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 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. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Ain Shams University.

Automated summary

This paper introduces a new algorithm for generating the Pareto frontier for a bi-level multi-objective rough nonlinear programming problem by transforming it into four deterministic models and using a combination of the weighted method and KKT optimality condition to obtain the Pareto front of each model. The proposed solution aims to avoid solving four problems and is demonstrated through a numerical example.