Rank-Based Solution Methods and their Applications in Determination of Non-Dominated Points Set For A Multi-Objective Integer Programming Model

Abstract

For any single-objective mathematical programming model, rank-based optimal solutions are computationally difficult to find compared to an optimal solution to the same single-objective mathematical programming model. In this paper, several methods have been presented to find these rank-based optimal solutions and based on them a new rank-based solution method (RBSM) is outlined to identify non-dominated points set of a multi-objective integer programming model. Each method is illustrated by a numerical example, and for each approach, we have discussed its limitations, advantages and computational complexity.

An Insight into the Characteristic Equation for an Integer Program

“…These ordered optimal solutions play a useful role to find non-dominated point set for a bi-objective and multi-objective linear integer program. Using the CE approach, Al-Rabeeah et al ( 2019) obtained a non-dominated point set for a bi-objective linear integer problem, and Al-Hasani et al (2020) developed a rank-based solution method for finding a non-dominated point set of a given multiobjective integer program. Nyamugure et al (2017) applied the CE concept for a mixed integer program and Kumar et al (2009) solved a binary integer program using the CE approach.…”