scholarly journals On a method of solving of possibilistic-probabilistic programming problems

2021 ◽  
pp. 21-33
Author(s):  
Юлия Евгеньевна Егорова
Keyword(s):  
Optimization Problems ◽  
Probabilistic Programming ◽  
Probabilistic Optimization ◽  
Stochastic Analog ◽  
Fuzzy Parameters

В статье исследуется задача возможностно-вероятностной оптимизации, основанная на принципе ожидаемой возможности, и метод решения ее стохастического аналога в случае слабейшей t-нормы, описывающей взаимодействие нечетких параметров. Получены более простые для проверки условия, обеспечивающие сходимость метода стохастических квазиградиентов решения эквивалентного стохастического аналога. The paper studies possibilistic-probabilistic optimization problems, based on the principle of expected possibility, and a method for solving its stochastic analogue in the case of the weakest t-norm describing the interaction of fuzzy parameters. The conditions that are easier to verify and ensure the convergence of the method of stochastic quasigradients of the solution of an equivalent stochastic analog are obtained.

Towards a Better Understanding of Modeling Feasibility Robustness in Engineering Design

1999 ◽  
Vol 122 (4) ◽  
pp. 385-394 ◽  
Author(s):  
Xiaoping Du ◽  
Wei Chen
Keyword(s):  
Robust Design ◽  
Optimization Problems ◽  
Practical Significance ◽  
Engineering Practice ◽  
Probabilistic Optimization ◽  
Importance Sampling Method ◽  
Feasibility Evaluation ◽  
Feasibility Robustness ◽  
Computationally Intensive ◽  
Six Sigma Approach

In robust design, it is important not only to achieve robust design objectives but also to maintain the robustness of design feasibility under the effect of variations (or uncertainties). However, the evaluation of feasibility robustness is often a computationally intensive process. Simplified approaches in existing robust design applications may lead to either over-conservative or infeasible design solutions. In this paper, several feasibility-modeling techniques for robust optimization are examined. These methods are classified into two categories: methods that require probability and statistical analyses and methods that do not. Using illustrative examples, the effectiveness of each method is compared in terms of its efficiency and accuracy. Constructive recommendations are made to employ different techniques under different circumstances. Under the framework of probabilistic optimization, we propose to use a most probable point (MPP) based importance sampling method, a method rooted in the field of reliability analysis, for evaluating the feasibility robustness. The advantages of this approach are discussed. Though our discussions are centered on robust design, the principles presented are also applicable for general probabilistic optimization problems. The practical significance of this work also lies in the development of efficient feasibility evaluation methods that can support quality engineering practice, such as the Six Sigma approach that is being widely used in American industry. [S1050-0472(00)00904-1]

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

scholarly journals A METHOD FOR SOLVING LINEAR PROGRAMMING PROBLEMS WITH FUZZY PARAMETERS BASED ON MULTIOBJECTIVE LINEAR PROGRAMMING TECHNIQUE

2007 ◽  
Vol 24 (04) ◽  
pp. 557-573 ◽  
Author(s):  
M. ZANGIABADI ◽  
H. R. MALEKI
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Multiobjective Linear Programming ◽  
Programming Technique ◽  
Linear Programming Problems ◽  
Linear Programming Technique ◽  
Fuzzy Parameters

In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters based on those for multiobjective linear programming problems. Then by using the concept of comparison of fuzzy numbers, we transform a linear programming problem with fuzzy parameters to a multiobjective linear programming problem. To this end, we propose several theorems which are used to obtain optimal solutions of linear programming problems with fuzzy parameters. Finally some examples are given for illustrating the proposed method of solving linear programming problem with fuzzy parameters.

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.

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