Methods of Optimal Set Partitioning for Some Start Control Problems with Quadratic Functional

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

Download Full-text

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

EurasianUnionScientists ◽

10.31618/esu.2413-9335.2020.6.71.615 ◽

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.

Download Full-text