# Reference-Point-Based Branch and Bound Algorithm for Multiobjective Optimization

## TL;DR

This paper introduces a reference-point-based branch and bound algorithm for multiobjective optimization that efficiently guides the search towards preferred Pareto front regions using a new discarding test and provides convergence guarantees.

## Contribution

It proposes a novel branch and bound method incorporating reference points and a discarding test to focus on preferred solutions in multiobjective optimization.

## Key findings

- Algorithm effectively guides search towards preferred Pareto regions.
- Proven to obtain ε-efficient solutions within the region of interest.
- Provides bounds on the number of iterations needed for desired precision.

## Abstract

In this paper, a branch and bound algorithm that incorporates the decision maker's preference information is proposed for multiobjective optimization. In the proposed algorithm, a new discarding test is designed to check whether a box contains preferred solutions according to the preference information expressed by means of reference points. In this way, the proposed algorithm is able to gradually guide the search towards the region of interest on the Pareto fronts during the solution process. We prove that the proposed algorithm obtains $\varepsilon$-efficient solutions distributed in the region of interest. Moreover, lower bound on the total finite number of required iterations for predefined precision is also provided. Finally, the algorithm is illustrated with a number of test problems.