Application of the optimal set partitioning method to problems of wireless network engineering

2013 ◽  
pp. 185-192
Keyword(s):  
Wireless Network ◽  
Set Partitioning ◽  
Network Engineering ◽  
Optimal Set

scholarly journals Optimal set partitioning, matchings and lagrangian duality

1979 ◽  
Vol 26 (4) ◽  
pp. 553-563 ◽  
Author(s):  
George L. Nemhauser ◽  
Glenn M. Weber
Keyword(s):  
Set Partitioning ◽  
Lagrangian Duality ◽  
Optimal Set

scholarly journals Optimization Algorithm of Control Channel Selection for Wireless Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Jian Chen ◽  
Huahui Yu ◽  
Jingyu Hua ◽  
Xiaoyan Zhang
Keyword(s):  
Wireless Network ◽  
Channel Selection ◽  
Control Channel ◽  
Network Nodes ◽  
Data Channel ◽  
Bandwidth Requirement ◽  
Simulation Results ◽  
Selection For ◽  
Limited Spectrum ◽  
Optimal Set

Control channel is used to transmit protocol or signal information between wireless network nodes and is a key component of wireless network. Compared with data information, protocol or signal information is usually much less, so the spectrum bandwidth requirement of control channel is also much less than that of data channel. In order to optimize the usage of the limited spectrum resources, this paper focuses on the issue of control channel selection. We propose a greedy algorithm which minimizes the total spectrum bandwidth of the set of control channels. Theoretical analysis proves that the proposed algorithm can achieve the optimal set of control whose sum of the spectrum bandwidth is the minimum. Simulation results also show that the proposed algorithm consumes less spectrum resources than other algorithms in the same wireless network environment.

scholarly journals Solving an infinite-dimensional problem of location-allocation with fuzzy parameters

2018 ◽  
Author(s):  
O. M. Kiselova ◽  
O. M. Prytomanova ◽  
S. V. Zhuravel ◽  
V. V. Sharavara
Keyword(s):  
Mathematical Description ◽  
Mathematical Formulation ◽  
Set Partitioning ◽  
Production Costs ◽  
Dimensional Problem ◽  
Location Allocation ◽  
Infinite Dimensional ◽  
Wide Range ◽  
Optimal Set ◽  
Fuzzy Parameters

The problem of enterprises location with the simultaneous allocation of this region, coninuously filled by consumers, into consumer areas, where each of them is served by one enterprise, in order to minimize transportation and production costs, in the mathematical definition, are illustrated as infinite-dimensional optimal set partitioning problems (OSP) in non-intersecting subsets with the placement of centers of these subsets. A wide range of methods and algorithms have been developed to solve practical tasks of location-allocation, both finite-dimensional and infinite-dimensional. However, infinite-dimensional location-allocation problems are significantly complicated in uncertainty, in particular case when a number of their parameters are fuzzy, inaccurate, or an unreliable mathematical description of some dependencies in the model is false. Such models refer to the fuzzy OSP tasks, and special solutions and methods are needed to solve them. This pa-per is devoted to the solution of an infinite-dimensional problem of location-allocation with fuzzy parameters, which in mathematical formulation are defined as continuous line-ar single-product problem of n-dimensional Euclidean space Еn optimal set partitioning into a subset with the search for the coordinates of the centers of these subsets with con-straints in the form of equalities and inequalities whose target functionality has fuzzy pa-rameters. The software to solve the illustrated problem was developed. It works on the ba-sis of neuron-fuzzy technologies with r-algorithm of Shore application. The object-oriented programming language C# and the Microsoft Visual Studio development envi-ronment were used. The results for a model-based problem of location-allocation with fuzzy parameters obtained in developed software are presented. The results comparison for the solution to solve the infinite-dimensional problem of location-allocation with de-fined parameters and for the case where some parameters of the problem are inaccurate, fuzzy or their mathematical description is false

scholarly journals APPLICATION OF THE THEORY OF OPTIMAL SET PARTITIONING BEFORE BUILDING MULTIPLICATIVELY WEIGHTED VORONOI DIAGRAM WITH FUZZY PARAMETERS

2020 ◽  
Vol 6 (2(71)) ◽  
pp. 30-35
Author(s):  
O.M. Kiseliova ◽  
O.M. Prytomanova ◽  
V.H. Padalko
Keyword(s):  
Euclidean Space ◽  
Finite Number ◽  
Nonsmooth Optimization ◽  
Voronoi Diagram ◽  
Optimization Problems ◽  
Optimal Location ◽  
Set Partitioning ◽  
Dimensional Euclidean Space ◽  
Optimal Set ◽  
Fuzzy Parameters

An algorithm for constructing a multiplicatively weighted Voronoi diagram involving fuzzy parameters with the optimal location of a finite number of generator points in a limited set of n-dimensional Euclidean space 𝐸𝑛 has been suggested in the paper. The algorithm has been developed based on the synthesis of methods of solving the problems of optimal set partitioning theory involving neurofuzzy technologies modifications of N.Z. Shor 𝑟 -algorithm for solving nonsmooth optimization problems.

scholarly journals Algorithm for solving one problem of optimal partition with fuzzy parameters in the target functional

2018 ◽  
Author(s):  
O. M. Kiselova ◽  
O. M. Prytomanova ◽  
S. V. Zhuravel ◽  
V. V. Sharavara
Keyword(s):  
Optimization Problems ◽  
Target Function ◽  
Optimization Methods ◽  
Set Partitioning ◽  
Modern Theory ◽  
Single Product ◽  
Infinite Dimensional ◽  
Partitioning Problems ◽  
Optimal Set ◽  
Fuzzy Parameters

The mathematical theory of optimal set partitioning (OSP) of the n-dimensional Eu-clidean space, which has been formed for todays, is the field of the modern theory of opti-mization, namely, the new section of non-classical infinite-dimensional mathematical pro-gramming. The theory is built based on a single, theoretically defined approach that sum up initial infinitedimensional optimization problems in a certain way (with the function of Lagrange) to nonsmooth, usually, finite-dimensional optimization problems, where lat-est numerical nondifferentiated optimization methods may be used - various variants r-algorithm of N.Shor, that was developed in V. Glushkov Institute of Cybernetics of the Na-tional Academy of Sciences of Ukraine. For now, the number of directions have been formed in the theory of continuous tasks of OSP, which are defined with different types of mathematical statements of partitioning problems, as well as various spheres of its application. For example, linear and nonlinear, single-product and multiproduct, deterministic and stochastic, in the conditions of com-plete and incomplete information about the initial data, static and dynamic tasks of the OSP without limitations and with limitations, both with the given position of the centers of subsets, and with definition the optimal variant of their location. Optimal set partitioning problems in uncertainty are the least developed for today is the direction of this theory, in particular, tasks where a number of parameters are fuzzy, inaccurate, or there are insuffi-cient mathematical description of some dependencies in the model. Such models refer to the fuzzy OSP problems, and special solutions and methods are needed to solve them. In this paper, we propose an algorithm for solving a continuous linear single-product problem of optimal set partitioning of n-dimensional Euclidean spaces Еn into a subset with searching of coordinates of the centers of these subsets with restrictions in the form of equalities and inequalities where target function has fuzzy parameters. The algorithm is built based on the application of neuro-fuzzy technologies and N.Shor r-algorithm

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