# A LP Relaxation based Matheuristic for Multi-objective Integer Programming

### Duleabom An, Sophie Parragh, Markus Sinnl, Fabien Tricoire

#### Abstract

Motivated by the success of matheuristics in the single-objective domain, we propose a very simple linear programming-based matheuristic for three-objective binary integer programming. To tackle the problem, we obtain lower bound sets by means of the vector linear programming solver Bensolve. Then, simple heuristic approaches, such as rounding and path relinking, are applied to this lower bound set to obtain high-quality approximations of the optimal set of trade-off solutions. The proposed algorithm is compared to a recently suggested algorithm which is, to the best of our knowledge, the only existing matheuristic method for three-objective integer programming. Computational experiments show that our method produces a better approximation of the true Pareto front using significantly less time than the benchmark method on standard benchmark instances for the three-objective knapsack problem.

Download#### Paper Citation

#### in Harvard Style

An D., Parragh S., Sinnl M. and Tricoire F. (2021). **A LP Relaxation based Matheuristic for Multi-objective Integer Programming**.In *Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-485-5, pages 88-98. DOI: 10.5220/0010347000880098

#### in Bibtex Style

@conference{icores21,

author={Duleabom An and Sophie Parragh and Markus Sinnl and Fabien Tricoire},

title={A LP Relaxation based Matheuristic for Multi-objective Integer Programming},

booktitle={Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2021},

pages={88-98},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010347000880098},

isbn={978-989-758-485-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - A LP Relaxation based Matheuristic for Multi-objective Integer Programming

SN - 978-989-758-485-5

AU - An D.

AU - Parragh S.

AU - Sinnl M.

AU - Tricoire F.

PY - 2021

SP - 88

EP - 98

DO - 10.5220/0010347000880098