# A Two-stage Stochastic Programming Approach for the Traveling Salesman Problem

### Pablo Adasme, Rafael Andrade, Janny Leung, Abdel Lisser

#### Abstract

In the context of combinatorial optimization, recently some efforts have been made by extending classical optimization problems under the two-stage stochastic programming framework. In this paper, we introduce the two-stage stochastic traveling salesman problem (STSP). Let G = (V,ED ∪ES) be a non directed complete graph with set of nodes V and set of weighted edges ED ∪ES where ED ∩ES = 0/. The edges in ED and ES have deterministic and uncertain weights, respectively. Let K = {1,2,··· ,|K|} be a given set of scenarios referred to the uncertain weights of the edges in ES. The STSP consists in determining Hamiltonian cycles of G, one for each scenario s ∈ K, sharing the same deterministic edges while minimizing the sum of the deterministic weights plus the expected weight over all scenarios associated with the uncertain edges. We propose two compact models and a formulation with an exponential number of constraints which are adapted from the classic TSP. One of the compact models allows to solve instances with up to 40 nodes and 5 scenarios to optimality. Finally, we propose an iterative procedure that allows to compute optimal solutions and tight lower bounds within very small CPU time.

#### References

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#### Paper Citation

#### in Harvard Style

Adasme P., Andrade R., Leung J. and Lisser A. (2016). **A Two-stage Stochastic Programming Approach for the Traveling Salesman Problem** . In *Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-171-7, pages 163-169. DOI: 10.5220/0005738801630169

#### in Bibtex Style

@conference{icores16,

author={Pablo Adasme and Rafael Andrade and Janny Leung and Abdel Lisser},

title={A Two-stage Stochastic Programming Approach for the Traveling Salesman Problem},

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

year={2016},

pages={163-169},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005738801630169},

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 - A Two-stage Stochastic Programming Approach for the Traveling Salesman Problem

SN - 978-989-758-171-7

AU - Adasme P.

AU - Andrade R.

AU - Leung J.

AU - Lisser A.

PY - 2016

SP - 163

EP - 169

DO - 10.5220/0005738801630169