A smoothing heuristic for a bilevel pricing problem |
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| Institution: | 1. Département de Mathématiques et d’Informatique, Université de Sherbrooke, Sherbrooke, Qué., Canada;2. Département d’Informatique et de Recherche Opérationnelle, Université de Montréal, Montréal, Qué., Canada;3. Department of Statistics, University of California, Berkeley, CA, USA;4. Département de Mathématiques et de Génie Industriel, École Polytechnique de Montréal, C.P. 6079, Succ. Centre-ville, Montréal, Qué., Canada;1. DS&OR Lab, University of Paderborn, Warburger Str. 100, 33098 Paderborn, Germany;2. Department of Informatics, Kecskemét College, 10 Izsáki út, 6000 Kecskemét, Hungary;3. Goethe University Frankfurt, Grüneburgplatz 1, 60323 Frankfurt am Main, Germany;1. Institute of Mechanics, Helmut Schmidt University/University of the Federal Armed Forces Hamburg, Holstenhofweg 85, 22043 Hamburg, Germany;2. Rolls-Royce Deutschland Ltd & Co KG, Eschenweg 11, Dahlewitz, 15827 Blankenfelde-Mahlow, Germany;1. State Key Lab of Synthetical Automation of Process Industry, Dept. of System Engineering, Northeastern University (NEU), Shenyang, PR China;2. College of Management Science and Engineering, Dongbei University of Finance and Economics (DUFE), Dalian, PR China;3. Smart Mobility & Intelligent Transportation, IBM China Research Lab, Beijing, PR China;1. Engineering Faculty, Federal University of Juiz de Fora (UFJF), Juiz de Fora, MG, Brazil;2. Department of Electrical Engineering, Pontifical Catholic University of Rio de Janeiro – (PUC-Rio), Rio de Janeiro, RJ, Brazil;3. Department of Industrial Engineering, Pontifical Catholic University of Rio de Janeiro – (PUC-Rio), Rio de Janeiro, RJ, Brazil |
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| Abstract: | In this paper, we provide a heuristic procedure, that performs well from a global optimality point of view, for an important and difficult class of bilevel programs. The algorithm relies on an interior point approach that can be interpreted as a combination of smoothing and implicit programming techniques. Although the algorithm cannot guarantee global optimality, very good solutions can be obtained through the use of a suitable set of parameters. The algorithm has been tested on large-scale instances of a network pricing problem, an application that fits our modeling framework. Preliminary results show that on hard instances, our approach constitutes an alternative to solvers based on mixed 0–1 programming formulations. |
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