[Job-offers-cs] Post Doc Position INRIA Lille , INOCS team

[Pekka Orponen]

-------- Forwarded Message --------
Subject: [DMANET] Post Doc Position INRIA Lille , INOCS team
Date: Thu, 14 Mar 2019 17:11:38 +0100
From: Luce Brotcorne <luce.brotcorne at inria.fr>
To: dmanet <DMANET at zpr.uni-koeln.de>


Solving Integer Bilevel Bilinear problems

Supervisors: Luce Brotcorne ( Luce.brotcorne at inria.fr ) , Bernard Fortz 
( bfortz at ulb.ac.be ) , Martine Labbé ( mlabbe at ulb.ac.be )

Location INRIA team INOCS, Lille Nord Europe
Duration : 18 months starting in october.

Application documents should contain a motivation letter, a curriculum 
vitae and a list of publications.


Bilevel programs allow the modeling of situations in which a 
decision-maker, hereafter the leader, optimizes his/her objective by 
taking explicitly into account the response of another decision maker or 
a set of decision makers (the follower) to his/her decisions. Bilevel 
programs are closely related to Stackelberg (leader-follower) games as 
well as to the principal-agent paradigm in economics. In other words, 
bilevel programs can be considered as demand-offer equilibrium models 
where the demand is the result of another mathematical problem. The 
structure of bilevel problems allows the modeling of a large number of 
real-life problems involving two decision makers interacting 
sequentially hierarchically (2) and (3).

Bilevel programming problems, being generically difficult due to their 
non-convexity and non-differentiability, it is not surprising that most 
research to date has focused on the simplest cases of bilevel programs, 
that is problems having nice properties such as linear, quadratic or 
convex objective and/or constraint functions.

When the second level problem is NP-hard, the single-level reformulation 
of the bilevel program based on the KKT conditions cannot be applied 
because no complete linear description of the convex envelope of the 
solution set is available. Up to now most of the research devoted to 
integer bilevel programs has been devoted to the case where the 
objective functions of both levels are linear (4) and (5).

The goal of the post-doc is to study the properties of mixed integer 
bilevel bilinear programs on two levels and develop efficient solution 
methods. This field of research is and very innovative and promising 
because of many problems of everyday life fall within this framework 
(e.g. pricing problems) (1). The particular cases of energy pricing 
problems or joint pricing and location problems could be considered.


Required Skills

Candidates should hold a PhD Thesis in Operations research, mathematics, 
computer science, or similar fields and should ideally have a solid 
background in discrete optimization, integer programming, decomposition 
techniques. Computer science skills in algorithmic and C/C++ development 
are also welcome.

Knowledge of French is not required, but good communication skills and a 
solid knowledge of English are essential.


Research environment

The INOCS team aims to develop new models, algorithmic techniques and 
implementations for optimization problems with complex structure (CS). 
More precisely, we consider that an optimization problem presents a CS 
when for example it involves some hierarchical leader-follower structure 
(bilevel optimization). Luce Brotcorne is specialist in bilevel 
optimization with a particular expertise to solve Stackelberg games, 
while Bernard Fortz has also a strong experience in decomposition 
methods that will be at the core of algorithms developed in the project.


References
(1) S. Afsar, L. Brotcorne, P. Marcotte and G. Savard, Algorithms for 
Load Balancing in Energy Systems with Smart Grids, soumis à Computers 
and Operations Research, 2019.
(2) L. Brotcorne, P. Marcotte, and G. Savard. Bilevel programming: The 
Montreal school. INFOR: Information Systems and Operational Research , 
56(4):231–246, 2008.
(3) B. Colson, P. Marcotte, and G. Savard. An overview of bilevel 
optimization. Annals of operations research , 153(1):235–256, 2007.

(4) S. DeNegre and T. K. Ralphs, “A Branch-and-Cut Algorithm for Bilevel 
Integer Programming,” in Proceedings of the Eleventh INFORMS Computing 
Society Meeting , 2009, pp. 65-78.

(5) I. Ljubic, M. Fischetti, M. Monaci and M. Sinnl, "On the use of 
intersection cuts for bilevel optimization", Mathematical Programming 
Series A & B , 2018, Vol. 172, Numéro 1-2, p. 77-103