E. Balas and R. Jeroslow, Canonical cuts on the unit hypercube, SIAM Journal on Applied Mathematics, vol.23, pp.61-69, 1972.
DOI : 10.1137/0123007

P. Belotti, C. Kirches, S. Leyffer, J. Linderoth, J. Luedtke et al., Mixed-integer nonlinear optimization, Acta Numerica, vol.22, pp.1-131, 2013.
DOI : 10.1017/s0962492913000032

P. Bonami, T. Lorenz, . Biegler, G. Andrew-r-conn, I. E. Cornuéjols et al., An algorithmic framework for convex mixed integer nonlinear programs, Discrete Optimization, vol.5, issue.2, pp.186-204, 2008.
DOI : 10.1016/j.disopt.2006.10.011

URL : https://hal.archives-ouvertes.fr/hal-00421753

G. Bonvin, S. Demassey, C. L. Pape, and N. Maïzi, Vincent Mazauric, and Alfredo Samperio. A convex mathematical program for pump scheduling in a class of branched water networks, Applied Energy, vol.185, pp.1702-1711, 2017.

C. Bragalli, D. Claudia, J. Ambrosio, A. Lee, P. Lodi et al., On the optimal design of water distribution networks: a practical minlp approach, Optimization and Engineering, vol.13, issue.2, pp.219-246, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00758043

J. Burgschweiger, B. Gnädig, and M. C. Steinbach, Nonlinear programming techniques for operative planning in large drinking water networks, Open Applied Mathematics Journal, vol.3, pp.14-28, 2009.
DOI : 10.2174/1874114200903010014

URL : http://benthamopen.com/contents/pdf/TOAMJ/TOAMJ-3-14.pdf

J. Burgschweiger, B. Gnädig, and M. C. Steinbach, Optimization models for operative planning in drinking water networks, Optimization and Engineering, vol.10, issue.1, pp.43-73, 2009.
DOI : 10.1007/s11081-008-9040-8

R. Carlson, The correct method of calculating energy savings to justify adjustable-frequency drives on pumps, IEEE Transactions on Industry Applications, vol.36, issue.6, pp.1725-1733, 2000.

, European Commission. 2030 energy strategy, p.18, 2014.

L. Costa, B. De-athayde, H. M. Prata, M. Ramos, and . Castro, A branch-and-bound algorithm for optimal pump scheduling in water distribution networks, Water resources management, vol.30, issue.3, pp.1037-1052, 2016.
DOI : 10.1007/s11269-015-1209-2

D. Claudia and A. Lodi, Mixed integer nonlinear programming tools: an updated practical overview, Annals of Operations Research, vol.204, issue.1, pp.301-320, 2013.

A. Claudia-d'ambrosio, S. Lodi, C. Wiese, and . Bragalli, Mathematical programming techniques in water network optimization, European Journal of Operational Research, vol.243, issue.3, pp.774-788, 2015.

T. Dan, A. Lodi, and P. Marcotte, An Exact Algorithm for a Class of Mixed-Integer Programs with Equilibrium Constraints, 2018.

L. De, L. Perrière, A. Jouglet, A. Nace, and D. Nace, Water planning and management: An extended model for the real-time pump scheduling problem, Advances in hydroinformatics, pp.153-170, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01175797

C. Ambrosio, A. Frangioni, L. Liberti, and A. Lodi, On intervalsubgradient and no-good cuts, Operations Research Letters, vol.38, issue.5, pp.341-345, 2010.

J. Bradley, M. Eck, and . Mevissen, Valve placement in water networks: Mixed-integer non-linear optimization with quadratic pipe friction, 2012.

, An Electricity Market for Germany's Energy Transition (Green Paper), October, 2014.

M. Feldman, Aspects of energy efficiency in water supply systems, The 5th IWA water loss reduction Specialist Conference, pp.85-89, 2009.

B. Geißler, O. Kolb, J. Lang, G. Leugering, A. Martin et al., Mixed integer linear models for the optimization of dynamical transport networks, Mathematical Methods of Operations Research, vol.73, issue.3, pp.339-362, 2011.

B. Ghaddar, J. Naoum-sawaya, A. Kishimoto, N. Taheri, and B. Eck, A lagrangian decomposition approach for the pump scheduling problem in water networks, European Journal of Operational Research, vol.241, issue.2, pp.490-501, 2015.

C. Giacomello, Z. Kapelan, and M. Nicolini, Fast hybrid optimization method for effective pump scheduling, J. Water Resour. Plann. Manage, p.175, 2013.
DOI : 10.1061/(asce)wr.1943-5452.0000239

A. Gleixner, T. Berthold, B. Müller, and S. Weltge, Three enhancements for optimization-based bound tightening, Journal of Global Optimization, vol.67, issue.4, pp.731-757, 2017.
DOI : 10.1007/s10898-016-0450-4

A. M. Gleixner, H. Held, W. Huang, and S. Vigerske, Towards globally optimal operation of water supply networks, Control and Optimization, vol.2, issue.4, pp.695-711, 2012.

. Inc and . Gurobi, Optimization. Gurobi optimizer reference manual, 2016.

W. E. Hart, C. D. Laird, J. Watson, D. L. Woodruff, G. A. Hackebeil et al., Pyomo-optimization modeling in python, vol.67, 2017.
DOI : 10.1007/978-1-4614-3226-5

URL : https://calhoun.nps.edu/bitstream/10945/37919/1/Dimitrov-PyomoReview.pdf

J. Humpola and A. Fügenschuh, A new class of valid inequalities for nonlinear network design problems, Zuse-Institut, 2013.

J. Humpola and F. Serrano, Sufficient pruning conditions for minlp in gas network design, EURO Journal on Computational Optimization, vol.5, issue.1-2, pp.239-261, 2017.

V. Krakowski, E. Assoumou, V. Mazauric, and N. Maïzi, Reprint of feasible path toward 40-100power supply in france by 2050: A prospective analysis, Applied Energy, vol.184, pp.1529-1550, 2016.

E. Kevin, K. Lansey, and . Awumah, Optimal pump operations considering pump switches, Journal of Water Resources Planning and Management, vol.120, issue.1, pp.17-35, 1994.

M. López-ibáñez, T. D. Prasad, and B. Paechter, Ant colony optimization for the optimal control of pumps in water distribution networks, J. Water Resour. Plann. Manage, p.337, 2008.

G. Mackle, G. A. Savic, and G. A. Walters, Application of genetic algorithms to pump scheduling for water supply, First International Conference on Genetic Algorithms in Engineering Systems: Innovations and Applications, pp.400-405, 1995.
DOI : 10.1049/cp:19951082

H. Mala-jetmarova, N. Sultanova, and D. Savic, Lost in optimisation of water distribution systems? a literature review of system operation, Environmental Modelling & Software, vol.93, pp.209-254, 2017.

G. Mccormick and R. Powell, Derivation of near-optimal pump schedules for water distribution by simulated annealing, Journal of the Operational Research Society, vol.55, issue.7, pp.728-736, 2004.
DOI : 10.1057/palgrave.jors.2601718

. Rmm-menke, . Abraham, and . Stoianov, Modeling variable speed pumps for optimal pumpscheduling, World Environmental and Water Resources Congress, pp.199-209, 2016.

R. Menke, E. Abraham, P. Parpas, and I. Stoianov, Demonstrating demand response from water distribution system through pump scheduling, Applied Energy, vol.170, pp.377-387, 2016.
DOI : 10.1016/j.apenergy.2016.02.136

URL : https://doi.org/10.1016/j.apenergy.2016.02.136

R. Menke, E. Abraham, P. Parpas, and I. Stoianov, Exploring optimal pump scheduling in water distribution networks with branch and bound methods, Water Resources Management, pp.1-17, 2016.
DOI : 10.1007/s11269-016-1490-8

URL : https://link.springer.com/content/pdf/10.1007%2Fs11269-016-1490-8.pdf

A. Morsi, B. Geißler, and A. Martin, Mixed integer optimization of water supply networks, Mathematical Optimization of Water Networks, pp.35-54, 2012.
DOI : 10.1007/978-3-0348-0436-3_3

J. Naoum-sawaya, B. Ghaddar, E. Arandia, and B. Eck, Simulation-optimization approaches for water pump scheduling and pipe replacement problems, European Journal of Operational Research, vol.246, issue.1, pp.293-306, 2015.
DOI : 10.1016/j.ejor.2015.04.028

L. Ormsbee, T. Walski, D. Chase, and W. Sharp, Methodology for improving pump operation efficiency, Journal of Water Resources Planning and Management, vol.115, issue.2, pp.148-164, 1989.
DOI : 10.1061/(asce)0733-9496(1989)115:2(148)

E. Lindell, K. E. Ormsbee, and . Lansey, Optimal control of water supply pumping systems, Journal of Water Resources Planning and Management, vol.120, issue.2, pp.237-252, 1994.

J. Nault and F. Papa, Lifecycle assessment of a water distribution system pump, Journal of Water Resources Planning and Management, vol.141, issue.12, 2015.
DOI : 10.1061/(asce)wr.1943-5452.0000546

F. Pecci, E. Abraham, and I. Stoianov, Quadratic head loss approximations for optimisation problems in water supply networks, Journal of Hydroinformatics, vol.19, issue.4, pp.493-506, 2017.
DOI : 10.2166/hydro.2017.080

URL : https://iwaponline.com/jh/article-pdf/19/4/493/391756/jh0190493.pdf

I. Quesada and I. E. Grossmann, An lp/nlp based branch and bound algorithm for convex minlp optimization problems, Computers & chemical engineering, vol.16, pp.937-947, 1992.
DOI : 10.1016/0098-1354(92)80028-8

A. U. Raghunathan, Global optimization of of nonlinear network design, SIAM Journal on Optimization, vol.23, issue.1, pp.268-295, 2013.

Z. Rao and F. Alvarruiz, Use of an artificial neural network to capture the domain knowledge of a conventional hydraulic simulation model, Journal of Hydroinformatics, vol.9, issue.1, pp.15-24, 2007.

L. Rossman and . Epanet, , 2000.

N. V. Sahinidis, Global Optimization of Mixed-Integer Nonlinear Programs, User's Manual, vol.17, 2017.

R. Salgado-castro, Computer modelling of water supply distribution networks using the gradient method, 1988.

. Semo, Single electricity market operator, 2016.

H. Shi and F. You, Energy optimization of water supply system scheduling: Novel minlp model and efficient global optimization algorithm, AIChE Journal, vol.62, issue.12, pp.4277-4296, 2016.
DOI : 10.1002/aic.15332

P. Skworcow, D. Paluszczyszyn, and B. Ulanicki, Pump schedules optimisation with pressure aspects in complex large-scale water distribution systems, Drinking Water Engineering and Science, vol.7, issue.1, pp.53-62, 2014.
DOI : 10.5194/dwesd-7-121-2014

URL : https://www.dora.dmu.ac.uk/bitstream/2086/10505/1/dwes-7-53-2014_published_version.pdf

E. Smith and C. Pantelides, Global optimisation of nonconvex minlps, Computers & Chemical Engineering, vol.21, pp.791-796, 1997.
DOI : 10.1016/s0098-1354(97)00146-4

E. S. Thorsteinsson, Branch-and-check: A hybrid framework integrating mixed integer programming and constraint logic programming, International Conference on Principles and Practice of Constraint Programming (CP'01), vol.2239, pp.16-30, 2001.
DOI : 10.1007/3-540-45578-7_2

E. Todini and S. Pilati, A gradient algorithm for the analysis of pipe networks, Computer Applications in Water Supply: Vol. 1-systems Analysis and Simulation, pp.1-20, 1988.

J. E. Van-zyl, D. A. Savic, and G. A. Walters, Operational optimization of water distribution systems using a hybrid genetic algorithm, J. Water Resour. Plann. Manage, p.160, 2004.

D. Verleye and E. Aghezzaf, Optimising production and distribution operations in large water supply networks: A piecewise linear optimisation approach, International Journal of Production Research, vol.51, pp.7170-7189, 2013.
DOI : 10.1080/00207543.2013.850550

. Thomas-m-walski, J. Downey-brill, . Gessler, C. Ian, R. M. Goulter et al., Battle of the network models: Epilogue, Journal of Water Resources Planning and Management, vol.113, issue.2, pp.191-203, 1987.