rounding based algorithms, ubiquitous in bin packing algorithms. We have shown that any algorithm that rounds at least one side of each large item to some number in a constant size collection values chosen independent of the problem instance, cannot achieve an asymptotic approximation ratio better than 3/2. In d-dimensional vector bin packing (VBP), each item is a d-dimensional vector that needs to be packed into unit vector bins. The problem is of great significance in resource constrained scheduling and also appears in recent virtual machine placement in cloud computing. Even in two dimensions, it has novel applications in layout design, logistics, loading and scheduling problems. We obtain a polynomial time algorithm with an asymptotic approximation ratio of $\ln(1.5) + 1 \approx 1.405$ for 2-D VBP. We also obtain a polynomial time algorithm with almost tight (absolute) approximation ratio of $1+\ln(1.5)$ for 2-D VBP. For $d$ dimensions, we give a polynomial time algorithm with an asymptotic approximation ratio of $\ln(d/2) + 1.5 \approx \ln d+0.81$. We also consider vector bin packing under resource augmentation. We give a polynomial time algorithm that packs vectors into $(1+\epsilon)Opt$ bins when we allow augmentation in (d - 1) dimensions and $Opt$ is the minimum number of bins needed to pack the vectors into (1,1) bins. In weighted bipartite edge coloring problem, we are given an edge-weighted bipartite graph $G=(V,E)$ with weights $w: E \rightarrow [0,1]$. The task is to find a proper weighted coloring of the edges with as few colors as possible. An edge coloring of the weighted graph is called a proper weighted coloring if the sum of the weights of the edges incident to a vertex of any color is at most one. This problem is motivated by rearrangeability of 3-stage Clos networks which is very useful in various applications in interconnected networks and routing. We show a polynomial time approximation algorithm that returns a proper weighted coloring with at most $\lceil 2.2223m \rceil$ colors where $m$ is the minimum number of unit sized bins needed to pack the weight of all edges incident at any vertex. We also show that if all edge weights are $>1/4$ then $\lceil 2.2m \rceil$ colors are sufficient.
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Books on the topic "Multidimensional Vector Packing Problem"

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Csirik, J. On the multidimensional vector bin packing. Brussels: European Institute for Advanced Studies in Management, 1990.

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Babeshko, Lyudmila, and Irina Orlova. Econometrics and econometric modeling in Excel and R. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1079837.

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The textbook includes topics of modern econometrics, often used in economic research. Some aspects of multiple regression models related to the problem of multicollinearity and models with a discrete dependent variable are considered, including methods for their estimation, analysis, and application. A significant place is given to the analysis of models of one-dimensional and multidimensional time series. Modern ideas about the deterministic and stochastic nature of the trend are considered. Methods of statistical identification of the trend type are studied. Attention is paid to the evaluation, analysis, and practical implementation of Box — Jenkins stationary time series models, as well as multidimensional time series models: vector autoregressive models and vector error correction models. It includes basic econometric models for panel data that have been widely used in recent decades, as well as formal tests for selecting models based on their hierarchical structure. Each section provides examples of evaluating, analyzing, and testing models in the R software environment. Meets the requirements of the Federal state educational standards of higher education of the latest generation. It is addressed to master's students studying in the Field of Economics, the curriculum of which includes the disciplines Econometrics (advanced course)", "Econometric modeling", "Econometric research", and graduate students."
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Solving the Multidimensional Multiple Knapsack Problem with Packing constraints using Tabu Search. Storming Media, 1999.

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Book chapters on the topic "Multidimensional Vector Packing Problem"

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Hu, Qian, Andrew Lim, and Wenbin Zhu. "The Two-Dimensional Vector Packing Problem with Courier Cost Structure." In Recent Trends in Applied Artificial Intelligence, 212–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38577-3_22.

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Bougeret, Marin, Guillerme Duvillié, Rodolphe Giroudeau, and Rémi Watrigant. "Multidimensional Binary Vector Assignment Problem: Standard, Structural and Above Guarantee Parameterizations." In Fundamentals of Computation Theory, 189–201. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22177-9_15.

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Bougeret, Marin, Guillerme Duvillié, and Rodolphe Giroudeau. "Approximability and Exact Resolution of the Multidimensional Binary Vector Assignment Problem." In Lecture Notes in Computer Science, 148–59. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45587-7_13.

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Dahmani, Nadia, Saoussen Krichen, El-Ghazali Talbi, and Sanaa Kaddoura. "Solving the Multi-objective 2-Dimensional Vector Packing Problem Using $$\epsilon $$-constraint Method." In Advances in Intelligent Systems and Computing, 96–104. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72654-6_10.

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Arkin, Esther M., Refael Hassin, Shlomi Rubinstein, and Maxim Sviridenko. "Approximations for Maximum Transportation Problem with Permutable Supply Vector and Other Capacitated Star Packing Problems." In Algorithm Theory — SWAT 2002, 280–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45471-3_29.

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Borisovsky, Pavel, and Evgeniya Fedotova. "Genetic Algorithm for the Variable Sized Vector Bin-Packing Problem with the Limited Number of Bins." In Communications in Computer and Information Science, 55–67. Cham: Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-16224-4_3.

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Dahmani, Nadia, Saoussen Krichen, François Clautiaux, and El-Ghazali Talbi. "A Comparative Study of Multi-objective Evolutionary Algorithms for the Bi-objective 2-Dimensional Vector Packing Problem." In Combinatorial Optimization and Applications, 37–48. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-03780-6_4.

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Pawlowsky-Glahn, Vera, and Richardo A. Olea. "Spatial covariance structure." In Geostatistical Analysis of Compositional Data. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780195171662.003.0009.

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For any component in time series analysis (Natke 1983), the concept of covariance between components of a spatially distributed random vector Z(u) leads to: direct covariances, Cov[Zi(u),Zj(u)]; shifted covariances or spatial covariances, Cov [Zi(u), Zj-(u+ h)], also known as cross-covariance functions; and autocovariance functions, Cov[Zi(u),Zi(u + h)]. The direct covariances may be thought of as a special case of the cross-covariance functions (for h = 0), and the same holds for the autocovariance functions (for i = j), so there is no need for a separate discussion. To simplify the exposition, hereafter the term function is dropped, and only the terms cross-covariance and autocovariance are used. Pawlowsky (1984) stated that if the vector random function constitutes an r-composition, then the problem of spurious spatial correlations appears. This is evident from the fact that at each point of the domain W, as in the nonregionalized case, the natural sample space of an r-composition is the D-simplex. This aspect will be discussed in Section 3.1.1. Aitchison (1986) discussed the problematic nature of the covariance analysis of nonregionalized compositions. He circumvents the problem of spurious correlations by using the fact that the ratio of two arbitrary components of a basis is identical to the ratios of the corresponding components of the associated composition. To avoid working with ratios, which is always difficult, Aitchison takes logarithms of the ratios. Then dependencies among variables of a composition can be examined in real space by analyzing the covariance structure of the log-quotients. The advantages of using this approach are not only numerical or related to the facility of subsequent mathematical operations. Essentially they relate to the fact that the approach consists of a projection of the original sample space, the simplex SD, onto a new sample space, namely real space IRD-1. Thus the door is open to many available methods and models based on the multivariate normal distribution. Recall that the multivariate normal distribution requires the sample space to be precisely the multidimensional, unconstrained real space. For this kind of model, strictly speaking, this is equivalent to saying that you need unconstrained components of the random vector to be analyzed.
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Pawlowsky-Glahn, Vera, and Richardo A. Olea. "Cokriging." In Geostatistical Analysis of Compositional Data. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780195171662.003.0011.

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The problem of estimation of a coregionalization of size q using cokriging will be discussed in this chapter. Cokriging—a multivariate extension of kriging—is the usual procedure applied to multivariate regionalized problems within the framework of geostatistics. Its fundament is a distribution-free, linear, unbiased estimator with minimum estimation variance, although the absence of constraints on the estimator is an implicit assumption that the multidimensional real space is the sample space of the variables under consideration. If a multivariate normal distribution can be assumed for the vector random function, then the simple kriging estimator is identical with the conditional expectation, given a sample of size N. See Journel (1977, pp. 576-577), Journel (1980, pp. 288-290), Cressie (1991, p. 110), and Diggle, Tawn, and Moyeed (1998, p. 300) for further details. This estimator is in general the best possible linear estimator, as it is unbiased and has minimum estimation variance, but it is not very robust in the face of strong departures from normality. Therefore, for the estimation of regionalized compositions other distributions must also be taken into consideration. Recall that compositions cannot follow a multivariate normal distribution by definition, their sample space being the simplex. Consequently, regionalized compositions in general cannot be modeled under explicit or implicit assumptions of multivariate Gaussian processes. Here only the multivariate lognormal and additive logistic normal distributions will be addressed. Besides the logarithmic and additive logratio transformations, others can be applied, such as the multivariate Box-Cox transformation, as stated by Andrews et al. (1971), Rayens and Srinivasan (1991), and Barcelo-Vidal (1996). Furthermore, distributions such as the multiplicative logistic normal distribution introduced by Aitchison (1986, p. 131) or the additive logistic skew-normal distribution defined by Azzalini and Dalla Valle (1996) can be investigated in a similar fashion. References to the literature for the fundamental principles of the theory discussed in this chapter were given in Chapter 2. Among those, special attention is drawn to the work of Myers (1982), where matrix formulation of cokriging was first presented and the properties included in the first section of this chapter were stated.
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Conference papers on the topic "Multidimensional Vector Packing Problem"

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Stakic, Dorde, Ana Anokic, and Raka Jovanovic. "Comparison of Different Grasp Algorithms for the Heterogeneous Vector Bin Packing Problem." In 2019 China-Qatar International Workshop on Artificial Intelligence and Applications to Intelligent Manufacturing (AIAIM). IEEE, 2019. http://dx.doi.org/10.1109/aiaim.2019.8632779.

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Jain, P., and A. M. Agogino. "Global Optimization Using the Multistart Method." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0072.

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Abstract Multistart is a novel stochastic global optimization method for finding the global optimum of highly nonlinear mechanical problems. In this paper we introduce and develop a variant of the multistart method in which a fraction of the sample points in the feasible region with smallest function value are clustered using the Vector Quantization technique. The theories of lattices and sphere packing are used to define optimal lattices. These lattices are optimal with respect to quantization error and are used as code points for vector quantization. The implementation of these ideas has resulted in the VQ-multistart algorithm for finding the global optimum with substantial reductions in both the incore memory requirements and the computation time. We solve several mathematical test problems and a mechanical optimal design problem using the VQ-multistart algorithm.
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Sinha, S. C., Der-Ho Wu, Vikas Juneja, and Paul Joseph. "Analysis of Dynamic Systems With Periodically Varying Parameters via Chebyshev Polynomials." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0207.

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Abstract In this paper a general method for the analysis of multidimensional second-order dynamic systems with periodically varying parameters is presented. The state vector and the periodic matrices appearing in the equations are expanded in Chebyshev polynomials over the principal period and the original differential problem is reduced to a set of linear algebraic equations. The technique is suitable for constructing either numerical or approximate analytical solutions. As an illustrative example, approximate analytical expressions for the Floquet characteristic exponents of Mathieu’s equation are obtained. Stability charts are drawn to compare the results the proposed method with those obtained by Runge-Kutta and perturbation methods. Numerical solutions for the flap-lag motion of a three blade helicopter rotor are constructed in the next example. The numerical accuracy and efficiency of the proposed technique is compared with standard numerical codes based on Runge-Kutta, Adams-Moulton and Gear algorithms. The results obtained in the both examples indicate that the suggested approach extremely accurate and is by far the most efficient one.
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