# Hyperbolic Optimization over the Integer Efficient Set of MOILFP

## TL;DR

This paper introduces a branch and bound method to optimize a linear fractional function over the efficient set of a multi-objective linear fractional integer program, avoiding exhaustive enumeration of solutions.

## Contribution

It presents a novel global optimization approach tailored for discrete efficient sets in multi-objective fractional integer programming.

## Key findings

- Successful tests on instances with up to 120 variables and 6 criteria.
- Efficiently finds optimal solutions without enumerating all efficient solutions.
- Demonstrates applicability to large-scale problems.

## Abstract

The aim of this study is to find the optimum of a linear fractional function over the efficient set of a multi-objective linear fractional integer program without generating all efficient solutions. By its nature, it is a global optimization problem since the efficient set is discrete, hence not convex. For this purpose, a branch and bound based method is described with a double mission to search for an optimal solution for a given linear fractional function which is moreover, efficient for a multi-objective linear fractional integer programming problem. Tests performed on instances randomly generated up to 120 variables, 100 constraints and 6 criteria are successful.