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An application of a decomposed ortho-diagonal method to discrete polyoptimization of a hall with a spatial grid structure

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Bibliographic Details
Title: An application of a decomposed ortho-diagonal method to discrete polyoptimization of a hall with a spatial grid structure
Authors: Paczkowski, Witold M., Jendo, Stefan
Publisher Information: Polish Academy of Sciences (Polska Akademia Nauk - PAN), Institute of Fundamental Technological Research, Warsaw
Subject Terms: consecutive nondominated solutions, Numerical optimization and variational techniques, Compliance or weight optimization in solid mechanics, ortho-diagonal method, polyoptimization of hall, dicrete polyoptimization problems, vector objective function, spatial grid structure, Optimization of other properties in solid mechanics, monotonicity
Description: Summary: The paper deals with application of the ortho-diagonal (O-D) method of finding the nondominated sets of solutions and evaluations for dicrete polyoptimization problems. First, the O-D method is modified for finding minimum of a scalar function. The monotonicity property of a vector objective function is used by the O-D method for consecutive finding of \(j\)th-criterion partial nondominated sets, \(j\in \{1,2,\dots, J\}\). To find the nondominated evaluations sets, the discrete neighbourhoods \(S\) of the point \({\mathbf x}_i\) are investigated starting from the solution \({\mathbf x}^*_1\) which minimizes the first objective function. In this way we are able to determine the consecutive nondominated solutions \({\mathbf x}^k_{ND}\). The accuracy of solution and CPU time depend on the definition discrete neighbourhoods \(S\) of the point \({\mathbf x}_i\) in the design space. The he algorithm of the O-D method is applied to solve the discrete polyoptimization of a hall with spatial grid structure.
Document Type: Article
File Description: application/xml
Access URL: https://zbmath.org/1462979
Accession Number: edsair.c2b0b933574d..bd2b92b97c12f897c89a1b91ffdf71a2
Database: OpenAIRE
Description
Abstract:Summary: The paper deals with application of the ortho-diagonal (O-D) method of finding the nondominated sets of solutions and evaluations for dicrete polyoptimization problems. First, the O-D method is modified for finding minimum of a scalar function. The monotonicity property of a vector objective function is used by the O-D method for consecutive finding of \(j\)th-criterion partial nondominated sets, \(j\in \{1,2,\dots, J\}\). To find the nondominated evaluations sets, the discrete neighbourhoods \(S\) of the point \({\mathbf x}_i\) are investigated starting from the solution \({\mathbf x}^*_1\) which minimizes the first objective function. In this way we are able to determine the consecutive nondominated solutions \({\mathbf x}^k_{ND}\). The accuracy of solution and CPU time depend on the definition discrete neighbourhoods \(S\) of the point \({\mathbf x}_i\) in the design space. The he algorithm of the O-D method is applied to solve the discrete polyoptimization of a hall with spatial grid structure.