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.