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Authors: Pablo Adasme 1 ; Abdel Lisser 2 and Chen Wang 2

Affiliations: 1 Universidad de Santiago de Chile, Chile ; 2 Universite Paris-Sud XI, France

ISBN: 978-989-8565-40-2

Keyword(s): Distributionally Robust Optimization, Stochastic Programming, Binary Quadratic Bi-level Programming, Mixed Integer Programming.

Related Ontology Subjects/Areas/Topics: Artificial Intelligence ; Knowledge Discovery and Information Retrieval ; Knowledge-Based Systems ; Mathematical Modeling ; Methodologies and Technologies ; Operational Research ; Optimization ; Stochastic Processes ; Symbolic Systems

Abstract: In this paper, we propose a distributionally robust model for a (0-1) stochastic quadratic bi-level programming problem. To this purpose, we first transform the stochastic bi-level problem into an equivalent deterministic formulation. Then, we use this formulation to derive a bi-level distributionally robust model (Liao, 2011). The latter is accomplished while taking into account the set of all possible distributions for the input random parameters. Finally, we transform both, the deterministic and the distributionally robust models into single level optimization problems (Audet et al., 1997). This allows comparing the optimal solutions of the proposed models. Our preliminary numerical results indicate that slight conservative solutions can be obtained when the number of binary variables in the upper level problem is larger than the number of variables in the follower.

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Paper citation in several formats:
Adasme P., Lisser A. and Wang C. (2013). A Distributionally Robust Formulation for Stochastic Quadratic Bi-level Programming.In Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-8565-40-2, pages 24-31. DOI: 10.5220/0004207100240031

@conference{icores13,
author={Pablo Adasme and Abdel Lisser and Chen Wang},
title={A Distributionally Robust Formulation for Stochastic Quadratic Bi-level Programming},
booktitle={Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2013},
pages={24-31},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004207100240031},
isbn={978-989-8565-40-2},
}

TY - CONF

JO - Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - A Distributionally Robust Formulation for Stochastic Quadratic Bi-level Programming
SN - 978-989-8565-40-2
AU - Adasme P.
AU - Lisser A.
AU - Wang C.
PY - 2013
SP - 24
EP - 31
DO - 10.5220/0004207100240031

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