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A novel algorithm for generating Pareto frontier of bi-level multi-objective rough nonlinear programming problem
Ain Shams Engineering Journal • 2021
Publication Information
Authors
M.A. Elsisy, M.A. El Sayed, & Y. Abo-Elnaga
Keywords
Multi-objective programming
Bi-level programming
Rough set
KKT optimality
Journal
Ain Shams Engineering Journal
Publisher
Elsevier
Volume
in press
Issue
Not Available
Pages
Not Available
publication.type
International
Paper Link
Open Link
Supplementary Materials
Not Available
Abstract
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.
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.