Ali Al-Hasani
School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia. Department of Mathematics, College of Sciences, University of Basrah, Al- Basrah, Iraq.

Masar Al-Rabeeah
School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia. Department of Mathematics, College of Sciences, University of Basrah, Al- Basrah, Iraq.

Santosh Kumar
School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia. Department of Mathematics and Statistics, University of Melbourne, Melbourne, Australia.

Andrew Eberhard
School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia.

DOI https://doi.org/10.33889/IJMEMS.2020.5.6.093

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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.

Keywords- 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.

Citation

Al-Hasani, A., Al-Rabeeah, M., Kumar, S., & Eberhard, A. (2020). Rank-Based Solution Methods and their Applications in Determination of Non-Dominated Points Set For A Multi-Objective Integer Programming Model. International Journal of Mathematical, Engineering and Management Sciences, 5(6), 1249-1269. https://doi.org/10.33889/IJMEMS.2020.5.6.093.