PhD student (M/F) - Tackling Mixed Integer Non-Linear Programs with innovative approximating formulations

Job Description

Thesis Subject

Objectives: Classical methods for solving MINLPs are often about solving continuous or linear/convex relaxations. These are based on the fact that their feasible region is larger than the original one, so that the objective function underestimates the original one (in case of minimization problems). The PhD topic consists in proposing alternative methods based on approximations, i.e., reformulations of the problem that, in general, do not preserve the mentioned property. We aim at proposing new approximating formulations for classes of MINLPs, which, under some conditions, show some other interesting properties, for example: classical piecewise linear approximations (or relaxations) or random projections of mathematical optimisation problems. In particular, we shall consider the still relatively unexplored splines-based approximations (used in statistics), inexact convex hulls, and univariate approximations in higher dimensions. The challenge will be to find a good compromise between approximation quality and effectiveness of the solution methods, combining classical and unconventional approximations/relaxations. The new methods will be applied to real-world applications such as, e.g., the Alternating Current Optimal Power Flow (ACOPF), the Optimal Transmission Switching Problem (OTS), and the Hydro Unit Commitment Problem (HUC).

Expected Results: Studying new approximations for mixed integer non-linear programming problems; devising methods to solve such approximations; proving some properties of the approximations. For example, an upper bound on the error provided by the approximation or that, for same classes of mixed integer non-linear programs, some of the approximations are relaxations. Applying the new methods to solve notable real-world applications.

Planned secondment: 3 months at CNR (C. Gentile) during the 2nd year to learn about formulation strengthening; 3 months at EDF (W. van Ackooij) during the 3rd year to learn about Unit Commitment and apply the developed techniques to it.

Your Work Environment

The LIX (Computer Science Laboratory of l'X) is a joint research unit (UMR 7161) affiliated with CNRS and École Polytechnique. Its research activities span a broad spectrum of theoretical and applied computer science, with a strong emphasis on interdisciplinarity. Key cutting-edge research areas include: algorithms and complexity; mathematical optimization; artificial intelligence and machine learning; bioinformatics; systems and networks. The LIX maintains extensive industrial collaborations, partnering with leading companies in technology, finance, and energy sectors.

Compensation and benefits

Compensation

2300 € gross monthly

Annual leave and RTT

44 jours

Remote Working practice and compensation

Pratique et indemnisation du TT

Transport

Prise en charge à 75% du coût et forfait mobilité durable jusqu’à 300€

About the offer

About the CNRS

The CNRS is a major player in fundamental research on a global scale. The CNRS is the only French organization active in all scientific fields. Its unique position as a multi-specialist allows it to bring together different disciplines to address the most important challenges of the contemporary world, in connection with the actors of change.

CNRS

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