A novel algorithm for generating Pareto frontier of bi-level multi-objective rough nonlinear programming problem

This paper discusses a new algorithm for generating the Pareto frontier for bi-level multi-objective rough nonlinear programming problem (BL-MRNPP). In this algorithm, the uncertainty exists in constraints which are modeled as a rough set. Initially, BL-MRNPP is transformed into four deterministic m...

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Bibliographic Details
Published inAin Shams Engineering Journal Vol. 12; no. 2; pp. 2125 - 2133
Main Authors Elsisy, M.A., El Sayed, M.A., Abo-Elnaga, Y.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2021
Elsevier
Subjects
Bi-level programming
KKT optimality
Multi-objective programming
Rough set
Multi-objective programming
Bi-level programming
KKT optimality
Rough set
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Summary:This paper discusses a new algorithm for generating the Pareto frontier for bi-level multi-objective rough nonlinear programming problem (BL-MRNPP). In this algorithm, the uncertainty exists in constraints which are modeled as a rough set. Initially, BL-MRNPP is transformed into four deterministic models. The weighted method and the Karush-Kuhn-Tucker optimality condition are combined to obtain the Pareto front of each model. The nature of the problem solutions is characterized according to newly proposed definitions. The location of efficient solutions depending on the lower/upper approximation set is discussed. The aim of the proposed solution procedure for the BL-MRNPP is to avoid solving four problems. A numerical example is solved to indicate the applicability of the proposed algorithm.
ISSN:2090-4479
DOI:10.1016/j.asej.2020.11.006