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

• Main Authors: Ali Al-Hasani, Masar Al-Rabeeah, Santosh Kumar, Andrew Eberhard
• Format: Article
• Language: English
• Published: International Journal of Mathematical, Engineering and Management Sciences 2020-12-01
• Series: International Journal of Mathematical, Engineering and Management Sciences
• Subjects: exact and approximate methods for ranked-optimal solutions; ; k-ranked optimal solutions; multi-objective integer programming model; non-dominated point set; rank-based solution method
• Online Access: https://www.ijmems.in/volumes/volume5/number6/93-IJMEMS-20-32-5-6-1249-1269-2020.pdf

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.