Article: Method of solving optimal design problems based on flexible tolerance strategy Journal: International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO) 2020 Vol.10 No.3 pp.255 - 269 Abstract: In the work on solving problems of optimal design, structures working in aggressive external environments, a modified method is proposed, which is based on the flexible tolerance method. The proposed method allows to control the accuracy of solving systems of differential equations when calculating the constraint functions of an optimisation problem. Based on the information about the degree of closeness of the point of the solution space to the local extremum point, which is received by the neural network controller, its parameters change. For this purpose, various matrices of neural network synapses, trained for different precisions of calculating the functions of constraints, are used. This strategy is used to modify the flexible tolerance method, based on the use of a neural network controller. As a criterion of the flexible tolerance, the error of calculating the constraint functions is used. It is shown that the use of a neural network regulator of the accuracy of calculating the restriction functions in the modified flexible tolerance method allows to significantly increase its efficiency while simultaneously obtaining a solution to the problem with a given accuracy and compensating the computational costs connected with using the α-level generalisation principle. Inderscience Publishers - linking academia, business and industry through research

Title: Method of solving optimal design problems based on flexible tolerance strategy

Authors: Larysa Ivanivna Korotka; Dmitriy Gegegemonovich Zelentsov

Addresses: Department Information Systems, Ukrainian State Chemical Technology University, Dnipro, 49008, Ukraine ' Department Information Systems, Ukrainian State Chemical Technology University, Dnipro, 49008, Ukraine

Abstract: In the work on solving problems of optimal design, structures working in aggressive external environments, a modified method is proposed, which is based on the flexible tolerance method. The proposed method allows to control the accuracy of solving systems of differential equations when calculating the constraint functions of an optimisation problem. Based on the information about the degree of closeness of the point of the solution space to the local extremum point, which is received by the neural network controller, its parameters change. For this purpose, various matrices of neural network synapses, trained for different precisions of calculating the functions of constraints, are used. This strategy is used to modify the flexible tolerance method, based on the use of a neural network controller. As a criterion of the flexible tolerance, the error of calculating the constraint functions is used. It is shown that the use of a neural network regulator of the accuracy of calculating the restriction functions in the modified flexible tolerance method allows to significantly increase its efficiency while simultaneously obtaining a solution to the problem with a given accuracy and compensating the computational costs connected with using the α-level generalisation principle.

Keywords: neural network regulator; flexible tolerance; optimal design; fuzzy variables.

DOI: 10.1504/IJMMNO.2020.108613

International Journal of Mathematical Modelling and Numerical Optimisation, 2020 Vol.10 No.3, pp.255 - 269

Received: 25 May 2019
Accepted: 14 Aug 2019
Published online: 21 Jul 2020 *

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Title: Method of solving optimal design problems based on flexible tolerance strategy

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