A branch and cut algorithm to optimize a weighted sum-of-ratios in multiobjective mixed-integer fractional programming

Abstract

AbstractMultiobjective linear fractional programming is useful to model multiobjective problems where all or some of the objective functions are a ratio or proportion of one linear/affine function to another linear/affine function. In practice, many of such problems include integer variables. If the weighted-sum scalarization is used to compute efficient solutions to the multiobjective problem, then the scalar problem to be solved for each weight vector turns out to be a weighted sum-of-ratios. There are several algorithms reported in the literature to optimize weighted sum-of-ratios, but almost all of them cannot deal with integer variables. In this paper we propose a Branch & Cut algorithm to optimize weighted-sums of the objective functions in multiobjective mixed integer fractional programming (MOMIFP). Several theoretical properties that support the algorithm are presented and proved. Computational experiments with randomly generated general problems are presented and discussed, which show that the algorithm is able to deal with practical MOMIFP problems.