# Prize Collecting Travelling Salesman Problem - Fast Heuristic Separations

### Kamyar Khodamoradi, Ramesh Krishnamurti

#### Abstract

The Prize Collecting Travelling Salesman Problem (PCTSP) is an important generalization of the famous Travelling Salesman Problem. It also arises as a sub problem in many variants of the Vehicle Routing Problem. In this paper, we provide efficient methods to solve the linear programming relaxation of the PCTSP. We provide efficient heuristics to obtain the Generalized Subtour Elimination Constraints (GSECs) for the PCTSP, and compare its performance with an optimal separation procedure. Furthermore, we show that a heuristic to separate the primitive comb inequalities for the TSP can be applied to separate the primitive comb inequalities introduced for the PCTSP. We evaluate the effectiveness of these inequalities in reducing the integrality gap for the PCTSP.

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#### Paper Citation

#### in Harvard Style

Khodamoradi K. and Krishnamurti R. (2016). **Prize Collecting Travelling Salesman Problem - Fast Heuristic Separations** . In *Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-171-7, pages 380-387. DOI: 10.5220/0005758103800387

#### in Bibtex Style

@conference{icores16,

author={Kamyar Khodamoradi and Ramesh Krishnamurti},

title={Prize Collecting Travelling Salesman Problem - Fast Heuristic Separations},

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

year={2016},

pages={380-387},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005758103800387},

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 - Prize Collecting Travelling Salesman Problem - Fast Heuristic Separations

SN - 978-989-758-171-7

AU - Khodamoradi K.

AU - Krishnamurti R.

PY - 2016

SP - 380

EP - 387

DO - 10.5220/0005758103800387