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. |
