# Mixed Integer Program Heuristic for Linear Ordering Problem

### Ehsan Iranmanesh, Ramesh Krishnamurti

#### Abstract

The Linear Ordering Problem is a classic optimization problem which can be used to model problems in graph theory, machine scheduling, and voting theory, many of which have practical applications. Relatively recently, there has been some success in using Mixed Integer Program (MIP) heuristic for NP-hard optimization problems. We report our experience with using a MIP heuristic for the problem. Our heuristic generates a starting feasible solution based on the Linear Programming solution to the IP formulation for the Linear Ordering Problem. For each starting solution, a neighborhood is defined, again based on the LP solution to the problem. A MIP solver is then used to obtain the optimal solution among all the solutions in the neighborhood. The MIP heuristic shows promise for large problems of hard instances.

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#### Paper Citation

#### in Harvard Style

Iranmanesh E. and Krishnamurti R. (2016). **Mixed Integer Program Heuristic for Linear Ordering Problem** . In *Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-171-7, pages 152-156. DOI: 10.5220/0005710701520156

#### in Bibtex Style

@conference{icores16,

author={Ehsan Iranmanesh and Ramesh Krishnamurti},

title={Mixed Integer Program Heuristic for Linear Ordering Problem},

booktitle={Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2016},

pages={152-156},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005710701520156},

isbn={978-989-758-171-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Mixed Integer Program Heuristic for Linear Ordering Problem

SN - 978-989-758-171-7

AU - Iranmanesh E.

AU - Krishnamurti R.

PY - 2016

SP - 152

EP - 156

DO - 10.5220/0005710701520156