Loïc CELLIER

Ph.D. in sciences, applied mathematics and computer science







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.
    Mathematical modelling.
    Graph theory. Directed acyclic graphs (DAG).
    Discrete and computational geometry. Oriented matroids.

  • Game theory.
    Dynamic games, with discret time (repeated games).
    Zero-sum games. Combinatorial games.
    Positional games.

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


PROJECTS


(in reverse chronological order)


  • Projects and perspectives

    "You are never sure whether or not a problem is good unless you actually solve it."
    Mikhaïl Gromov (Abel prize 2009)

    First, I have appreciated (since the beginning of my academic career) 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 consideration, modelling and solution approaches. Mathematical formulations are necessarily related to the development of analytical/numerical solution methods.

    Moreover, I want to continue to study the research topics explored so far.
    In particular, 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.
    Since my Master's degree, I am interested in continuing in game theory and optimization, both continuous point of view and discrete point of view.
    Previously, I had the opportunity to study discrete and 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 appreciate sharing ideas and challenging problems. I enjoy doing research, in particular for its atmosphere of discussions, challenges of tackling problems and rewarding collaborations.



  • Participation to a scientific project

    ATOMIC project, founded by the French national agency for research (ANR, agence nationale de la recherche) (web link), Member of the ATOMIC project -for young researchers-, within the research-team, lead by Prof. Dr. Sonia Cafieri. Air traffic optimization via mixed-integer computation (ATOMIC). (January 2013 - September 2016)
    Composition of the research group: Prof. Dr. Sonia Cafieri (responsible), Loïc Cellier, CR. CNRS Dr. Claudia D'Ambrosio, Dr. Alexandre Gondran, Dr. Riadh Omheni, Prof. Dr. Frédéric Messine, Prof. Dr. Marcel Mongeau and HDR Dr. Ahmed Touhami.

    The purpose of ATOMIC is developing of 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 particularly related to aircraft conflict avoidance.


    Motivations to study problems arising from Air Traffic Management (ATM).
    Representation (in 2009) of the main civil air traffic, offering a visualization of the civilian civil air traffic over a period of 24h (image credit: collective of Swiss students-engineers).
    Representation of civil commercial air traffic over France and neighboring countries, given in near real time (thanks to transmissions from the ADS-B transponder via satellites, in September 2017) (image credit: Flightradar24)


  • Optimal control applied to air traffic management

    I realized this work under the supervision of Prof. Dr. Sonia Cafieri and Prof. Dr. 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. The air traffic management, particularly to guarantee the separation distances between aircraft, representes a critical system. In this context, a crucial importance concerns the development of decision-support and automation tools, demanding mathematical formulations, models, numerical implementations, and validation.



    Standard protection volume for commercial en-route aircraft. Standard separation distances are 5 nautical miles horizontally and 1000 feet vertically, which can be considered as a cylindrical protection volume centered on each aircraft. Photography taken by the author walking on the "place du capitole", Toulouse, France.
    (images credit: Loïc Cellier)


    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.


    Detection of "potential rencontres" between aircraft, definition of "zones", spatial decomposition and temporal decomposition for the problem of aircraft conflict avoidance, via subliminal velocity regulation.
    (images credit: Loïc Cellier)



    Representation of trajectories of a thirteen-aircraft conflict avoidance problem, and solution through optimal control (using acceleration as command on the dynamic system) for subliminal velocity regulation.
    (images credit: Loïc Cellier)


  • Discrete and computational geometry: topological representation of oriented matroids

    I realized these this work for my Master degree in sciences (research) thesis, under the supervision of Prof. Dr. Michel Pocchiola (from May to September 2010). My master's thesis research is in the fields of discrete and computational geometry; 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 Dr. Jon H. Folkman and Prof. Dr. Jim Lawrence, in 1978, and Jack Edmonds and Dr. Arnaldo Mandel, in 1982). Therefore, in this presentation, I would like to highlight in particular the link between the topological axiomatic and the combinatorics 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.



    Geometric curiosities. Arrangement of nine non-Desargues pseudolinees and arrangement of nine non-Pappus pseudolines, these two arrangements are not stretchable (images credit: Loïc Cellier); and representation of the horned sphere of Prof. Dr. James Waddell Alexander II, whose the exterior is not "simply connected" (image credit: Wikipedia).





    Representation of a signed essential arrangement (in two pieces: S+4 and S-4) of four pseudospheres (in this case, pseudolines) in S2 (in the projective plane).
    (images credit: Loïc Cellier)



    Reconstruction of a signed essential arrangement of pseudospheres (in this case, pseudolines) in S2 (in the projective plane), corresponding to a oriented matroid of rank three, from its signed parts (co-circuits)
    (images credit: Loïc Cellier)


  • Combinatorial optimization and combinatorial games

    I realized this research under the supervision of Jack Edmonds (web link), John von Neumann Theory Prize 1985 (web link), (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 of "generalization" has allowed to identify some links and results shared by some impartial combinatorial games.

    To deal with the computational complexity of the proposed combinatorial game (generalization), in order to determine winning strategy algorithms, my approach is about decomposition algorithms, and I developed different ways of research, by studying particular cases and involving discrete optimization (especially, graph theory). Many perspectives in this work are also presented.



    As for the two-dimensional chomp game, the winning strategy existence theorem for any rectangle n by m (with n and m two different integers), thus admits as a immediat corollary a indication of some "bad cases"; and, representation of conjugate boxes and deduction of "the only good" first strike, in case of initiative.
    (images credit: Loïc Cellier)

    Always early 2010, after a discussion with Jack Edmonds (web link), John von Neumann Theory prize 1985 (web link), around an article by Prof. Dr. Alfred Lehman of 1964 ("Solution of the Shannon switching game", Journal of the Society for Industrial and Applied Mathematics 12 (4): 687-725), I began to take an interest in the notion of "connectivity".

    In particular, I studied the game of hex, discovered (invented) by Prof. Dr. Piet Hein, in 1942; and presented again, in 1948, by Prof. Dr. John F. Nash (Abel prize 2015). For this (partizan) combinatorial game, positional (connectivity) game, I worked more recently (more after 2012) on topological properties for "variants" of the rules of this game, for example, the belonging to a winning strategy, and the explicitation (construction) of it, if possible.



    Representation in the form of a tree, and representation (in rotation) in the form of a graph oriented without circuit, of a set of hex side two. Labeling of vertices and representation of winning strategies.
    (images credit: Loïc Cellier)



CONFERENCES


(30+ talks; in reverse chronological order)


  • 2017
    • Workshop Games and Graphs (Combinatorial Games Theory, Graph game parameters, Algorithmic complexity of games), (web link), at the University of Lyon 1 Claude Bernard, (web link), organized by a consortium from the ANR GAG project (web link), Lyon - Villeurbanne, France, 2017.

    • Seminar, Franche-Comté Research Institute of Mathematics Teaching (Institut de recherche sur l'enseignement des mathématiques IREM de Franche-Comté) (web link), University of Bourgogne - Franche-Comté (UBFC), 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 Institute Villebon - Georges Charpak (web link), Excellence initiatives in teaching and learning techniques (Initiatives d'excellence en formations innovantes IDEFI) (web 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 (web link), Champs-sur-Marne, France, 2017.

    • Conference, Commission of French Research Institutes of Mathematics Teaching, within the research group Popularization of Mathematics (in French, Commission inter-IREM, groupe "popularisation des mathématiques"), Halle aux Farines, University of Paris 7 Paris Diderot (UP7) (web link), 13th arrondissement, Paris, France, 2017.

    • Workshop, "Academic Days" ("Journées académiques"), at the Université de Lille 1, Lille Research Institute of Mathematics Teaching (Intitut de recherche sur l'enseignement des mathématiques IREM de Lille), University of Lille (web link), Lille - Villeneuve d'Ascq, France, 2017.

  • 2016
    • Workshop, "Explain me your PhD thesis" ("Raconte-moi ta thèse"), Paris Mathematical Sciences Fondation (Fondation des sciences mathématiques de Paris FSMP) (web link), National event "Science Festival" ("Fête de la science", Institut Henri Poincaré (IHP) (web link), 5th arrondissement, Paris, France, 2016.

    • Workshop, week of studies (for young researchers), topic: "Mathematics and Industrial/Business Problems" (Semaine d'Étude Maths-Entreprises SEME) (web link) The initiative is jointly founded by the research group Mathematics and Business, and by the French Agency AMIES "Mathematics in interaction with Business and Society" (GdR CNRS Mathématiques et Entreprises et de l'agence pour les mathématiques en interaction avec l'entreprise et la société AMIES) (web link). The aim of workshop is to create some research discussions/works between Industrial/Business people and Academic Mathematics people, via the modelling/mathematics studies of new problems arising from Industrial/Business environment. École centrale de Marseille (web link) Technopôle de Château-Gombert, 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 (web link), France, 2016.

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

    • International conference, Emerging Trends in Applied Mathematics and Mechanics (ETAMM) (web link), Université de Perpignan Via Domitia (UPVD) (web 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 French Institute of sciences and technologies about transport, development and networks (Institut français des sciences et technologies des transports, de l'aménagement et des réseaux IFSTTAR) (web link), Saint-Ouen, France, 2016.

    • Workshop, "SMAI-MODE Days" ("Journées annuelles"), French Society of Applied Mathematics and Industrial Mathematics (Société de mathématiques appliquées et industrielles), and research group Mathematics of Optimization and Decision (Mathématiques de l'optimisation et de la décision) (SMAI MODE) (web link), École nationale supérieure d'électrotechnique, d'électronique, d'informatique, d'hydraulique et des télécommunications (ÉNSÉÉIHT) (web link), Toulouse, France, 2016.

    • Seminar LIRMM-DALI, research group LIRMM and project-team DALI, (web link), Université de Perpignan Via Domitia (UPVD) (web link), Perpignan, France, 2016.

  • 2015
    • Workshop, "MOA Days" ("Journées annuelles"), research group Mathematics of Optimization and Applications (Groupe de recherche (GdR) 3273 Mathématiques de l'optimisation et applications MOA) (web link), Université Bourgogne Franche-Comté (UBFC) (web link), Dijon, France, 2015.

    • Ph.D. thesis defense ("Soutenance de thèse de doctorat en sciences"), The French University of Civil Aviation (École nationale de l'aviation civile ÉNAC), (web link), University of Toulouse, Toulouse, France, 2015.

    • Doctoral seminar, ("Séminaire des doctorants ÉNAC"), The French University of Civil Aviation École nationale de l'aviation civile ÉNAC) (web link), University of Toulouse, Toulouse, France, 2015.

  • 2014
    • Workshop, "3D'14 DALI Doctoral Days 2014", research group LIRMM project-team DALI (web link), research laboratory Arago, University Paris 6 Pierre et Marie Curie (UPMC) (web link), Banyuls-sur-Mer, France, 2014.

    • Workshop, days with mini-conferences (" International Friday"), Perpignan Institute of Technology for Management, Supply Chain and Transport (Institut universitaire de technologie, filière gestion, logistique et transport IUT GLT), University of Perpignan Via Domitia (UPVD) (web link), Perpignan, France, 2014.

    • Doctoral seminar, "Séminaire de doctorants DocToMe", University Toulouse 3 Paul Sabatier (UT3) (web link), Toulouse, France, 2014.

    • National Conference, ROADEF 2014, French commission of Operations Research and Decision-support (Congrès français de Recherche Opérationnelle et d'Aide à la Décision) (web link), Bordeaux Mathematical Institute (Institut de mathématiques de Bordeaux IMB) (web link), University of Bordeaux, Bordeaux, France, 2014.

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

    • International Conference, Recent Advances on Optimization, (web link) (poster presentation), European Center of basic and applied research specialized in modelling and numerical simulation (Centre européen de recherche et de formation avancée en calcul scientifique CERFACS) (web link), Toulouse, France, 2013.

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

    • Doctoral seminar, Mid-term PhD defense ("Soutenance de mi-parcours"), Doctoral School of Mathematics, Computer Science, and Telecommunications of Toulouse (École doctorale mathématiques, informatique et télécommunications de Toulouse ÉDMITT) (web link), Toulouse, France, 2013.

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

    • National Conference, ROADEF 2013, French commission of Operations Research and Decision-support (Congrès français de Recherche Opérationnelle et d'Aide à la Décision) (web link), University of Troyes (UTT) (web link), Troyes, France, 2013.

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

    • Doctoral seminar, ÉNSÉÉIHT PhD students Days ("Journée des doctorants ÉNSÉÉIHT"), École nationale supérieure d'électrotechnique, d'électronique, d'informatique et des télécommunications (ÉNSÉÉIHT) (web link), Toulouse, France, 2012.

    • Seminar, Lab MAIAA Seminar ("Séminaire du laboratoire MAIAA", Mathématiques Appliquées, Informatique et Automatique pour l'Aérien), The French University of Civil Aviation (École nationale de l'aviation civile ÉNAC) (web link), University of Toulouse, Toulouse, France, 2012.

    • National Conference, ROADEF 2012, French commission of Operations Research and Decision-support (Congrès français de Recherche Opérationnelle et d'Aide à la Décision) (web link), University of Angers (web link), Angers, France, 2012.


PUBLICATIONS



Summary of contributions for publications. Books (university teaching level, or popularization thematics), chapters of book (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 book


  • Loïc Cellier, Mickaël Launay and Chloé Milsonneau, chapters of book, number 73 "Les Mathématiques", Collection Sciences, Encyclopédie Tout l'Univers, Éditions Hachette, Paris, France, 2017. (12 pages in French, and participation to proofreading; collective book) (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, Optimal Control Applications and Methods (OCA2017), Wiley InterScience, Editions John Wiley & Sons, 2017. (23 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, in French) (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, in French) (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, in French) (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 (Thèse de Doctorat en sciences), Toulouse, France, 2015. (161 pages, in French) (pdf)

  • Loïc Cellier, Topological Representation Theorem for Oriented Matroids (French title: Théorème de représentation topologique pour les matroïdes orientés), Master Research degree thesis (Mémoire de Master Recherche), Paris, France, 2010. (84 pages, in French) (pdf)

Technical reports


  • Loïc Cellier, Jésua Chavez, Guillaume Garrigos and Souhil Tairi, Detection of time-frequency templates (French title: Détection de motifs dans le plan temps-fréquence), rapport de Semaine d'Études Maths Entreprise (SEME), AMIES, Marseille, France, 2016. (-- pages, in French) (pdf)

  • Loïc Cellier, Collection of informations and web links for popularization of mathematics (in French title: Pour la diffusion des mathématiques), volunteer CIJM report (rapport bénévole CIJM), Paris, France, 2015 (15 pages, in French) (pdf)

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

  • Benjamin Blum and Loïc Cellier, Business strategy: Horizontal Mergers (French title: Les fusions horizontales), Master research degree report (rapport de Master Recherche), Paris, France, 2010. (25 pages, in French) (pdf)

Others


  • Concerning "accessibility" to publications (means) of research
    • Thanks to Prof. Dr. Paul Ginsparg (web link), for arXiv (web link). In the same idea, acknowledgments to the association Center for Direct Scientific Communication (Centre pour la communication scientifique directe, CCSD) for HAL (web link)
    • Acknowledgments to the association Committee for the accessibility of publications in sciences and humanities (Comité pour l'accéssibilité des publications en sciences et humanités, CAPSH) (web link). in particular, thanks to Prof. Dr. Marie Farge (web link) for the discussions and its communicative enthusiam about ideas sharing, and means (dissemination) of research; and thanks to Antonin Delpeuch (web link) for the realization of Dissemin (web link)
    • Acknowledgments to Prof. Dr. John Willinsky (web link) for Open Journal Systems (OJS), with the association Public Knowledge Project (PKP) (web link)

  • Concerning "bibliometrics and indicators" (to be considered with caution), associated with "productivity"
    • Acknowledgments to Prof. Dr. Jean-Paul Delahaye (web link) for his section "Logique et Calcul", in "New Scientist" ("Pour la Science"), and a vulgarization text about this topic "Measuring researchers" ("Mesurer les chercheurs"), pp. 88-93, March 2011 (6 pages, in French) (pdf)
    • Thanks to Dr. Nathaniel Eldrege (web link), and the truculent remarks from Mathgen (web link) ; so, a final document, although I am one of the co-authors, I have not contributed to its drafting. (9 pages) (pdf)