Loïc CELLIER

Ph.D. in Sciences, numerical and mathematical thematics







RESEARCH




MAIN INTERESTS


  • Optimal control.
    Dynamic systems.
    Pontryagin maximum principle.
    Numerical methods.

  • Applications in air traffic management.
    Decision-support.
    Aircraft conflict avoidance problems.
    Velocity regulation.

  • Operations research.
    Mahtematical modelling.
    Graph theory.
    Oriented matroids.

  • Game theory.
    Zero-sum games.
    Two-players games.
    Combinatorial games.

  • Teaching and exacting popularization of mathematics.
    History, epistemology and philosophy of mathematics.
    Didactics of mathematics; inter-disciplinar projects.
    Scientific mediation and exacting vulgarization.


WORKS AND PROJECTS


(in reverse chronological order)


  • Projects and perspectives

    First, I have appreciated during my career that the decompartmentalization between disciplines (or thematics) is conducive to breakthroughs. Moreover, the problems arising from applications (e.g., industrial and biomedical applications) are usually challenging, in terms of hypothesis, modeling and solution approaches. Mathematical formulations are necessarily related to the development of analytical/numerical solution methods. On the one hand, I want to continue to study the research topics explored so far. First, I want to develop works on the perspectives of my PhD thesis in Toulouse, about optimal control and optimization, dealing with problems arising from air traffic management. On the other hand, according to the image of my M.Sc. degree (specialization), performed in Paris, I have at heart to continue in game theory and optimization, both continuous point of view and discrete point of view. Previously, I had the opportunity to study in particular computational geometry: the topological representation of oriented matroids, and graph theory, in particular directed acyclic graphs as part of the study on combinatorial games. I love to share ideas, and I enjoy doing research in particular for its atmosphere of discussions, challenges to tackle the problems and rewarding collaborations.

  • Participation to scientific projects

    Projet Agence Nationale de la Recherche (ANR) jeunes chercheuses jeunes chercheurs ATOMIC (link), Member of the ATOMIC project for young reseachers - founded by the French national agency (ANR) - member of the team, lead by Prof. Sonia Cafieri. Air traffic optimization via mixed-integer computation (ATOMIC). (January 2013 - September 2016)
    Composition of the research group: Prof. Sonia Cafieri (responsible), CR. CNRS Claudia D'Ambrosio, Dr. Alexandre Gondran, Dr. Riadh Omheni, Prof. Frédéric Messine, Prof. Marcel Mongeau, Dr. HDR Ahmed Touhami and I.
    The main aim of ATOMIC is to develop mathematical programming formulations and efficient solution methods from Mixed-Integer Nonlinear Programming to address large-scale optimization problems arising in Air Traffic Management (ATM). The problems of interest are in particular related to aircraft conflict avoidance.

  • Optimal control applied to air traffic management

    I realized this work under the supervision of Prof. Sonia Cafieri and Prof Frédéric Messine (from October 2011 to September 2015). My research is about optimal control numerical solution approaches applied to aircraft conflict avoidance problems. This kind of problems is subject to a special attention - for many decades - among the (aerial or space) applications specific to the region of Toulouse, France. Within the critical system, represented by the air traffic management, in particular to garantee the separation distances between aircraft, a crucial importance concerns the development of decision-support and automation tools, which need mathematical formulations, models, numerical implementations and validation. The purpose of this doctoral thesis is to study models and solution techniques based on optimal control approaches to address air traffic management problems. Motivated by the growth of air traffic volume, and by the advances in optimal control theory, this research works focus on analysing aircraft conflict avoidance problem. This study allows development of new approaches and algorithms to help air traffic controllers. In the framework of air traffic management, to ensure the minimum safety distances between aircraft, in tactical phases and en-route flight configurations, this thesis focusses on a subliminal velocity regulation strategy to perform the separation, while preserving the aircraft predefined trajectories. A numerical optimal control solution approach as the direct shooting method, wherein involves a total or partial discretization of the problem, transforms the initial problem into a large scale nonlinear programming problem. This kind of methods could generate large-size optimization problems which are numerically difficult to solve. Depending on the number of variables which involved, this approaches could be too expensive in terms of computation time. Moreover, the state-variables constraints of the problem lead to numerical difficulties, e.g., considering the indirect numerical shooting method. Tailored on aircraft conflict avoidance problems, a detection and a determination of a priori conflict zones allow the decomposition of the optimal control problem into sub-problems, easier to solve than the original one. Solving the off-zones sub-problems can be addressed using the Pontryagin maximum principle, which allows in this case directly the solution. A combination of direct numerical shooting method and application of conditions of Pontryagin’s maximum principle is proposed, and numerical experiments validate this approach.

  • Algorithmic geometry: topological representation of oriented matroids

    I realized these this work for my M.Sc. degree thesis, under the supervision of Prof. Michel Pocchiola (from May to September 2010). My master's thesis research is in the fields of geometry and combinatorics; and proposed to tackle the rich objects that are oriented matroids. I made a presentation of the topological representation theorem for oriented matroids (due to the works of Folkman and Lawrence, 1978, and Edmonds and Mandel, 1982). The latter would therefore like to highlight in particular the link between the topological combinatorics and axiomatic. I presented in details why, as stated in the theorem in question, the isomorphism classes of oriented matroids of rank d+1 without loops can be seen as the equivalence classes of the signed pseudosphere essential arrangements of the sphere Sd.

  • Combinatorial optimization and combinatorial games

    I realized this research under the supervision of Dr. Jack Edmonds, John von Neumann Theory Prize 1985 (from January to March 2010). On one hand, I presented some results - about the existence of optimal strategy - on an impartial combinatorial game (the game of Chomp). On the other hand, by considering some impartial combinatorial games in a more general impartial combinatorial game (Chomp with directed acyclic graphs), my approach has identified common results shared by many combinatorial games. To deal with the computational complexity of the proposed combinatorial game, my approach was to determine winning strategy algorithms and decomposition algorithms. So, I developed different lines of research, studying particular cases and involving discrete optimization (especially, graph theory). Many perspectives in this work are also presented.


CONFERENCES


(30+ talks; description below in French; in reverse chronological order)


  • Seminar, Institut de recherche sur l'enseignement des mathématiques (IREM) de Franche-Comté (link), Besançon, France, 2017.

  • Audition, for a temporary academic position: teaching fellow (in French, enseignant ou professeur agrégé PRAG) in mathematics and innovative pedagogies, at the Institut Villebon - Georges Charpak (link), Initiatives d'excellence en formations innovantes (IDEFI) (link), Orsay, France, 2017.

  • Audition, for a permanent academic position: associate professor (in French, maître de conférences MCF), in mathematics, epistemology and numerical culture, at the Université de La Réunion (link), Champs-sur-Marne, France, 2017.

  • Conference, commission inter-IREM, group « popularisation des mathématiques », Halle aux Farines, Université Paris 7 Paris Diderot (UP7) (link), 13th arrondissement, Paris, France, 2017.

  • Workshop « Journées académiques », at the Université de Lille 1, Intitut de recherche sur l'enseignement des mathématiques (IREM) de Lille, (link), Lille - Villeneuve d'Ascq, France, 2017.

  • Workshop « Raconte-moi ta thèse », Fondation des sciences mathématiques de Paris (FSMP) (link), Fête de la science, Institut Henri Poincaré (IHP) (link), 5th arrondissement, Paris, France, 2016.

  • Workshop « Semaine d'Étude Maths-Entreprises (SEME) » ; initiative du groupe de recherche (GdR) CNRS Mathématiques et Entreprises et de l'agence pour les mathématiques en interaction avec l'entreprise et la société (AMIES) (link), École centrale de Marseille, Technopôle de Château-Gombert (link), Marseille, France, 2016.

  • Audition, for a temporary academic position: assistant professor (in French, enseignant-chercheur temporaire ou maître assistant associé MAA), in operations research and industry production, at the École des Mines de Nantes (link), France, 2016.

  • Audition, for a permanent academic position: associate professor (in French, enseignant-chercheur ou maître associé MA) en mathématiques appliquées, at the École Centrale de Paris (link), Salle des Conseils, Grande Voie des Vignes, Châtenay-Malabry, France, 2016.

  • Emerging Trends in Applied Mathematics and Mechanics (ETAMM) (link), Université de Perpignan Via Domitia (UPVD) (link), Perpignan, France, 2016.

  • Audition, for a permanent academic position: researcher (in French, chargé de recherche CR2), in operations research, planification and railway capacity management, at the Institut français des sciences et technologies des transports, de l'aménagement et des réseaux (IFSTTAR) (link), Saint-Ouen, France, 2016.

  • Workshop « Journées annuelles », Société de mathématiques appliquées et industrielles, Mathématiques de l'optimisation et de la décision (SMAI MODE) (link), École nationale supérieure d'électrotechnique, d'électronique, d'informatique, d'hydraulique et des télécommunications (ÉNSÉÉIHT) (link), Toulouse, France, 2016.

  • Seminar « LIRMM équipe DALI » (link), Université de Perpignan Via Domitia (UPVD) (link), Perpignan, France, 2016.

  • Workshop, Groupe de recherche (GdR) 3273 Mathématiques de l'optimisation et applications (MOA) « Journées annuelles » (link), Université Bourgogne Franche-Comté (UBFC) (link), Dijon, France, 2015.

  • Ph.D. thesis defense, « Soutenance de thèse de doctorat », École nationale de l'aviation civile (ÉNAC) (link), Toulouse, France, 2015.

  • Doctoral seminar, « Séminaire des doctorants ÉNAC », École nationale de l'aviation civile (ÉNAC) (link), Toulouse, France, 2015.

  • Workshop 3D'14 DALI Doctoral Days, DALI-LIRMM équipe-projet DALI (link), laboratoire Arago, Université Paris 6 Pierre et Marie Curie (UPMC) (link), Banyuls-sur-Mer, France, 2014.

  • Workshop « International Friday », Institut universitaire de technologie, filière gestion, logistique et transport (IUT GLT), Université de Perpignan Via Domitia (UPVD) (link), Perpignan, France, 2014.

  • Doctoral seminar, « Séminaire de doctorants DocToMe », Université Toulouse 3 Paul Sabatier (UT3) (link), Toulouse, France, 2014.

  • ROADEF 2014, Congrès français de Recherche Opérationnelle et d'Aide à la Décision (link), Institut de mathématiques de Bordeaux (IMB) (link), Université de Bordeaux, Bordeaux, France, 2014.

  • ICCOPT 2013, International Conference on Continuous Optimization (link), Universidade de Coimbra (link), Lisbonne, Portugal, 2013.

  • Recent Advances on Optimization, (link) (poster presentation), Centre européen de recherche et de formation avancée en calcul scientifique (CERFACS) (link), Toulouse, France, 2013.

  • ISIATM 2013, 2nd International Conference on Interdisciplinary Science for Innovative Air Traffic Management (link), École nationale de l'aviation civile (ÉNAC) (link), Toulouse, France, 2013.

  • Doctoral seminar, « Soutenance de mi-parcours », École doctorale mathématiques, informatique et télécommunications de Toulouse (ÉDMITT) (link), Toulouse, France, 2013.

  • ATACCS 2013, (poster presentation), 3rd International Conference on Application and Theory of Automation in Command and Control Systems (link), Università degli Studi di Napoli 'Federico II' (UNINA) (link), Naples, Italie, 2013.

  • ROADEF 2013, Congrès français de Recherche Opérationnelle et d'Aide à la Décision (link), Université de technologie de Troyes (UTT) (link), Troyes, France, 2013.

  • ADVCOMP 2012, 6th International Conference on Advanced Engineering Computing and Applications in Sciences (link), Barcelone, Espagne, 2012.

  • Doctoral seminar, « Journée des doctorants ÉNSÉÉIHT », École nationale supérieure d'électrotechnique, d'électronique, d'informatique et des télécommunications (ÉNSÉÉIHT) (link), Toulouse, France, 2012.

  • Seminar, « Séminaire du laboratoire MAIAA », Mathématiques Appliquées, Informatique et Automatique pour l'Aérien, École nationale de l'aviation civile (ÉNAC) (link), Toulouse, France, 2012.

  • ROADEF 2012, Congrès français de Recherche Opérationnelle et d'Aide à la Décision (link), Université d'Angers (link), Angers, France, 2012.


PUBLICATIONS



Summary of contributions for publications. Books (university teaching level, or popularization thematics), chapters of books (collaborative/collective books), peer-reviewed international journals, peer-reviewed international conference proceedings, peer-reviewed national conference proceedings, thesis and technical reports ; in terms of the number of publications (* preprints available upon request). Number of coauthors.


 Books  Chap. books  Int. J. Articles  Int. C. Proc.  Nat. C. Proc.  Thesis  Reports  Coauthors 
2* 4* 



Peer-reviewed books


  • Loïc Cellier, - work in progress -, book of university teaching level, lectures and exercises (main topic: decision-support; operations research and quantitative techniques; --- pages, in French) (pdf)
  • Loïc Cellier, - work in progress -, book of a strategy game, problems and tactical templates (main topic: the game of Hex; --- pages, in French) (pdf)

Peer-reviewed collaborative/collective books or chapters of books


  • Loïc Cellier, Chloé Milsonneau and Mickaël Launay, chapters of book, number 73 « Les Mathématiques », Collection Sciences, Encyclopédie Tout l'Univers, Éditions Hachette, Paris, France, 2017. (accepted for publication; chapters of book; 18 feuillets et relecture) (pdf)

Peer-reviewed international journals


  • Sonia Cafieri, Loïc Cellier, Frédéric Messine and Riadh Omheni, Combination of optimal control approaches for aircraft conflict avoidance via velocity regulation (accepted for publication, 2017), Optimal Control Applications and Methods, Wiley InterScience, Editions John Wiley & Sons, 2017. (26 pages) (pdf)

Peer-reviewed international conference proceedings


  • Loïc Cellier, Sonia Cafieri and Frédéric Messine. Optimal control approaches for aircraft conflict avoidance using speed regulation: a numerical study, in Proceedings of ISIATM 2013, Interdisciplinary Science for Innovative Air Traffic Management, Toulouse, France, 2013. (9 pages) (pdf)

  • Loïc Cellier, Sonia Cafieri and Frédéric Messine. A decomposition-based optimal control approach for aircraft conflict avoidance performed by velocity regulation, in Proceedings of ATACCS 2013, Application and Theory of Automation in Command and Control Systems, pp.129-131, Naples, Italy, 2013. (3 pages) (pdf)

  • Loïc Cellier, Sonia Cafieri and Frédéric Messine. Hybridizing direct and indirect optimal control approaches for aircraft conflict avoidance, in Proceedings of ADVCOMP 2012, Advanced Engineering Computing and Applications in Sciences, pp.42-45, Barcelona, Spain, 2012. (4 pages) (pdf)

Peer-reviewed national conference proceedings


  • Loïc Cellier, Sonia Cafieri and Frédéric Messine. Régulation en vitesse pour un problème d'évitement de conflit aérien : combinaison des résolutions directe et indirecte de contrôle optimal, in Proceedings of ROADEF 2014, Congrès français de Recherche Opérationnelle et d'Aide a la Décision, Bordeaux, France, 2014. (2 pages) (pdf)

  • Loïc Cellier, Sonia Cafieri and Frédéric Messine. Combinaison de méthodes de contrôle optimal pour l'évitement de collision dans le trafic aérien, in Proceedings of ROADEF 2013, Congrès français de Recherche Opérationnelle et d'Aide a la Décision, Troyes, France, 2013. (2 pages) (pdf)

  • Loïc Cellier, Sonia Cafieri and Frédéric Messine. Résolution de conflit aérien par contrôle optimal basée sur la régulation en vitesse, in Proceedings of ROADEF 2012, Congrès français de Recherche Opérationnelle et d'Aide la Décision, Angers, France, 2012. (2 pages) (pdf)

Thesis


  • Loïc Cellier, Velocity-based aircraft conflict avoidance through optimal control model and solution approaches (French title: Évitement de conflits aériens par une régulation subliminale en vitesse : modélisation et résolution via le contrôle optimal), Ph.D. thesis, Toulouse, France, 2015. (161 pages) (pdf)

  • Loïc Cellier, Théorème de représentation topologique pour les matroïdes orientés, Master Recherche thesis, Paris, France, 2010. (84 pages) (pdf)

Technical reports


  • Loïc Cellier, Jésua Chavez, Guillaume Garrigos and Souhil Tairi, Détection de motifs dans le plan temps-fréquence, rapport de Semaine d'Études Maths Entreprise (SEME), AMIES, Marseille, France, 2016. (work in progress, -- pages) (pdf)

  • Loïc Cellier, Pour la diffusion des mathématiques ; concernant la popularisation et la vulgarisation exigeante des mathématiques : recueil de liens sur les associations mathématiques, instituts et événements ; rapport bénévole CIJM, Paris, France, 2015 (15 pages) (pdf)

  • Loïc Cellier, Invitation to the game of Chomp with Directed Acyclic Graphs, rapport de Master Recherche, Paris, France, 2010. (21 pages) (pdf)

  • Benjamin Blum and Loïc Cellier, Business strategy: Horizontal Mergers (les fusions horizontales), rapport de Master Recherche, Paris, France, 2010. (25 pages) (pdf)