Maximum Concurrent Flow with Incomplete Data

Pierre-Olivier Bauguion (1) , Claudia d'Ambrosio (2) , Leo Liberti (2)

1 IRT SystemX
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

The Maximum Concurrent Flow Problem (MCFP) is often used in the planning of transportation and communication networks. We discuss here the MCFP with incomplete data. We call this new problem the Incomplete Maximum Concurrent Flow Problem (IMCFP). The main objective of IMCFP is to complete the missing information assuming the known and unknown data form a MCFP and one of its optimal solutions. We propose a new solution technique to solve the IMCFP which is based on a linear programming formulation involving both pri-mal and dual variables, which optimally decides values for the missing data so that they are compatible with a set of scenarios of different incomplete data sets. We prove the correctness of our formulation and benchmark it on many different instances.

Mots clés: Maximum concurrent flow; multi-commodity flow problems; incomplete data; unknown data; uncertainty; inverse optimization; transportation systems

Domaines: Recherche opérationnelle [math.OC]

Pierre-Olivier Bauguion, Claudia d'Ambrosio, Leo Liberti. Maximum Concurrent Flow with Incomplete Data. Combinatorial Optimization 5th International Symposium, ISCO 2018, Marrakesh, Morocco, April 11–13, 2018, Revised Selected Papers, pp.77-88, 2018, 978-3-319-96150-7. ⟨10.1007/978-3-319-96151-4_7⟩. ⟨hal-02105082⟩