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Authors: Pablo Adasme 1 ; Janny Leung 2 and Ismael Soto 1

Affiliations: 1 Universidad de Santiago de Chile, Chile ; 2 The Chinese University of Hong Kong (Shenzhen), China

ISBN: 978-989-758-218-9

Keyword(s): Two-stage Stochastic Programming, Traveling Salesman Problem, Progressive Hedging Algorithm, Sample Average Approximation Method.

Related Ontology Subjects/Areas/Topics: Agents ; Artificial Intelligence ; Bioinformatics ; Biomedical Engineering ; Enterprise Information Systems ; Information Systems Analysis and Specification ; Knowledge Discovery and Information Retrieval ; Knowledge-Based Systems ; Methodologies and Technologies ; Operational Research ; Optimization ; Simulation ; Stochastic Optimization ; Symbolic Systems

Abstract: In this paper, we propose an adapted version of the progressive hedging algorithm (PHA) (Rockafellar and Wets, 1991; Lokketangen and Woodruff, 1996; Watson and Woodruff, 2011) for the two-stage stochastic traveling salesman problem (STSP) introduced in (Adasme et al., 2016). Thus, we compute feasible solutions for small, medium and large size instances of the problem. Additionally, we compare the PHA method with the sample average approximation (SAA) method for all the randomly generated instances and compute statistical lower and upper bounds. For this purpose, we use the compact polynomial formulation extended from (Miller et al., 1960) in (Adasme et al., 2016) as it is the one that allows us to solve large size instances of the problem in short CPU time with CPLEX. Our preliminary numerical results show that the results obtained with the PHA algorithm are tight when compared to the optimal solutions of small and medium size instances. Moreover, we obtain significantly better feasib le solutions than CPLEX for large size instances with up to 100 nodes and 10 scenarios in significantly low CPU time. Finally, the bounds obtained with SAA method provide an average reference interval for the stochastic problem. (More)

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Paper citation in several formats:
Adasme, P.; Adasme, P.; Leung, J.; Leung, J. and Soto, I. (2017). Progressive Hedging and Sample Average Approximation for the Two-stage Stochastic Traveling Salesman Problem.In Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-218-9, pages 440-446. DOI: 10.5220/0006241304400446

@conference{icores17,
author={Pablo Adasme. and Pablo Adasme. and Janny Leung. and Janny Leung. and Ismael Soto.},
title={Progressive Hedging and Sample Average Approximation for the Two-stage Stochastic Traveling Salesman Problem},
booktitle={Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2017},
pages={440-446},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006241304400446},
isbn={978-989-758-218-9},
}

TY - CONF

JO - Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - Progressive Hedging and Sample Average Approximation for the Two-stage Stochastic Traveling Salesman Problem
SN - 978-989-758-218-9
AU - Adasme, P.
AU - Adasme, P.
AU - Leung, J.
AU - Leung, J.
AU - Soto, I.
PY - 2017
SP - 440
EP - 446
DO - 10.5220/0006241304400446

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