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Authors: Pablo Adasme 1 ; Rafael Andrade 2 ; Janny Leung 3 and Abdel Lisser 4

Affiliations: 1 Universidad de Santiago de Chile, Chile ; 2 Universidade Federal do Ceará, Brazil ; 3 Chinese University of Hong Kong, Hong Kong ; 4 Université de Paris-Sud 11, France

Keyword(s): Bilevel Programming, Traveling Salesman Problem, Mixed Integer Linear Programming Formulations, Iterative Sub-tour Elimination Constraint Procedure.

Related Ontology Subjects/Areas/Topics: Agents ; Applications ; Artificial Intelligence ; Bioinformatics ; Biomedical Engineering ; Enterprise Information Systems ; Information Systems Analysis and Specification ; Knowledge Discovery and Information Retrieval ; Knowledge-Based Systems ; Linear Programming ; Methodologies and Technologies ; Network Optimization ; Operational Research ; Optimization ; OR in Telecommunications ; Pattern Recognition ; Resource Allocation ; Routing ; Simulation ; Software Engineering ; Symbolic Systems

Abstract: In this paper, we consider a linear bilevel programming problem where both the leader and the follower maximize their profits subject to budget constraints. Additionally, we impose a Hamiltonian cycle topology constraint in the leader problem. In particular, models of this type can be motivated by telecommunication companies when dealing with traffic network flows from one server to another one within a ring topology framework. We transform the bilevel programming problem into an equivalent single level optimization problem that we further linearize in order to derive mixed integer linear programming (MILP) formulations. This is achieved by replacing the follower problem with the equivalent Karush Kuhn Tucker conditions and with a linearization approach to deal with the complementarity constraints. The topology constraint is handled by the means of two compact formulations and an exponential one from the classic traveling salesman problem. Thus, we compute optimal solutions and upper bounds with linear programs. One of the compact models allows to solve instances with up to 250 nodes to optimality. Finally, we propose an iterative procedure that allows to compute optimal solutions in remarkably less computational effort when compared to the compact models. (More)


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Paper citation in several formats:
Adasme, P.; Andrade, R.; Leung, J. and Lisser, A. (2017). On a Traveling Salesman based Bilevel Programming Problem. In Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - ICORES, ISBN 978-989-758-218-9; ISSN 2184-4372, pages 329-336. DOI: 10.5220/0006190503290336

author={Pablo Adasme. and Rafael Andrade. and Janny Leung. and Abdel Lisser.},
title={On a Traveling Salesman based Bilevel Programming Problem},
booktitle={Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - ICORES,},


JO - Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - ICORES,
TI - On a Traveling Salesman based Bilevel Programming Problem
SN - 978-989-758-218-9
IS - 2184-4372
AU - Adasme, P.
AU - Andrade, R.
AU - Leung, J.
AU - Lisser, A.
PY - 2017
SP - 329
EP - 336
DO - 10.5220/0006190503290336