Title: Solving quadratic programming problems through a fully rough scheme and its applications

Authors: Amr A. Abohany; Rizk M. Rizk-Allah; Diana T. Mousa; Aboul Ella Hassanien

Addresses: Faculty of Computers and Information, Kafrelsheikh University, Egypt ' Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Egypt ' Faculty of Computers and Information, Kafrelsheikh University, Egypt ' Faculty of Computers and Artificial Intelligence, Cairo University, Egypt

Abstract: Real-life problems are generally solved with some uncertain parameters. Naturally, these parameters may be determined based on the opinions of experts. Therefore, all consenting and opposing opinions should be considered. This works aims to present an approach for solving quadratic programming (QP) problems. The proposed approach combines the merits of the slice sum method (SSM), linearisation, and the Frank and Wolfe algorithm to find optimal solutions. The proposed approach has two features: first, it elicits four crisp problems from the fully rough QP (FRQP) problem using the SSM. Second, the proposed method employs a linearised Frank and Wolfe algorithm for solving crisp problems. Finally, a numerical example and a case study of the economic dispatch (ED) problem of a power system are investigated. The obtained results prove that the proposed methodology can serve as a significant tool for decision-makers to handle several types of logistic problems with rough parameters.

Keywords: quadratic programming; rough set theory; RST; rough intervals; slice sum method; SSM.

DOI: 10.1504/IJMOR.2021.119962

International Journal of Mathematics in Operational Research, 2021 Vol.20 No.3, pp.355 - 372

Received: 06 Nov 2019
Accepted: 31 Jul 2020
Published online: 04 Jan 2022 *

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