# Primal Heuristic for the Linear Ordering Problem

### Ravi Agrawal, Ehsan Iranmanesh, Ramesh Krishnamurti

#### Abstract

In this paper, we propose a new primal heuristic for the Linear Ordering Problem (LOP) that generates an integer feasible solution from the solution to the LP relaxation at each node of the branch-and-bound search tree. The heuristic first finds a partition of the set of vertices S into an ordered pair of subsets {S1,S2} such that the difference between the weights of all arcs from S1 to S2 and the weights of all arcs from S2 to S1 is maximized. It then assumes that all vertices in S1 precede all vertices in S2 thus decomposing the original problem instance into subproblems of smaller size i.e. on subsets S1 and S2. It recursively does so until the subproblems can be solved quickly using an MIP solver. The solution to the original problem instance is then constructed by concatenating the solutions to the subproblems. The heuristic is used to propose integer feasible solutions for the branch-and-bound algorithm. We also devise an alternate node selection strategy based on the heuristic solutions where we select the node with the best heuristic solution. We report the results of our experiments with the heuristic and the node selection strategy based on the heuristic.

Download#### Paper Citation

#### in Harvard Style

Agrawal R., Iranmanesh E. and Krishnamurti R. (2019). **Primal Heuristic for the Linear Ordering Problem**.In *Proceedings of the 8th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-352-0, pages 151-156. DOI: 10.5220/0007406301510156

#### in Bibtex Style

@conference{icores19,

author={Ravi Agrawal and Ehsan Iranmanesh and Ramesh Krishnamurti},

title={Primal Heuristic for the Linear Ordering Problem},

booktitle={Proceedings of the 8th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2019},

pages={151-156},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007406301510156},

isbn={978-989-758-352-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 8th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Primal Heuristic for the Linear Ordering Problem

SN - 978-989-758-352-0

AU - Agrawal R.

AU - Iranmanesh E.

AU - Krishnamurti R.

PY - 2019

SP - 151

EP - 156

DO - 10.5220/0007406301510156