Frédéric Gardi
Frédéric Gardi
Mathematical Optimization Expert, M.Sc., Ph.D., Dr. habil.
Co-Founder & CEO, Hexaly, Brooklyn, NY, USA

Research


I have been working in Mathematical Optimization, Operations Research, Decision Science, and Software Engineering for 25 years. The originality of my work is to balance theory and practice, research and applications, with the constant will to benefit society and transfer my knowledge to younger people.

After a Ph.D. thesis devoted to issues related to workforce and job scheduling mixing algorithmics and graph theory [5, 9, 11, 12, 15, 16, 17], I have worked on problems arising in banking, particularly in real-estate financial planning [7, 13]. Since then, I have focused my research on local search techniques for combinatorial and mixed-variable optimization [2, 4, 6, 8, 10, 14] and their integration into a general-purpose, model-and-run mathematical optimization solver [3, Hexaly Optimizer]. I also pursue the study of fundamental questions extracted from the concrete problems encountered in business (see, for example, [1]).

In 2004, we draw with Bertrand Estellon and Karim Nouioua the outlines of a methodology to tackle systematically combinatorial optimization problems by local search, in particular large-scale real-life problems. This methodology advocates a pure (without hybridization) and direct (without decomposition) approach, even for mixed-variable problems with discrete and continuous decision variables. Contrary to the idea now prevalent that "local search = metaheuristics", our methodology focuses on the diversification by the moves and on the performance of the evaluation machinery behind these moves. In this way, we would say that "local search = diversified neighborhoods + incremental algorithmics" (by "diversified", we mean multiple, variable-sized, and rich). Our methodology also provide keys to ensure the quality of a software based on local search (reliability, maintainability). Ultimately, this one aims at industrializing the design and engineering of optimization software based on local search, numerous in industry, in order to reduce their development, integration and maintenance costs, while increasing their performances. This methodology has been successfully applied during several operational projects with high economic stakes, particularly at Bouygues [2, 4], as well as during several international OR competitions (2005, 2007, 2010 ROADEF Challenges) [6, 8, 10, 14]. Some of the developed software are still in production today and offers significant returns on investment.

In 2007, I initiated a research project to develop a model-and-run solver for combinatorial optimization based on the local search paradigm. Relying on a suitable declarative formalism, the user models his problem and the solver resolves it autonomously by relying on local search. Hence, we seek to overcome the weaknesses of traditional tree-search solvers, particularly Mixed-Integer Linear Programming solvers like Cplex or Gurobi, powerless against large-scale highly-combinatorial problems. A team has rallied around this project: Thierry Benoist, Bertrand Estellon, Karim Nouioua, then Romain Megel and Julien Darlay. Our software, originally named "LocalSolver" when publicly released in 2010 and introduced in [3], now known as Hexaly Optimizer, allows to solve in minutes some combinatorial optimization problems that integer or constraint programming cannot resolve within hours.

In 2012, we incorporated this project into a company, now called Hexaly, operating as a subsidiary of Bouygues, in partnership with Aix-Marseille University and CNRS LIS lab. Over the past 10 years, we have worked with the team to develop a global optimization solver hybridizing exact and heuristic techniques for large-scale, real-world, mixed-variable, non-convex, and possibly black-box, optimization problems. Our software product, Hexaly Optimizer, is renowned as the world's fastest solver for Routing, Scheduling, Packing, Clustering, and Location problems, among others. The Hexaly team now counts 40 people and our solver is used by 1,000 developers in 200 companies worldwide, including Amazon, FedEx, Starbucks, Chewy, J.B. Hunt, Bosch, Renault, Sony, TotalEnergies, Repsol, Air Liquide, ENGIE, Veolia.

In 2022, in addition to our solver, we have lauched Hexaly Studio, a low-code platform for Mathematical Optimization. The goal of this web-based (SaaS) platform is to make the protoypting, development, and deployment of optimization apps easier and faster for data scientists and software developers, allowing them to save 80% of the time and cost spent on optimization projects. News about Hexaly can also be found on LinkedIn and Twitter.

Below is an extended abstract overviewing my research over the years:

F. Gardi (2012).
What's OR: theorem or software?
French Operations Research and Decision Support Society (ROADEF),
Bulletin Semestriel, Spring-Summer 2012, No. 28, pp. 8-12. [paper] (invited communication, in French)

The following monograph provides a synthesis of our original ideas and experiments about the integration of local search methods into a general-purpose, model-and-run mathematical optimization solver:

F. Gardi, T. Benoist, J. Darlay, B. Estellon, R. Megel (2014).
Mathematical Programming Solver based on Local Search.
FOCUS Series in Computer Engineering, ISTE Wiley, 112 pages.
ISBN 9781848216860

Below are short communications written in different languages summarizing the above monograph:

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, K. Nouioua (2011).
LocalSolver: local search in mathematical programming.
French Operations Research and Decision Support Society (ROADEF),
Bulletin Semestriel, Autumn-Fall 2011, No. 27, pp. 4-7. [paper] (invited communication, in French)

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2013).
Integrating local search techniques into a mathematical programming solver.
International Federation of Operational Research Societies (IFORS),
Newsletter, September 2013, pp. 19-20. [paper] (invited communication, in English)

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2013).
Optimizing with Big Data: how to break through the scalability wall?
Netherlands Society for Statistics and Operations Research (VVSOR),
STAtOR Newsletter, Number 3-4, pp. 48-52. [paper] (invited communication, in Dutch)

Wan Baocheng, Niu Taiyang, Wang Tiane (2014).
Introduction of LocalSolver optimization modeling software.
Modern Computer, Practice and Experience, Number 4, pp. 55-58. [paper] (in Chinese)

Tomoaki Miyazaki (2020).
Latest trends in mathematical programming systems: LocalSolver.
Operations Research Society of Japan (ORSJ),
Communications, Vol. 65, No. 4, pp. 212-219. [paper] (in Japanese)

Awards


1st Junior and Senior Prize of 2005 ROADEF Challenge (with Bertrand Estellon and Karim Nouioua), awarded by the French Operations Research Society (ROADEF) and the companies EURODECISION and RENAULT, for the best software for sequencing cars in RENAULT plants (55 participating teams from 15 countries, 12 finalists from 7 countries: Bosnia-Herzegovina, Brazil, Canada, France, Germany, Netherlands, Poland).

    Excerpt from the ROADEF newsletter
    Excerpt from the Aix-Marseille II University newsletter
    Excerpt from the magazine OR/MS Today
    Excerpt from the magazine Industrie et Technologies
2nd Senior Prize of 2007 ROADEF Challenge (with Bertrand Estellon and Karim Nouioua), awarded by the ROADEF and the companies EURODECISION, FRANCE TELECOM and ILOG, for the best software for scheduling maintenance interventions on the FRANCE TELECOM network (35 participating teams, 11 finalists).

Finalist of 2009 ROADEF Challenge (with Bertrand Estellon), organized by the ROADEF and the company AMADEUS, on disruption management for commercial aviation (29 participating teams, 9 finalists).

Finalist of 2010 ROADEF/EURO Challenge (with Karim Nouioua), organized by the ROADEF and the company EDF, on medium-term management of the French thermal power park (44 participating teams from 25 countries, 16 finalists from 11 countries). Ranked 1st at the qualification stage.

1st Prize for "Industrial Applications" at ROADEF 2011 (with Karim Nouioua), yearly meeting of the French Operations Research Society, for the communication "High-performance local search for the mid-term management of the French nuclear power park".

Finalist of 2012 ROADEF/EURO Challenge (with LocalSolver's founders), organized by the ROADEF and the company GOOGLE, on the reassignment of processes to machines (82 participating teams coming from 33 countries, 30 finalists). Ranked 25th, LocalSolver qualified for the final round with a 100-line optimization model developed in 1 day of work.

Finalist of 2012 EURO Excellence in Practice Award (with Thierry Benoist and Antoine Jeanjean), awarded by the Association of European Operational Research Societies (EURO). Selected among 6 finalists over 56 worldwide submissions for our paper "Lessons learned from 15 years of operations research for French TV channel TF1" in the INFORMS journal Interfaces. This prize awards some exceptional works in the practice of operations research, through a recent paper describing an original application of OR, in methodology, application, or engineering.

2012 Robert Faure 1st Prize, awarded every 3 years by the French Operations Research and Decision Support Society (ROADEF), to the best researcher under 35. This prize awards an original contribution in the field of operations research. A particular attention is given to works which couple the development of theoretical methods to applications, in the spirit of the works of Professor Robert Faure, pioneer in Operations Research in France.

Publications

Books (1)

F. Gardi, T. Benoist, J. Darlay, B. Estellon, R. Megel (2014).
Mathematical Programming Solver based on Local Search.
FOCUS Series in Computer Engineering, ISTE Wiley, 112 pages.
ISBN 9781848216860

Selective international journals and conferences (17)

[1]  B. Estellon, F. Gardi (2013).
Car sequencing is NP-hard: a short proof.
Journal of the Operational Research Society 64(10), pp. 1503-1504. [paper] (impact factor: 3.051)

[2]  T. Benoist, F. Gardi, A. Jeanjean (2012).
Lessons learned from 15 years of operations research for French TV channel TF1.
Interfaces, now INFORMS Journal in Applied Analytics 42(6), pp. 577-584. [paper] (impact factor: 1.434)

[3]  T. Benoist, B. Estellon, F. Gardi, R. Megel, K. Nouioua (2011).
LocalSolver 1.x: a black-box local-search solver for 0-1 programming.
4OR, A Quarterly Journal of Operations Research 9(3), pp. 299-316. [paper] (impact factor: 1.763)

[4]  T. Benoist, B. Estellon, F. Gardi, A. Jeanjean (2011).
Randomized local search for real-life inventory routing.
Transportation Science 45(3), pp. 381-398. [paper] [extended version] (impact factor: 4.898)

[5]  F. Gardi (2011).
On partitioning interval graphs into proper interval subgraphs and related problems.
Journal of Graph Theory 68(1), pp. 38-54. [paper] (impact factor: 0.921)

[6]  F. Gardi, K. Nouioua (2011).
Local search for mixed-integer nonlinear optimization: a methodology and an application.
In Proceedings of EvoCOP 2011, the 11th European Conference on Evolutionary Computation in Combinatorial Optimization
(P. Merz, J.-K. Hao, eds.), Lecture Notes in Computer Science 6622, pp. 167-178.
Springer, Berlin, Germany. [paper] (acceptance rate: 50%)

[7]  F. Gardi (2010).
Optimisation de plans de financement immobiliers.
RAIRO Operations Research 44(3), pp. 207-239. [paper] [extended version] (impact factor: 2.526)

[8]  B. Estellon, F. Gardi, K. Nouioua (2009).
High-performance local search for task scheduling with human resource allocation.
In Proceedings of SLS 2009, the 2th International Workshop on Engineering Stochastic Local Search Algorithms
(T. Stützle, M. Birattari, H.H. Hoos, eds.), Lecture Notes in Computer Science 5752, pp. 1-15.
Springer, Berlin, Germany. [paper] [slides] (acceptance rate: 25%)

[9]  F. Gardi (2009).
Mutual exclusion scheduling with interval graphs or related classes. Part I.
Discrete Applied Mathematics 157(1), pp. 19-35. [paper] (impact factor: 1.254)

[10]  B. Estellon, F. Gardi, K. Nouioua (2008).
Two local search approaches for solving real-life car sequencing problems.
In Special Issue: The Car Sequencing Problem (C. Solnon, V.D. Cung, A. Nguyen, C. Artigues, eds.),
European Journal of Operational Research 191(3), pp. 928-944. [paper] (impact factor: 6.363, acceptance rate: 18%)

[11]  F. Gardi (2008).
Mutual exclusion scheduling with interval graphs or related classes. Part II.
Discrete Applied Mathematics 156(5), pp. 794-812. [paper] (impact factor: 1.254)

[12]  F. Gardi (2007).
The Roberts characterization of proper and unit interval graphs.
Discrete Mathematics 307(22), pp. 2906-2908. [paper] (impact factor: 0.961)

[13]  F. Gardi, A. David (2007).
Optimisation de plans de financement immobiliers : de la recherche opérationnelle en actuariat bancaire.
Bulletin Français d'Actuariat 7(13), pp. 107-121. [paper] (edited by the French Actuarial Society)

[14]  B. Estellon, F. Gardi, K. Nouioua (2006).
Large neighborhood improvements for solving car sequencing problems.
In Special Issue: Journées Francophones de Programmation par Contraintes 2005 (F. Fages, N. Jussien, C. Solnon, eds.),
RAIRO Operations Research 40(4), pp. 355-379. [paper] (impact factor: 2.526)

[15]  F. Gardi (2006).
Mutual exclusion scheduling with interval graphs or related classes: complexity and algorithms.
4OR, A Quarterly Journal of Operations Research 4(1), pp. 87-90. [paper] (impact factor: 1.763)

[16]  F. Gardi (2004).
On partitioning interval and circular-arc graphs into proper interval subgraphs with applications.
In Proceedings of LATIN 2004, the 6th Latin American Symposium on Theoretical Informatics
(M. Farach-Colton, ed.), Lecture Notes in Computer Science 2976, pp. 129-140.
Springer, Berlin, Germany. [paper] (acceptance rate: 33%)

[17]  F. Gardi (2003).
Efficient algorithms for disjoint matchings among intervals and related problems.
In Proceedings of DMTCS 2003, the 4th International Conference on Discrete Mathematics and Theoretical Computer Science
(C.S. Calude, M.J. Dinneen, V. Vajnovszki, eds.), Lecture Notes in Computer Science 2731, pp. 168-180.
Springer, Berlin, Germany. [paper] (acceptance rate: 50%)

International conferences (39)

F. Gardi (2020).
Live Industry Panel: From Applied Mathematicians to Entrepreneurs.
In AN20, the 2nd Joint SIAM/CAIMS Annual Meeting (AN20).
Toronto, Ontario, Canada. (invited panelist) [video]

F. Gardi (2018).
Designing and optimizing an LNG supply chain using LocalSolver.
In EU/ME 2018, the 19th Workshop of the EURO Working Group on Metaheuristics.
Geneva, Switzerland. [abstract]

F. Gardi (2018).
Designing and optimizing an LNG supply chain using LocalSolver.
In EU/ME 2018, the 19th Workshop of the EURO Working Group on Metaheuristics.
Geneva, Switzerland. [abstract]

J. Darlay, F. Gardi (2017).
Everything you have always wanted to know about LocalSolver.
In EA 2017, the 13th Biennial International Conference on Artificial Evolution.
Paris, France. [slides]

F. Gardi (2017).
LocalSolver, a new kind of mathematical optimization solver.
In ETP4MSO 1st Workshop, Towards a European Technology Platform for Mathematical Modelling, Simulation and Optimisation.
Amsterdam, Netherlands. [slides]

T. Benoist, F. Gardi, R. Megel, C. Pajean, M. Ben Belgacem, D. Leblanc, F. Legrand, S. Pietrasz (2016).
Designing and optimizing an LNG supply chain using LocalSolver.
In VeRoLog 2016, the Annual Workshop of the EURO Working Group on Vehicle Routing and Logistics Optimization.
Nantes, France. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, C. Pajean (2016).
Solving routing and scheduling problems using LocalSolver.
In VeRoLog 2016, the Annual Workshop of the EURO Working Group on Vehicle Routing and Logistics Optimization.
Nantes, France. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, C. Pajean (2016).
Solving routing and scheduling problems using LocalSolver.
In OR 2016, the International Conference on Operations Research.
Hamburg, Germany. [abstract][slides]

J. Darlay, F. Gardi (2015).
Extension of Bouygues Telecom's ADSL network.
In OR 2016, the International Conference on Operations Research.
Hamburg, Germany. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, C. Pajean (2016).
LocalSolver: a new kind of math programming solver.
In MIM 2016, the 8th IFAC Conference on Manufacturing Modelling, Management and Control.
Troyes, France. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, C. Pajean (2016).
Solving routing and scheduling problems through set-based modeling.
In ESGI 2016, the 117th European Study Group with Industry.
Avignon, France. (invited plenary speaker) [abstract][slides]

F. Gardi (2016).
Introduction to LocalSolver, a new kind of mathematical optimization solver, with applications to Vehicle Routing.
In EURO PhD School 2016 on Matheuristics with Applications to Vehicle Routing.
Lorient, France. (invited plenary speaker) [slides - first part][slides - second part]

J. Darlay, F. Gardi (2015).
Extension of Bouygues Telecom's ADSL network.
In PGMO DAYS 2015, the Gaspard Monge Program for Optimization and Operations Research.
Palaiseau, France. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, C. Pajean (2015).
LocalSolver: a mathematical optimization solver based on neighborhood search.
In OR 2015, the International Conference on Operations Research.
Vienna, Austria. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, C. Pajean (2015).
LocalSolver: a mathematical optimization solver based on neighborhood search.
In MIC 2015, the 11th Metaheuristics International Conference.
Agadir, Moroccow. (invited plenary speaker) [abstract][slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, C. Pajean (2015).
LocalSolver: a mathematical optimization solver based on neighborhood search.
In EURO 2015, the 27th European Conference on Operational Research.
Glasgow, UK. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, C. Pajean (2015).
LocalSolver: toward a mathematical optimization solver based on neighborhood search.
In DORS AOO 2015, the Danish Operations Research Society Workshop on Applications of Optimization.
Copenhagen, Denmark. (invited plenary speaker) [abstract][slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2014).
LocalSolver: a new kind of math programming solver.
In OR 2014, the International Conference on Operations Research.
Aachen, Germany. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2014).
LocalSolver: a new kind of math programming solver.
In EUROPT 2014, the 12th Workshop on Advances in Continuous Optimization.
Perpignan, France. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2014).
LocalSolver 4.0: hybrid math programming.
In INFORMS 2014 Conference on Business Analytics and Operations Research.
Boston, MA, USA. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2013).
Mathematical programming by local search.
In OR55, the Annual Conference of the Operations Research Society.
Exeter, UK. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2013).
LocalSolver: toward a full mathematical programming solver based on local search.
In OR 2013, the International Conference on Operations Research.
Rotterdam, The Netherlands. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2013).
LocalSolver: toward a full mathematical programming solver based on local search.
In EURO 2013, the 26th International Symposium on Mathematical Programming.
Roma, Italy. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2013).
Mathematical programming by local search.
In ECCO XXVI, the 26th Conference of the European Chapter on Combinatorial Optimization.
Paris, France.

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, K. Nouioua (2012).
LocalSolver: a mathematical programming solver based on local search.
In ISMP 2012, the 21th International Symposium on Mathematical Programming.
Berlin, Germany. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, K. Nouioua (2012).
ROADEF/EURO/Google Challenge: how a 100-line LocalSolver model qualifies for the final round.
In EURO 2012, the 25th European Conference of Operational Research.
Vilnius, Lithuania. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, K. Nouioua (2012).
LocalSolver: black-box local-search for combinatorial optimization.
In EURO 2012, the 25th European Conference of Operational Research.
Vilnius, Lithuania. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, K. Nouioua (2012).
LocalSolver: black-box local-search for combinatorial optimization.
In 2012 Optimization Days. Montreal, Canada. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, K. Nouioua (2012).
LocalSolver: black-box local search for combinatorial optimization.
In 16th Aussois Combinatorial Optimization Workshop (organized by F. Margot, D. Naddef, L. Wolsey).
Aussois, France. (invited plenary speaker) [slides]

T. Benoist, F. Gardi, A. Jeanjean (2012).
Optimization of advertisement revenue for the French TV group TF1.
In EURO 2012, the 25th European Conference of Operational Research.
Vilnius, Lithuania. [slides]

F. Gardi (2012).
High-performance local search for TV media planning on TF1.
In EURO 2012, the 25th European Conference of Operational Research.
Vilnius, Lithuania. [slides]

T. Benoist, B. Estellon, F. Gardi, A. Jeanjean, K. Nouioua (2011).
Local search for mixed-integer nonlinear optimization: methodology and applications.
In EDF Workshop on Advanced Optimisation Methods and their Applications to Unit Commitment in Energy Management.
Clamart, France. [abstract] [slides]

T. Benoist, B. Estellon, F. Gardi, A. Jeanjean (2010).
Recherche locale pour un problème d'optimisation de tournées de véhicules avec gestion des stocks.
In Proceedings of MOSIM 2010, the 8th International Conference of Modeling and Simulation
(A. Hadj-Alouane, H. Pierreval, eds.). Hammamet, Tunisia. [paper]

T. Benoist, B. Estellon, F. Gardi, K. Nouioua (2010).
Toward Local Search Programming: LocalSolver 1.0.
In EURO 2010, the 24th European Conference of Operational Research.
Lisbon, Portugal. [slides]

T. Benoist, B. Estellon, F. Gardi, K. Nouioua (2010).
Toward local search programming: LocalSolver 1.0.
In CPAIOR 2010 Workshop : Open Source Tools for Constraint Programming and Mathematical Programming.
Bologna, Italy. [paper]

F. Gardi, K. Nouioua (2010).
High-performance local search for a large-scale energy management problem.
In EURO 2010, the 24th European Conference of Operational Research.
Lisbon, Portugal. [slides]

T. Benoist, B. Estellon, F. Gardi, S. Jain, A. Jeanjean, E. Patay (2009).
Inventory routing optimization for bulk gas transportation.
In INFORMS 2009, Annual Meeting. San Diego, CA, USA. [abstract]

T. Benoist, B. Estellon, F. Gardi, A. Jeanjean (2009).
High-performance local search for solving real-life inventory routing problems.
In Proceedings of SLS 2009, the 2th International Workshop on Engineering Stochastic Local Search Algorithms
(T. Stützle, M. Birattari, H.H. Hoos, eds.), Lecture Notes in Computer Science 5752, pp. 105-109.
Springer, Berlin, Germany. [extended abstract]

F. Gardi (2004).
A sufficient condition for optimality in mutual exclusion scheduling for interval graphs and related classes.
In Abstracts of PMS 2004, the 9th International Workshop on Project Management and Scheduling
(A. Oulamara, M.-C. Portmann, eds.), pp. 154-157. Nancy, France. [extended abstract]

National conferences (42)

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, C. Pajean (2017).
Modélisation ensembliste avec LocalSolver.
In Actes de ROADEF 2017, le 18ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Metz, France. [abstract][slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, C. Pajean (2016).
Résolution de problèmes black-box avec LocalSolver.
In Actes de ROADEF 2016, le 17ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Compiègne, France. [abstract][slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, C. Pajean (2016).
Modélisation ensembliste avec LocalSolver.
In Actes de ROADEF 2016, le 17ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Compiègne, France. [abstract][slides]

C. Pajean, R. Megel, F. Gardi (2016).
Optimisation de plans de financement immobiliers pour les Caisses d'Epargne et le Crédit Foncier.
In Actes de ROADEF 2016, le 17ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Compiègne, France. [abstract][slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, C. Pajean (2015).
Résolution de problèmes black-box avec LocalSolver.
In Journée du GT Programmation Mathématique (PM), GDR RO du CNRS.
Paris, France. [slides]

C. Pajean, F. Gardi (2015).
Ordonnancement de la production de médicaments cytotoxiques avec LocalSolver.
In Journée du GT RO et Santé (ROSa), GDR RO du CNRS.
AP-HP, Paris, France. [slides]

T. Benoist, F. Gardi (2015).
Optimisation de campagnes publicitaires multi-TV avec LocalSolver.
In Actes de ROADEF 2015, le 16ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Marseille, France. [abstract][slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2015).
LocalSolver: recent advances in solving hydro valley optimization problems.
In Actes de ROADEF 2015, le 16ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Marseille, France. [abstract][slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, C. Pajean (2015).
Set-based modeling and black-box optimization.
In Journée Optimisation et Réseaux.
IHP, Paris, France. [slides]

J. Darlay, F. Gardi (2015).
Extension du réseau ADSL de Bouygues Telecom.
In Journée du GT Optimisation et Réseaux, GDR RO du CNRS.
ENGIE, Paris, France. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2014).
LocalSolver: recent advances in solving hydro valley optimization problems.
In PGMO-COST Workshop on Validation and Software (WG3-4), Gaspard Monge Program for Optimization and Operations Research (PGMO)
and COST Action "Mathematical Optimization in the Decision Support Systems for Efficient and Robust Energy Networks".
Ecole Polytechnique, Palaiseau, France. [slides]

T. Benoist, F. Gardi (2014).
Media planning TV et optimisation : du statique au (très) dynamique.
In Journée Industrielle du GDR RO du CNRS.
Paris, France. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2014).
LocalSolver 4.0 : programmation mathématique hybride.
In Journées SMAI-MODE 2014, Mathématiques de l'Optimisation de la Décision.
Rennes, France. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2014).
Modeling Patterns for LocalSolver.
In Actes de ROADEF 2014, le 15ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Bordeaux, France. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2014).
LocalSolver 4.0 : nouveautés et benchmarks.
In Actes de ROADEF 2014, le 15ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Bordeaux, France. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2014).
LocalSolver: a new kind of math programming solver.
In 9th Paris Machine Learning Meetup.
Paris, France. [slides]

F. Gardi (2013).
Toward a mathematical programming solver based on neighborhood search.
In ORO 2013, Workshop on Optimization in Operations Research.
Nantes, France. [slides]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel (2013).
Vers un solveur de programmation mathématique généralisée basé sur la recherche locale.
In Actes de ROADEF 2013, le 14ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Troyes, France. [abstract] [slides]

J.-Y. Lucas, D. Marcel, T. Benoist, F. Gardi, R. Megel (2013).
Une modélisation LocalSolver pour le placement des assemblages combustibles en piscine.
In Actes de ROADEF 2013, le 14ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Troyes, France. [abstract]

T. Benoist, J. Darlay, B. Estellon, F. Gardi, R. Megel, K. Nouioua (2012).
LocalSolver 2.0 : premier solveur de programmation mathématique fondé sur la recherche locale.
In Actes de ROADEF 2012, le 13ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Angers, France. (invited semi-plenary speaker) [slides]

F. Gardi (2012).
C'est quoi la RO : des théorèmes ou des logiciels ?
In Actes de ROADEF 2012, le 13ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Angers, France. (invited semi-plenary speaker) [slides]

T. Benoist, B. Estellon, F. Gardi, R. Megel, K. Nouioua (2011).
LocalSolver : un solveur boîte noire a base de recherche locale pour l'optimisation combinatoire.
In JFRO 2011, la 25ème Journée Francilienne de Recherche Opérationnelle : Recherche Opérationnelle et Intelligence Artificielle.
Paris, France. (invited plenary speaker) [slides]

T. Benoist, B. Estellon, F. Gardi, R. Megel, K. Nouioua (2011).
LocalSolver 1.x : un solveur boîte noire à base de recherche locale pour la programmation 0-1.
In Actes des JFPC 2011, les 7ème Journées Francophones de Programmation par Contraintes.
Lyon, France. [paper]

T. Benoist, B. Estellon, F. Gardi, R. Megel, K. Nouioua (2011).
Vers une programmation par recherche locale : LocalSolver 1.1.
In Actes de ROADEF 2011, le 12ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Saint-Étienne, France. [abstract] [slides]

T. Benoist, B. Estellon, F. Gardi, R. Megel, K. Nouioua (2011).
Génération automatique de voisinages de grande taille pour la recherche locale autonome.
In Actes de ROADEF 2011, le 12ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Saint-Étienne, France. [slides]

F. Gardi (2011).
Recherche locale haute performance pour la résolution d'un problème riche de tournées d'inventaires.
In 5ème Journée du GT Transport-Logistique du GdR Recherche Opérationnelle du CNRS.
Paris, France. (invited plenary speaker) [slides]

F. Gardi, K. Nouioua (2011).
Recherche locale haute performance pour la gestion moyen-terme du parc nucléaire français.
In Actes de ROADEF 2011, le 12ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Saint-Étienne, France. (1st Prize for Industrial Apllications) [abstract]

T. Benoist, B. Estellon, F. Gardi, K. Nouioua (2010).
Vers une programmation par recherche locale : LocalSolver.
In Actes de ROADEF 2010, le 11ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision,
Toulouse, France. [abstract]

T. Benoist, B. Estellon, F. Gardi, A. Jeanjean (2009).
Algorithme de recherche locale pour la résolution d'un problème réel de tournée d'inventaires.
In JOR 2009, la 4ème Journée de Recherche Opérationnelle et Optimisation dans les Réseaux.
Paris, France. [slides]

T. Benoist, B. Estellon, F. Gardi, A. Jeanjean (2009).
Recherche locale haute performance pour l'optimisation des livraisons de gaz industriels par camions-citernes.
In Actes de ROADEF 2009, le 10ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision,
pp. 49-50. Nancy, France. [abstract]

F. Gardi (2009).
Composition optimale d'équipes d'athlétisme.
In Actes de ROADEF 2009, le 10ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision,
pp. 81-82. Nancy, France. [abstract]

B. Estellon, F. Gardi, K. Nouioua (2008).
Recherche locale haute performance pour la planification des interventions à France Télécom.
In Actes des JFPC 2008, les 4èmes Journées Francophones de Programmation par Contraintes,
pp. 69-78. Nantes, France. [paper]

B. Estellon, F. Gardi, K. Nouioua (2008).
Recherche locale haute performance.
In Actes de ROADEF 2008, le 9ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision,
pp. 189-190. Clermond-Ferrand, France. [abstract]

F. Gardi, T. Benoist (2008).
Programmation de campagnes publicitaires sur les chaînes thématiques du groupe TF1.
In Actes de ROADEF 2008, le 9ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision,
pp. 203-204. Clermond-Ferrand, France. [abstract]

B. Estellon, F. Gardi, K. Nouioua (2007).
Une heuristique à base de recherche locale pour la planification de tâches avec affectation de ressources.
In ROADEF 2007, le 8ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Grenoble, France. [abstract]

F. Gardi, A. David (2006).
Optimisation de plans de financements immobiliers.
In Actes des JFPC 2006, les 2èmes Journées Francophones de Programmation par Contraintes,
pp. 167-172. Nîmes, France. [extended abstract]

F. Gardi, A. David (2006).
Optimisation de plans de financements immobiliers.
In Actes de ROADEF 2006, le 7ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision.
Lille, France. [abstract]

B. Estellon, F. Gardi, K. Nouioua (2005).
Ordonnancement de véhicules : une approche par recherche locale à voisinage large.
In Actes des JFPC 2005, les 1ères Journées Francophones de Programmation par Contraintes,
pp. 21-28. Lens, France. [extended abstract]

B. Estellon, F. Gardi, K. Nouioua (2005).
Ordonnancement de véhicules dans les usines Renault : une approche par recherche locale à voisinage large.
In Actes de ROADEF 2005, le 6ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision,
pp. 33-34. Tours, France. [abstract]

B. Estellon, F. Gardi, K. Nouioua (2005).
Ordonnancement de véhicules dans les usines Renault : une approche par recherche locale à voisinage réduit.
In Actes de ROADEF 2005, le 6ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision,
pp. 35-36. Tours, France. [abstract]

F. Gardi (2003).
Planification d'horaires de travail et colorations de graphes.
In Actes de GRM 2003, les 1ères Journées Graphes, Réseaux et Modélisation.
Paris, France. [abstract]

F. Gardi (2003).
Planification d'horaires de travail et théorie des graphes.
In Actes de ROADEF 2003, le 5ème Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision,
pp. 99-100. Avignon, France. [abstract]

Habilitation thesis


Title: Toward a mathematical programming solver based on local search.

Date and place of defense: November 25, 2013, at Sorbonne Université, Campus Pierre et Marie Curie, Paris.

Jury: Keywords: combinatorial optimization, local/neighborhood search, mathematical programming.

Abstract:

This dissertation deals with local search for combinatorial optimization and its extension to mixed-variable optimization. Our goal is to present local search in a new light. Although not yet understood from the theoretical point of view, local search is the paradigm of choice to tackle large-scale real-life optimization problems. Today end-users ask for interactivity with decision support systems. For optimization software, it means obtaining good-quality solutions quickly. Fast iterative improvement methods, like local search, are suited to satisfy such needs.

When a solution space is gigantic, a complete search becomes unpractical. Given a (possibly infeasible) solution to the problem, local search consists in modifying some parts of this one - that is, some decision variables - to reach a new, hopefully better solution. Exploring a so-called neighborhood of the incumbent has a major advantage: the new solution can be evaluated quickly through incremental calculation. Then, local search can be viewed as an incomplete and nondeterministic but efficient way to explore a solution space.

First, an iconoclast methodology is presented to design and engineer local search algorithms. We show that the performance of a local search mainly relies on the richness of the neighborhoods explored, as well as on the efficiency of their exploration. Ultimately, implementing high-performance local search algorithms is a matter of expertise in incremental algorithmics and of dexterity in computer programming. Our concern to industrialize local search approaches shall be of a particular interest for practitioners. As examples, this methodology is applied to solve two industrial problems with high economic stakes.

Nevertheless, software applications based on local search induce extra costs in development and maintenance in comparison with the direct use of mixed-integer linear programming solvers. We present the LocalSolver project whose goal is to offer the power of local search through a model-and-run solver for large-scale 0-1 nonlinear programming. Having outlined its modeling formalism, the main ideas on which LocalSolver relies are described and some benchmarks are presented to assess its performance. We conclude the dissertation by presenting our ongoing and future works on LocalSolver toward a full mathematical programming solver based on neighborhood search.

The dissertation was edited as a monograph:

F. Gardi, T. Benoist, J. Darlay, B. Estellon, R. Megel (2014).
Mathematical Programming Solver based on Local Search.
FOCUS Series in Computer Engineering, ISTE Wiley, 112 pages.
ISBN 9781848216860

The slides of the presentation in French: [slides]

PhD thesis


Title: Mutual exclusion scheduling with interval graphs or related classes: complexity and algorithms.

Date and place of defense: June 14, 2005, at the Luminy Faculty of Sciences, Marseille.

Jury: Keywords: mutual exclusion scheduling, graph coloring, workforce planning, interval graphs, classes of graphs.

Abstract:

The mutual exclusion scheduling problem can be formulated as follows in graph-theoretic terms: given an undirected graph G and an integer k, determine a minimum coloring of G such that each color is used at most k times. When the graph G is an interval graph, this problem has some applications in workforce planning. Then, the subject of this thesis is to detail the complexity of the mutual exclusion scheduling problem for interval graphs and related classes.

The first two chapters of the thesis deal with the complexity of the problem for interval graphs, as well as two extensions, circular-arc graphs and tolerance graphs. When the problem is proved to be polynomial, we propose some simple and efficient algorithms for its resolution (in particular linear time and space algorithms).

Motivated by practical aspects, we also analyse the impact of the following property on the complexity of the problem: the graph G admits a coloring such that each color appears at least k times. We show that if an interval graph satisfies this property, then it admits an optimal partition into n/k stable sets of size at most k which can be computed in linear time and space. Then, this assertion is extended to claw-free graphs, circular-arc graphs, as well as chordal graphs for k <= 4.

The last chapter is devoted to partition problems related to interval graphs. We investigate particularly the problem of partitioning interval ou circular-arc graphs into proper interval subgraphs, for which the following proposition is established: any interval graph admits a partition into less than O( log n) proper interval graphs and this one can be computed in O(n log n + m) time and linear space. This result is used in the design of polynomial approximation algorithms for a workforce planning problem related to mutual exclusion scheduling for interval or circular-arc graphs.

The manuscript in French: [thesis]
The slides of the presentation in French: [slides - ppt] [slides - pdf]

Publications:

The main results of my thesis have been announced in the following note:

F. Gardi (2006).
Mutual exclusion scheduling with interval graphs or related classes: complexity and algorithms.
4OR, A Quarterly Journal of Operations Research 4(1), pp. 87-90. [paper]

From my thesis have been published the 4 following papers which contain some updated proofs:

F. Gardi (2007).
The Roberts characterization of proper and unit interval graphs.
Discrete Mathematics 307(22), pp. 2906-2908. [paper]

F. Gardi (2008).
Mutual exclusion scheduling with interval graphs or related classes. Part II.
Discrete Applied Mathematics 156(5), pp. 794-812. [paper]

F. Gardi (2009).
Mutual exclusion scheduling with interval graphs or related classes. Part I.
Discrete Applied Mathematics 157(1), pp. 19-35. [paper]

F. Gardi (2011).
On partitioning interval graphs into proper interval subgraphs and related problems.
Journal of Graph Theory 68(1), pp. 38-54. [paper]

Education


November, 2013. Habilitation in Computer Science from Sorbonne Université.
Thesis: "Toward a mathematical programming solver based on local search". ISBN 9781848216860
Reviewers: Prof. Michel Gendreau, Prof. Jin-Kao Hao, Dr. Geir Hasle.

June, 2005. Ph.D. in Computer Science from Aix-Marseille Université.
Thesis: "Ordonnancement avec exclusion mutuelle par un graphe d'intervalles ou d'une classe apparentée : complexité et algorithmes". [thesis]
Advisor: Prof. Michel Van Caneghem. Reviewers: Prof. Dominique De Werra, Dr. Frédéric Maffray. Summa cum laude.

June, 2001. M.Sc. in Computer Science from Aix-Marseille Université, major Discrete Structures and Operations Research.
Thesis: "Sur certains problèmes de planification d'horaires de travail". [thesis]
Advisor: Prof. Michel Van Caneghem. Magna cum laude.

June, 2000. B.Sc. in Computer Science from Luminy Faculty of Sciences, Aix-Marseille Université.
Thesis: "Étude de la complexité de quelques variantes de l'algorithme de tri Quicksort". [thesis]
Advisor: Prof. Michel Van Caneghem. Magna cum laude.

Teaching


I started my teaching activities as Assistant Professor at the Luminy Faculty of Sciences of the Aix-Marseille University during my PhD studies. Then, I was qualified to the position of Associate Professor in 2006 by the 27th section of CNU. Despite I pursued a career in industry, I was always concerned by teaching and popularizing the scientific discipline I was involved in. I was invited to talk as part of the operations research and mathematical optimization courses given by: Here is a sample of the courses that I have given (all are in French): Overall, I have completed 1,000 hours of teaching for various student audiences: Bachelor, Master, and Doctoral programs.

Student supervision & mentoring


I have attracted and supervised directly several M.Sc. students during their graduation internship:
Since then, LocalSolver has grown to 30 people, including 25 scientists and engineers, and the team has trained 30 additional Master students. A lot of them have joined us immediately after their graduation. Besides, I have mentored several young deserving students all along their graduate studies, who were awarded a long-term scholarship from the Fondation Francis Bouygues after their baccalaureate: I have attracted and supervised directly or indirectly several Ph.D. students at Bouygues e-lab and LocalSolver:

Academic activities and responsibilities


Here are my main academic memberships:

Below are my main academic duties over the years:
I was part of the program committee of following conferences: I was part of the jury of several Ph.D. thesis:
I was sollicitated as scientific expert by several research institutions to evaluate peer's work and projects : I was co-chair of national conferences: ROADEF 2015 (Marseille, France) and ROADEF 2016 (Compiègne, France). In addition, I was chair of thematic sessions in many in national and international conferences and involved in several panels in charge of awarding prizes for best papers, talks, posters (ROADEF 2012-2019, PGMO 2014-2015, IFAC MIM 2016).

In 2020, I was invited by the Society for Industrial and Applied Mathematics (SIAM) to participate to the Industry Panel entitled "From Applied Mathematicians to Entrepreneurs" in the SIAM Annual Meeting 2020; the video of the interview and the subsequent discussions with the three other panelists can be found here. This event was announced and relayed on several networks related to applied and industrial Mathematics in the US and Europe like the BIG Math Network launched by the Mathematical Association of America for promoting careers in Business, Industry and Government to students and departments of the mathematical sciences in the US, the European Network for Mathematical Technologies (EU-MATHS-IN) to boost mathematics for industry in Europe, and the German Network for Mathematical Modeling, Simulation, and Optimization (KoMSO).

Over the past 15 years, I was a reviewer for several national (JFPC, ROADEF) and international (MIC, Matheuristics, CIE, PGMO-COPI, LAGOS) conferences, and for the following international journals: I was also sollicitated by American Mathematical Society (AMS) to contribute to the Mathematical Reviews: MR2457513, MR2478580, MR2519325, MR2479161, MR2480522, MR2567933.

I participated in the European project IST-2001-35304 AMETIST (Advanced Methods for Timed Systems), for which I have written 5 research reports. In addition to the conferences mentioned above, I was invited to present my works in several research seminars: LIF (Marseille), G-SCOP (Grenoble), Bouygues e-lab (Paris) [slides], LIX (Palaiseau), EDF R&D/OSIRIS (Clamart) [slides].

Last update: December 2023