scholarly journals Solving a two-step continuous-discrete optimal split-distribution problem with fuzzy parameters

2019 ◽  
Author(s):  
O. M. Kiselova ◽  
O. M. Prytomanova ◽  
S. V. Dzyuba ◽  
V. G. Padalko
Keyword(s):  
Optimization Problems ◽  
Set Partitioning ◽  
Dimensional Euclidean Space ◽  
Discrete Problem ◽  
Optimal Partition ◽  
Distribution Problem ◽  
Two Stage ◽  
Method Of Potentials ◽  
Optimal Set ◽  
Fuzzy Parameters

The theory of optimal set partitioning from an n-dimensional Euclidean space En is an important part of infinite-dimensional mathematical programming. The mostly reason of high interest in development of the theory of optimal set partitioning is that its results can be applied to solving the classes of different theoretical and applied optimization problems, which are transferred into continuous optimal set partitioning problem. This paper investigates the further development of the theory of optimal set partitioning from En in the case of a two-stage continuous-discrete problem of optimal partitioningdistribution with non-determined input data, which is frequently appear in solving practical problems. The two-stage continuous-discrete problem of optimal partition-distribution under constraints in the form of equations and determined position of centers of subsets is generalized by proposed continuous-discrete problem of optimal partition-distribution in case if some parameters are presented in incomplete, inaccurate or unreliable form. These parameters can be represented as linguistic variables and the method of neurolinguistic identification of unknown complex, nonlinear dependencies can be used in purpose to recovery them. A method for solving the two-stage continuous-discrete optimal partitioning-distribution problem with fuzzy parameters in target functional which based on usage of neurolinguistic identification of unknown dependencies for recovering precise values of fuzzy parameters, methods of the theory of optimal set partitioning and the method of potentials for solving a transportation problem is proposed.

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 Solving a Two-stage Continuous-discrete Problem of Optimal Partitioning-Allocation with Subsets Centers Placement

2020 ◽  
Vol 10 (1) ◽  
pp. 124-136
Author(s):  
Elena Kiseleva ◽  
Olha Prytomanova ◽  
Liudmyla Hart
Keyword(s):  
Transportation Problem ◽  
Set Partitioning ◽  
Dimensional Euclidean Space ◽  
Discrete Problem ◽  
Two Stage ◽  
Optimal Partitioning ◽  
Finite Dimensional ◽  
Partitioning Problem ◽  
The Given ◽  
Optimal Set

AbstractA two-stage continuous-discrete optimal partitioning-allocation problem is studied, and a method and an algorithm for its solving are proposed. This problem is a generalization of a classical transportation problem to the case when coordinates of the production points (collection, storage, processing) of homogeneous products are continuously allocated in the given domain and the production volumes at these points are unknown. These coordinates are found as a solution of the corresponding continuous optimal set-partitioning problem in a finite-dimensional Euclidean space with the placement (finding coordinates) of these subsets’ centers. Also, this problem generalizes discrete two-stage production-transportation problems to the case of continuously allocated consumers. The method and algorithm are illustrated by solving two model problems.

scholarly journals Construction of a multiplicatively weighted diagram of a crow with fuzzy parameters

2019 ◽  
Author(s):  
O. M. Kiselova ◽  
O. M. Prytomanova ◽  
S. V. Dzyuba ◽  
V. G. Padalko
Keyword(s):  
Euclidean Space ◽  
Finite Number ◽  
Voronoi Diagram ◽  
Optimization Problems ◽  
Optimal Location ◽  
Set Partitioning ◽  
Dimensional Euclidean Space ◽  
Bounded Set ◽  
Optimal Set ◽  
Fuzzy Parameters

An algorithm for constructing a multiplicatively weighted Voronoi diagram in the presence of fuzzy parameters with optimal location of a finite number of generator points in a bounded set of n-dimensional Euclidean space En is proposed in the paper. The algorithm is based on the formulation of a continuous set partitioning problem from En into non-intersecting subsets with a partitioning quality criterion providing the corresponding form of Voronoi diagram. Algorithms for constructing the classical Voronoi diagram and its various generalizations, which are based on the usage of the methods of the optimal set partitioning theory, have several advantages over the other used methods: they are out of thedependence of En space dimensions, which containing a partitioned bounded set into subsets, independent of the geometry of the partitioned sets, the algorithm’s complexity is not growing under increasing of number of generator points, it can be used for constructing the Voronoi diagram with optimal location of the points and others. The ability of easily construction not only already known Voronoi diagrams but also the new ones is the result of this general-purpose approach. The proposed in the paper algorithm for constructing a multiplicatively weighted Voronoi diagram in the presence of fuzzy parameters with optimal location of a finite number of generator points in a bounded set of n-dimensional Euclidean space En is developed using a synthesis of methods for solving optimal set partitioning problems, neurofuzzy technologies and modifications of the Shor’s r-algorithm for solving non-smooth 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

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

OPTIMAL SET-PARTITIONING BASED ON GROUP QUALITY LIKELIHOOD USING PARTITION-GROWING ALGORITHM

2013 ◽  
Vol 05 (04) ◽  
pp. 1350022
Author(s):  
CHAIVATNA SUMETPHONG ◽  
SUPACHAI TANGWONGSAN
Keyword(s):  
Branch And Bound ◽  
Set Partitioning ◽  
Experimental Results ◽  
Historical Documents ◽  
Optimal Partition ◽  
Document Images ◽  
Efficient Manner ◽  
Degraded Document ◽  
Optimal Set

We consider the problem of partitioning a set of elements X into a minimum of m blocks to maximize the probability that each block constitutes a well-grouped subset of X. We employ certain characteristics of the Group Quality Likelihood to limit our search for an optimal partition within a smaller set of partitions. We develop a novel Partition-Growing algorithm based on the Branch and Bound strategy that produces the optimal partition in an efficient manner. We demonstrate how the algorithm can be applied to recognize Broken Characters in degraded document images. Experimental results conducted on Thai historical documents are very promising.

Solving a Two-Stage Continuous-Discrete Problem of Optimal Partition–Allocation with a Given Position of the Centers of Subsets

2020 ◽  
Vol 56 (1) ◽  
pp. 1-12
Author(s):  
Å. Ì. Kiseleva ◽  
O. M. Prytomanova ◽  
S. A. Us
Keyword(s):  
Discrete Problem ◽  
Optimal Partition ◽  
Two Stage

scholarly journals Construction of a generalized Voronoi diagram with optimal placement of generator points based on the theory of optimal set partitioning

2020 ◽  
Vol 53 (1) ◽  
pp. 109-112
Author(s):  
E.M. Kiseleva ◽  
L.L. Hart ◽  
O.M. Prytomanova ◽  
S.V. Zhuravel
Keyword(s):  
Euclidean Space ◽  
Voronoi Diagram ◽  
Quality Criterion ◽  
Set Partitioning ◽  
Optimal Placement ◽  
Dimensional Euclidean Space ◽  
Bounded Set ◽  
Optimal Set ◽  
Continuous Problem ◽  
Generalized Voronoi Diagram

The problem of construction of a generalized Voronoi diagram with optimal placement of a finite number of generator points in a bounded set of \textit{n}-dimensional Euclidean space is considered. A method is proposed for solving such a problem based on the formulation of the corresponding continuous problem of optimal partitioning of a set in \textit{n}-dimensional Euclidean space with a partition quality criterion that provides the corresponding form of the Voronoi diagram. Further, to solve such a problem, the developed mathematical and algorithmic apparatus is used, the part of which is Shor's \textit{r}-algorithm.

scholarly journals Two-stage multi-tasking transform framework for large-scale many-objective optimization problems

2021 ◽  
Author(s):  
Lu Chen ◽  
Handing Wang ◽  
Wenping Ma
Keyword(s):  
Large Scale ◽  
Original Problem ◽  
Optimization Problems ◽  
Reference Points ◽  
Optimization Strategy ◽  
Two Stage ◽  
Decision Space ◽  
Second Stage ◽  
Decision Variables ◽  
Objective Space

AbstractReal-world optimization applications in complex systems always contain multiple factors to be optimized, which can be formulated as multi-objective optimization problems. These problems have been solved by many evolutionary algorithms like MOEA/D, NSGA-III, and KnEA. However, when the numbers of decision variables and objectives increase, the computation costs of those mentioned algorithms will be unaffordable. To reduce such high computation cost on large-scale many-objective optimization problems, we proposed a two-stage framework. The first stage of the proposed algorithm combines with a multi-tasking optimization strategy and a bi-directional search strategy, where the original problem is reformulated as a multi-tasking optimization problem in the decision space to enhance the convergence. To improve the diversity, in the second stage, the proposed algorithm applies multi-tasking optimization to a number of sub-problems based on reference points in the objective space. In this paper, to show the effectiveness of the proposed algorithm, we test the algorithm on the DTLZ and LSMOP problems and compare it with existing algorithms, and it outperforms other compared algorithms in most cases and shows disadvantage on both convergence and diversity.

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