E. Alba, J. Parallel, J. Alliot, N. Bosc, L. Durand et al., CATS : A complete Air Traffic Simulator. 16th Digital Avionics Systems Conference, Finding and Proving the Optimum : Cooperative Stochastic and Deterministic Search. 20th European Conference on Artificial Intelligence, pp.66-116, 1997.

J. Alliot, J. Gotteland, C. Vanaret, N. Durand, D. Gianazza et al., Implementing an interval computation library for OCaml on x86 Affine arithmetic. Interval 94 Exploiting monotonicity in interval constraint propagation, Proceedings of the 17th ACM SIGPLAN International Conference on Functional Programming Proc. AAAIAraya 12] Ignacio Araya, Gilles Trombettoni et Bertrand Neveu. A contractor based on convex interval taylor. Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems, pp.29-34, 1994.

E. Baumann, P. Belotti, J. Lee, L. Liberti, F. Margot et al., Optimal centered forms, CLP(Intervals) Revisited. ILPS, pp.80-87, 1988.
DOI : 10.1007/BF01934696

F. Benhamou, F. Goualard, L. Granvilliers, J. Benhamou-et-frédéric-goualard, J. Blum et al., Universally quantified interval constraints. Principles and Practice of Constraint Programming? CP Hybrid metaheuristics in combinatorial optimization : A surveyBrönnimann 06] Hervé Brönnimann, Guillaume Melquiond et Sylvain Pion. The design of the Boost interval arithmetic library, International Conference on Logic ProgrammingCafieri 10] S. Cafieri, P. Brisset et N. Durand. A mixed-integer optimization model for air traffic deconfliction. Proceedings of the Toulouse Global Optimization Workshop, pp.230-244, 1999.

O. Caprani and K. Madsen, Mean value forms in interval analysis Cité p, Gilles Chabert et Luc Jaulin. Hull consistency under monotonicity. Principles and Practice of Constraint Programming-CP 2009, pp.147-154, 1980.

G. John and . Cleary, Logical arithmetic, Future Computing Systems, vol.2, pp.125-149, 1987.

H. Collavizza, F. Delobel, and M. Rueher, Comparing partial consistencies Reliable computing, pp.213-228, 1999.
DOI : 10.1007/978-94-017-1247-7_17
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.8787

H. Collavizza, F. Delobel, and M. Rueher, Extending consistent domains of numeric CSP, IJCAI, vol.99, pp.406-413, 1993.

J. Luiz, D. Comba, J. Stolfi, J. Aldana, A. Nebro et al., Affine Arithmetic and its Applications to Computer Graphics Hybridizing genetic algorithms with branch and bound techniques for the resolution of the TSP, Proceedings of SIBGRAPI'93 - VI Simpósio Brasileiro de Computação Gráfica e Processamento de Imagens Artificial Neural Nets and Genetic Algorithms, pp.9-18, 1993.

. Springer, Cotta 03] Carlos Cotta et José M Troya. Embedding branch and bound within evolutionary algorithms, Applied Intelligence, vol.18, issue.2, pp.68-137, 1995.

T. Csendes and D. Ratz, Subdivision Direction Selection in Interval Methods for Global Optimization, SIAM Journal on Numerical Analysis, vol.34, issue.3, pp.922-938, 1997.
DOI : 10.1137/S0036142995281528

L. Henrique-de-figueiredo, R. Van-iwaarden, and J. Stolfi, Fast interval branch-and-bound methods for unconstrained global optimization with affine arithmetic, p.160, 1997.

C. Delahaye, M. Peyronne, and . Mongeau, Aircraft Conflict Resolution by Genetic Algorithm and B-Spline Approximation, Proceedings of ENRI Int. Workshop on ATM/CNS, pp.113-114, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00956473

K. Du and . Baker-kearfott, The cluster problem in multivariate global optimization, Journal of Global Optimization, vol.9, issue.3, pp.253-265, 1994.
DOI : 10.1007/BF01096455

N. Durand, J. M. Alliot, and J. Noailles, Automatic aircraft conflict resolution using genetic algorithms, Proceedings of the 1996 ACM symposium on Applied Computing , SAC '96, pp.113-141, 1996.
DOI : 10.1145/331119.331195
URL : https://hal.archives-ouvertes.fr/hal-00937685

N. Durand, J. Alliot, and G. Granger, FACES : a Free flight Autonomous and Coordinated Embarked Solver, ATC Quarterly, p.113, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00937980

H. Feltl, R. Günther, . Feo, G. Mauricio, and . Resende, An improved hybrid genetic algorithm for the generalized assignment problem A probabilistic heuristic for a computationally difficult set covering problem, Proceedings of the 2004 ACM symposium on Applied computing, pp.990-995, 1989.

E. José, C. Gallardo, . Cotta, J. Antonio, and . Fernández, On the hybridization of memetic algorithms with branch-and-bound techniques, Systems, Man, and Cybernetics Part B : Cybernetics IEEE Transactions on, vol.37, issue.1, pp.77-83, 2007.

M. David and . Gay, Bounds from Slopes Rapport technique, Sandia National Laboratories Using Expression Graphs in Optimization Algorithms, Mixed Integer Nonlinear Programming, pp.155-247, 2010.

F. Glover, Tabu Search: A Tutorial, Interfaces, vol.20, issue.4, pp.74-94, 1990.
DOI : 10.1287/inte.20.4.74

E. David, J. Goldberg, and . Richardson, Genetic algorithms with sharing for multimodal function optimization. Genetic algorithms and their applications, Proceedings of the Second International Conference on Genetic Algorithms, pp.41-49, 1987.

E. David and . Goldberg, Genetic algorithms in search, optimization and machine learning, p.18, 1989.

D. Goldberg, What every computer scientist should know about floating-point arithmetic, ACM Computing Surveys, vol.23, issue.1, pp.5-48, 1991.
DOI : 10.1145/103162.103163

A. Goldsztejn, C. Michel, R. Michel-rueher-eldon, and . Hansen, On solving systems of equations using interval arithmetic, Goualard 03] Frédéric Goualard. Gaol, Not Just Another Interval Library, pp.117-135, 1968.

P. Hansen, J. Lagouanelle, and F. Messine, Comparison Between Baumann and Admissible Simplex Forms in Interval Analysis, Journal of Global Optimization, vol.30, issue.4, pp.215-228, 2007.
DOI : 10.1007/s10898-006-9045-9

J. Richard, M. R. Hanson, P. Hoare, J. H. Pal, and . Holland, Physical cluster mechanics : Statics and energy surfaces for monatomic systems Adaptation in natural and artificial systems, Jet Propulsion Laboratory report Advances in Physics, vol.197, issue.20 84, pp.30-161, 1968.

R. Hooke, A. To, Y. Jeeves, and . Fujii, `` Direct Search'' Solution of Numerical and Statistical Problems, Journal of the ACM, vol.8, issue.2, pp.212-229, 1961.
DOI : 10.1145/321062.321069

D. R. Isaacson and H. Erzberger, Design of a conflict detection algorithm for the Center/TRACON automation system, 16th DASC. AIAA/IEEE Digital Avionics Systems Conference. Reflections to the Future. Proceedings, p.113, 1997.
DOI : 10.1109/DASC.1997.637306

]. J. Jones, On the Determination of Molecular Fields. I. From the Variation of the Viscosity of a Gas with Temperature, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.106, issue.738, pp.441-462, 1924.
DOI : 10.1098/rspa.1924.0081

]. Jourdan, M. Basseur, and E. Talbi, Hybridizing exact methods and metaheuristics: A taxonomy, European Journal of Operational Research, vol.199, issue.3, pp.620-629, 2009.
DOI : 10.1016/j.ejor.2007.07.035
URL : https://hal.archives-ouvertes.fr/inria-00484922

W. Kahan, A more complete interval arithmetic. Lecture notes for a summer course at the University of Michigan, p.30, 1968.

L. Kang, Z. Kang, Y. Li, . Hugo, and . Garis, A Two Level Evolutionary Modeling System For Financial Data, GECCO, pp.1113-1118, 2002.

W. Karush, Minima of functions of several variables with inequalities as side constraints, p.8, 1939.

]. R. Kearfott-96a, . Baker, and . Kearfott, Einschlie??ungen nicht-glatter Funktionen f??r Codes zur globalen Optimierung und zur L??sung nichtlinearer Systeme, Computing, vol.20, issue.2, pp.57-149, 1996.
DOI : 10.1007/BF02276877

. Kearfott-96b-]-r-baker and . Kearfott, Rigorous global search : continuous problems, pp.73-92, 1996.

R. Baker, K. Et-siriporn, and . Hongthong, Validated linear relaxations and preprocessing : some experiments, SIAM Journal on Optimization, vol.16, issue.2, pp.418-433, 2005.

J. Kennedy and R. Eberhart, Particle swarm optimization, Proceedings of ICNN'95, International Conference on Neural Networks, pp.1942-1948, 1995.
DOI : 10.1109/ICNN.1995.488968

S. Kirkpatrick, . Daniel-gelatt, P. Mario, and . Vecchi, Optimization by Simulated Annealing, Science, vol.220, issue.4598, pp.671-680, 1983.
DOI : 10.1126/science.220.4598.671

O. Knüppel and . Profil, PROFIL/BIAS???Eine schnelle Intervallbibliothek, Computing, vol.5, issue.3-4, pp.277-287, 1994.
DOI : 10.1007/BF02307379

V. Lubomir and . Kolev, Use of interval slopes for the irrational part of factorable functions, Reliable Computing, vol.3, issue.1, pp.83-93, 1997.

R. Krawczyk and K. Nickel, The centered form in interval arithmetics: Quadratic convergence and inclusion isotonicity, Computing, vol.14, issue.2, pp.117-137, 1982.
DOI : 10.1007/BF02241818

R. Krawczyk and A. Neumaier, Interval Slopes for Rational Functions and Associated Centered Forms, SIAM Journal on Numerical Analysis, vol.22, issue.3, pp.604-616, 1985.
DOI : 10.1137/0722037

J. Lagouanelle and G. Soubry, Optimal Multisections in Interval Branch-and-Bound Methods of Global Optimization, Journal of Global Optimization, vol.30, issue.1, pp.23-38, 2004.
DOI : 10.1023/B:JOGO.0000049095.55259.61

L. Eugene, . Lawler, E. David, ]. R. Wood, and . Leary, Branch-and-bound methods : A survey Global Optima of Lennard-Jones Clusters, Operations research J. of Global Optimization, vol.14, issue.11 1, pp.699-719, 1966.

C. Lebbah-05a-]-yahia-lebbah, M. Michel, and . Rueher, Efficient pruning technique based on linear relaxations. Global Optimization and Constraint Satisfaction, pp.1-14, 2005.

C. Lebbah-05b-]-yahia-lebbah, M. Michel, D. Rueher, J. Daney, and . Merlet, Efficient and Safe Global Constraints for Handling Numerical Constraint Systems, SIAM Journal on Numerical Analysis, vol.42, issue.5, pp.2076-2097, 2005.
DOI : 10.1137/S0036142903436174

M. Lerch, G. Tischler, J. Wolff-von-gudenberg, W. Hofschuster, and W. Krämer, FILIB++ Interval Library, p.28, 2001.

M. Locatelli and F. Schoen, Efficient Algorithms for Large Scale Global Optimization : Lennard-Jones Clusters, Computational Optimization and Applications, vol.26, issue.2, pp.173-190, 2003.
DOI : 10.1023/A:1025798414605

K. Alan and . Mackworth, Consistency in networks of relations, Artificial intelligence, vol.8, issue.1, pp.99-118, 1977.

G. Stuart and . Mentzer, LP-form inclusion functions for global optimization, Computers & Mathematics with Applications, vol.21, issue.6, pp.51-65, 1991.

F. Frédéric-messine, J. Messine, and . Lagouanelle, Enclosure methods for multivariate differentiable functions and application to global optimization Cité p. 157 [Messine 02] Frédéric Messine. Extensions of Affine Arithmetic : Application to Unconstrained Global Optimization Cité p. 159, 160 [Michalewicz 96a] Zbigniew Michalewicz. Genetic algorithms + data structures = evolution programs Evolutionary algorithms for constrained parameter optimization problems, Michalewicz 96b] Zbigniew Michalewicz et Marc SchoenauerMicrosystems 01] SUN Microsystems. C++ interval arithmetic programming manual, pp.37-50, 1996.

S. Mimram, ]. S. Mishra-]-r, and . Moore, Some new test functions for global optimization and performance of repulsive particle swarm method Interval analysis, pp.75-98, 1966.

E. Ramon and . Moore, On computing the range of a rational function of n variables over a bounded region, Memetic algorithms . New optimization techniques in engineering, pp.1-15, 1976.

A. John, R. Nelder, and . Mead, A simplex method for function minimization . The computer journal, pp.308-313, 1965.

A. Neumaier, Interval methods for systems of equations, p.157, 1990.
DOI : 10.1017/CBO9780511526473

A. Neumaier and O. Shcherbina, Safe bounds in linear and mixedinteger linear programming, Mathematical Programming, pp.283-296, 2004.

A. Neumaier, O. Shcherbina, W. Huyer, and T. Vinkó, A comparison of complete global optimization solvers, Mathematical Programming, vol.99, issue.2, pp.335-356, 2005.
DOI : 10.1007/s10107-005-0585-4

J. Ninin, Optimisation Globale basée sur l'Analyse d'Intervalles : Relaxation Affine et Limitation de la Mémoire, p.160, 2010.

J. Ninin, P. Hansen, and F. Messine, A reliable affine relaxation method for global optimization. Groupe d'études et de recherche en analyse des décisions, pp.61-73, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01194735

J. A. Northby, ???147, The Journal of Chemical Physics, vol.87, issue.10, pp.6166-6177, 1987.
DOI : 10.1063/1.453492

B. João and . Oliveira, New slope methods for sharper interval functions and a note on Fischer's acceleration method, Reliable Computing, vol.2, issue.3, pp.299-320, 1996.

L. Pallottino, E. Feron, and A. Bicchi, Conflict resolution problems for air traffic management systems solved with mixed integer programming, IEEE Transactions on Intelligent Transportation Systems, vol.3, issue.1, pp.113-114, 2002.
DOI : 10.1109/6979.994791

J. Pohl, V. Jirsík, and P. Honzík, Stochastic Optimization Algorithm with Probability Vector in Mathematical Function Minimization and Travelling Salesman Problem, WSEAS Trans. Info. Sci. and App, vol.7, pp.975-984, 2010.

K. Price, R. Storn, and J. Lampinen, Differential evolution -a practical approach to global optimization. Natural Computing, pp.17-25, 2006.

J. Puchinger, R. Günther, and . Raidl, Combining metaheuristics and exact algorithms in combinatorial optimization : A survey and classification . Artificial intelligence and knowledge engineering applications : a bioinspired approach, pp.41-53, 2005.
URL : https://hal.archives-ouvertes.fr/hal-01299565

R. Günther and . Raidl, A unified view on hybrid metaheuristics, Hybrid Metaheuristics, pp.1-12, 2006.

D. Ratz, An optimized interval slope arithmetic and its application, Citeseer, p.154, 1996.

N. Revol and F. Rouillier, Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library, Reliable Computing, vol.2, issue.3, p.28, 2002.
DOI : 10.1007/s11155-005-6891-y
URL : https://hal.archives-ouvertes.fr/inria-00544998

T. Rogalsky, S. Kocabiyik, and R. Derksen, Differential evolution in aerodynamic optimization, Canadian Aeronautics and Space Journal, vol.46, issue.88, pp.183-190, 2000.

S. M. Rump, Algorithms for verified inclusions -theory and practice. Reliability in computing, pp.109-126, 1988.

]. S. Rump-96 and . Rump, Expansion and estimation of the range of nonlinear functions, Mathematics of Computation, vol.65, issue.216, pp.1503-1512, 1996.
DOI : 10.1090/S0025-5718-96-00773-9

S. Hong, . Ryoo, V. Nikolaos, and . Sahinidis, Global optimization of nonconvex NLPs and MINLPs with applications in process design, Computers & Chemical Engineering, vol.19, issue.5, pp.551-566, 1995.

A. Neumaier, Interval analysis on directed acyclic graphs for global optimization, Journal of Global Optimization, vol.33, issue.4, pp.541-562, 2005.

M. Schnurr, Computing slope enclosures by exploiting a unique point of inflection, Applied Mathematics and Computation, vol.204, issue.1, pp.249-256, 2008.
DOI : 10.1016/j.amc.2008.06.041

S. Skelboe, Computation of rational interval functions, BIT, vol.11, issue.1, pp.87-95, 1974.
DOI : 10.1007/BF01933121

]. N. Sloane, R. H. Hardin, T. D. Duff, and J. H. Conway, Minimal-energy clusters of hard spheres, Discrete & Computational Geometry, vol.133, issue.107, pp.237-259, 1995.
DOI : 10.1007/BF02570704

A. Slowik and M. Bialko, Training of artificial neural networks using differential evolution algorithm. Human System Interactions, Conference on, pp.60-65, 2008.

D. Sotiropoulos, E. Stavropoulos, and M. Vrahatis, A new hybrid genetic algorithm for global optimization. Nonlinear Analysis : Theory, Methods & Applications, vol.30, issue.7, pp.4529-4538, 1997.

D. Sotiropoulos and T. Grapsa, Optimal centers in branch-and-prune algorithms for univariate global optimization, Applied Mathematics and Computation, vol.169, issue.1, pp.247-277, 2005.
DOI : 10.1016/j.amc.2004.10.050

J. Stolfi-et-luiz-henrique-de and . Figueiredo, Self-Validated Numerical Methods and Applications, Monograph for 21st Brazilian Mathematics Colloquium, p.159, 1997.

R. Storn and K. Price, Differential Evolution -A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces, Journal of Global Optimization, pp.341-359, 1997.

E. Talbi, A taxonomy of hybrid metaheuristics, Journal of Heuristics, vol.8, issue.5, pp.541-564, 2002.
DOI : 10.1023/A:1016540724870

E. Talbi, Metaheuristics : from design to implementation, p.17, 2009.
DOI : 10.1002/9780470496916
URL : https://hal.archives-ouvertes.fr/hal-00750681

J. Tao and N. Wang, DNA computing based RNA genetic algorithm with applications in parameter estimation of chemical engineering processes, Computers & Chemical Engineering, vol.31, issue.12, pp.1602-1618, 2007.
DOI : 10.1016/j.compchemeng.2007.01.012

B. Tóth and T. Csendes, Empirical investigation of the convergence speed of inclusion functions in a global optimization context Reliable Computing Constructive interval disjunction . Principles and Practice of Constraint Programming?CP, pp.253-273, 2005.

G. Trombettoni, I. Araya, B. Neveu, and G. Chabert, Inner Regions and Interval Linearizations for Global Optimization, p.73, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00648085

C. Vanaret, D. Gianazza, N. Durand, and J. Gotteland, Benchmarking conflict resolution algorithms, 5th International Conference on Research in Air Transportation, p.114
URL : https://hal.archives-ouvertes.fr/hal-00863090

C. Vanaret, J. Gotteland, N. Durand, and J. Alliot, Preventing Premature Convergence and Proving the Optimality in Evolutionary Algorithms, International Conference on Artificial Evolution, pp.84-94, 2013.
DOI : 10.1007/978-3-319-11683-9_3
URL : https://hal.archives-ouvertes.fr/hal-00880716

C. Vanaret, J. Gotteland, and N. Durand, Nouvelle formulation pour la résolution de conflits aériens. 15ème congrès annuel de la Société française de recherche opé rationnelle et d'aide à la décision, pp.2014-129, 2014.

]. Vinkó, J. Lagouanelle, and T. Csendes, A New Inclusion Function for Optimization: Kite ? The One Dimensional Case, Journal of Global Optimization, vol.14, issue.4, pp.435-456, 1997.
DOI : 10.1007/s10898-004-8430-5

J. David, J. P. Wales, and . Doye, Global Optimization by Basin- Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms, The Journal of Physical Chemistry A, vol.101, issue.28, pp.5111-5116, 1997.

D. Whitley, K. Mathias, S. Rana, and J. Dzubera, Evaluating evolutionary algorithms, Artificial Intelligence, vol.85, issue.1-2, pp.245-276, 1996.
DOI : 10.1016/0004-3702(95)00124-7

K. Yamamura and S. Tanaka, Finding all solutions of systems of nonlinear equations using the dual simplex methodYin 93] Xiaodong Yin et Noel Germay. A fast genetic algorithm with sharing scheme using cluster analysis methods in multimodal function optimization, Artificial neural nets and genetic algorithms, pp.214-230, 2002.
DOI : 10.1023/A:1021938622923

X. Zhang and S. Liu, A new interval-genetic algorithm. Natural Computation, Third International Conference on, pp.193-197, 2007.

S. Zuhe, A. Michael, and . Wolfe, On interval enclosures using slope arithmetic, Applied Mathematics and Computation, vol.39, issue.1, pp.89-105, 1990.
DOI : 10.1016/0096-3003(90)90124-L