A ranking algorithm for bi-objective quadratic fractional integer programming problems

Abstract

An algorithm to solve bi-objective quadratic fractional integer programming problems is presented in this paper. The algorithm uses -scalarization technique and a ranking approach of the integer feasible solution to find all nondominated points. In order to avoid solving non-linear integer programming problems during this ranking scheme, the existence of a linear or a linear fractional function is established, which acts as a lower bound on the values of first objective function of the bi-objective problem over the entire feasible set. Numerical examples are also presented in support of the theory.

Keywords:

• Fractional programming
• multiobjective programming
• integer programming

Acknowledgements

Authors would like to thank the anonymous referees for providing many helpful suggestions which improved the paper. He gratefully acknowledges the support provided by the Thapar University to carry out this research.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of first author is supported by Thapar University, Patiala under Seed Money [project number TU/DORSP/57/581].