Optimization and Engineering

, Volume 20, Issue 2, pp 605–645 | Cite as

Resilient layout, design and operation of energy-efficient water distribution networks for high-rise buildings using MINLP

  • Lena C. Altherr
  • Philipp Leise
  • Marc E. PfetschEmail author
  • Andreas Schmitt
Research Article


Water supply of high-rise buildings requires pump systems to ensure pressure requirements. The design goals of these systems are energy and cost efficiency, both in terms of fixed cost as well as during operation. In this paper, cost optimal decentralized and tree-shaped water distribution networks are computed, where placements of pumps at different locations in the building are allowed. We propose a branch-and-bound algorithm for solving the corresponding mixed-integer nonlinear program, which exploits problem specific structure and outperforms state-of-the-art solvers. A further desirable feature is that the system is K-resilient, i.e., still able to operate under K pump failures during the use phase. Using a characterization of resilient solutions via a system of inequalities, the branch-and-bound scheme is extended by a separation algorithm to produce cost optimal resilient solutions. This implicitly solves a multilevel optimization problem which contains the computation of worst-case failures. Moreover, using a large set of test instances, the increased energy-efficiency of decentralized networks for the supply of building is shown and properties of resilient layouts are discussed.


MINLP Water supply Network Decentralization Resilience Branch-and-bound Pump system Energy-efficiency 



Funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project Number 57157498—SFB 805.


  1. Altherr LC, Brötz N, Dietrich I, Gally T, Geßner F, Kloberdanz H, Leise P, Pelz PF, Schlemmer P, Schmitt A (2018a) Resilience in mechanical engineering—a concept for controlling uncertainty during design, production and usage phase of load-carrying structures. In: Pelz PF, Groche P (eds) Uncertainty in Mechanical Engineering III, Applied Mechanics and Materials, vol 885, pp 187–198Google Scholar
  2. Altherr LC, Leise P, Pfetsch ME, Schmitt A (2018b) Algorithmic design and resilience assessment of energy efficient high-rise water supply systems. In: Pelz PF, Groche P (eds) Uncertainty in Mechanical Engineering III, Applied Mechanics and Materials, vol 885, pp 211–223Google Scholar
  3. Belotti P, Kirches C, Leyffer S, Linderoth J, Luedtke J, Mahajan A (2013) Mixed-integer nonlinear optimization. Acta Numer 22:1–131MathSciNetzbMATHGoogle Scholar
  4. Bienstock D, Verma A (2010) The \(n-k\) problem in power grids: New models, formulations, and numerical experiments. SIAM J Optim 20(5):2352–2380MathSciNetzbMATHGoogle Scholar
  5. Bieupoude P, Azoumah Y, Neveu P (2012) Optimization of drinking water distribution networks: computer-based methods and constructal design. Comput Environ Urban Syst 36(5):434–444Google Scholar
  6. Bonami P, Lodi A, Tramontani A, Wiese S (2015) On mathematical programming with indicator constraints. Math Program 151(1):191–223MathSciNetzbMATHGoogle Scholar
  7. Bonvin G, Demassey S, Le Pape C, Maïzi N, Mazauric V, Samperio A (2017) A convex mathematical program for pump scheduling in a class of branched water networks. Appl Energy 185:1702–1711Google Scholar
  8. Bragalli C, D’Ambrosio C, Lee J, Lodi A, Toth P (2012) On the optimal design of water distribution networks: a practical MINLP approach. Optim Eng 13(2):219–246MathSciNetzbMATHGoogle Scholar
  9. Brkić D (2011) Review of explicit approximations to the Colebrook relation for flow friction. J Petrol Sci Eng 77(1):34–48Google Scholar
  10. Brown G, Carlyle M, Salmerón J, Wood K (2006) Defending critical infrastructure. Interfaces 36(6):530–544Google Scholar
  11. Burgschweiger J, Gnädig B, Steinbach MC (2009) Optimization models for operative planning in drinking water networks. Optim Eng 10(1):43–73MathSciNetzbMATHGoogle Scholar
  12. Chatterjee S, Simonoff JS (2013) Handbook of regression analysis. Wiley, HobokenzbMATHGoogle Scholar
  13. Chen RLY, Cohn A, Fan N, Pinar A (2014) Contingency-risk informed power system design. IEEE Trans Power Syst 29(5):2087–2096Google Scholar
  14. Coelho B, Andrade-Campos A (2014) Efficiency achievement in water supply systems—a review. Renew Sustain Energy Rev 30:59–84Google Scholar
  15. D’Ambrosio C, Lodi A, Wiese S, Bragalli C (2015) Mathematical programming techniques in water network optimization. Eur J Oper Res 243(3):774–788MathSciNetzbMATHGoogle Scholar
  16. Dandy GC, Simpson AR, Murphy LJ (1994) Optimum design and operation of pumped water distribution systems. In: International Conference on hydraulics in civil engineering: “Hydraulics Working with the Environment”. Institution of Engineers, Australia, pp 149–155Google Scholar
  17. De Corte A, Sörensen K (2013) Optimisation of gravity-fed water distribution network design: a critical review. Eur J Oper Res 228(1):1–10MathSciNetzbMATHGoogle Scholar
  18. DIN 1988-500 (2011) Codes of practice for drinking water installations–Part 500: pressure boosting stations with RPM-regulated pumps; DVGW code of practiceGoogle Scholar
  19. DIN 1988-300 (2012) Codes of practice for drinking water installations–Part 300: pipe sizing; DVGW code of practiceGoogle Scholar
  20. Eck BJ, Mevissen M (2012) Valve placement in water networks: Mixed-integer non-linear optimization with quadratic pipe friction. Report no RC25307 (IRE1209-014), IBM ResearchGoogle Scholar
  21. Fischetti M, Ljubi I, Monaci M, Sinnl M (2017) A new general-purpose algorithm for mixed-integer bilevel linear programs. Oper Res 65(6):1615–1637MathSciNetzbMATHGoogle Scholar
  22. Fujiwara O, Khang DB (1990) A two-phase decomposition method for optimal design of looped water distribution networks. Water Resour Res 26(4):539–549Google Scholar
  23. Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, New YorkzbMATHGoogle Scholar
  24. Geißler B, Kolb O, Lang J, Leugering G, Martin A, Morsi A (2011) Mixed integer linear models for the optimization of dynamical transport networks. Math Methods Oper Res 73(3):339–362MathSciNetzbMATHGoogle Scholar
  25. Ghaddar B, Naoum-Sawaya J, Kishimoto A, Taheri N, Eck B (2015) A Lagrangian decomposition approach for the pump scheduling problem in water networks. Eur J Oper Res 241(2):490–501MathSciNetzbMATHGoogle Scholar
  26. Ghidaoui MS, Zhao M, McInnis DA, Axworthy DH (2005) A review of water hammer theory and practice. Appl Mech Rev 58(1):49–76Google Scholar
  27. Gleixner AM, Held H, Huang W, Vigerske S (2012) Towards globally optimal operation of water supply networks. Numer Algebra Control Optim 2(2):695–711MathSciNetzbMATHGoogle Scholar
  28. Gleixner A, Eifler L, Gally T, Gamrath G, Gemander P, Gottwald RL, Hendel G, Hojny C, Koch T, Miltenberger M, Müller B, Pfetsch ME, Puchert C, Rehfeldt D, Schlösser F, Serrano F, Shinano Y, Viernickel JM, Vigerske S, Weninger D, Witt JT, Witzig J (2018) The SCIP optimization suite 5.0. Technical report, optimization onlineGoogle Scholar
  29. Goemans MX, Bertsimas DJ (1993) Survivable networks, linear programming relaxations and the parsimonious property. Math Program 60(1–3):145–166MathSciNetzbMATHGoogle Scholar
  30. Groß T, Pöttgen P, Pelz PF (2017) Analytical approach for the optimal operation of pumps in booster systems. J Water Resour Plann Manag 143(8):04017029Google Scholar
  31. Grötschel M, Monma CL, Stoer M (1995) Design of survivable networks. Handb Oper Res Manag Sci 7:617–672MathSciNetzbMATHGoogle Scholar
  32. Gülich JF (2008) Centrifugal pumps. Springer, BerlinGoogle Scholar
  33. Herrera M, Abraham E, Stoianov I (2016) A graph-theoretic framework for assessing the resilience of sectorised water distribution networks. Water Resour Manag 30(5):1685–1699Google Scholar
  34. Jowitt PW, Germanopoulos G (1992) Optimal pump scheduling in water-supply networks. J Water Resour Plann Manag 118(4):406–422Google Scholar
  35. Kleniati PM, Adjiman CS (2015) A generalization of the branch-and-sandwich algorithm: from continuous to mixed-integer nonlinear bilevel problems. Comput Chem Eng 72:373–386Google Scholar
  36. Kolb O, Lang J (2012) Simulation and continuous optimization. In: Mathematical optimization of water networks. Springer, pp 17–33Google Scholar
  37. Leise P, Altherr LC (2018) Optimizing the design and control of decentralized water supply systems—a case-study of a hotel building. In: International conference on engineering optimization. Springer, pp 1241–1252Google Scholar
  38. Leise P, Altherr LC, Pelz PF (2018) Energy-efficient design of a water supply system for skyscrapers by mixed-integer nonlinear programming. In: Operations research proceedings 2017. Springer, pp 475–481Google Scholar
  39. Lejano RP (2006) Optimizing the layout and design of branched pipeline water distribution systems. Irrig Drain Syst 20(1):125–137Google Scholar
  40. Mala-Jetmarova H, Sultanova N, Savic D (2017) Lost in optimisation of water distribution systems? A literature review of system operation. Environ Model Softw 93:209–254Google Scholar
  41. Meng F, Fu G, Farmani R, Sweetapple C, Butler D (2018) Topological attributes of network resilience: a study in water distribution systems. Water Res 143:376–386Google Scholar
  42. Mitsos A (2010) Global solution of nonlinear mixed-integer bilevel programs. J Global Optim 47(4):557–582MathSciNetzbMATHGoogle Scholar
  43. Morsi A, Geißler B, Martin A (2012) Mixed integer optimization of water supply networks. In: Mathematical optimization of water networks. Springer, pp 35–54Google Scholar
  44. Narayanan I, Sarangan V, Vasan A, Srinivasan A, Sivasubramaniam A, Murt BS, Narasimhan S (2012) Efficient booster pump placement in water networks using graph theoretic principles. In: International green computing conference (IGCC), pp 1–6Google Scholar
  45. Nault J, Papa F (2015) Lifecycle assessment of a water distribution system pump. J Water Resour Plann Manag 141(12):A4015004Google Scholar
  46. Ostfeld A, Tubaltzev A (2008) Ant colony optimization for least-cost design and operation of pumping water distribution systems. J Water Resour Plann Manag 134(2):107–118Google Scholar
  47. Pedersen GK, Yang Z (2008) Efficiency optimization of a multi-pump booster system. In: Proceedings of the 10th annual conference on Genetic and evolutionary computation. ACM, pp 1611–1618Google Scholar
  48. Prasad TD (2009) Design of pumped water distribution networks with storage. J Water Resour Plann Manag 136(1):129–132Google Scholar
  49. Robinius M, Schewe L, Schmidt M, Stolten D, Thürauf J, Welder L (2018) Robust optimal discrete arc sizing for tree-shaped potential networks. Preprint, optimization online,
  50. Rossman LA (2000) EPANET 2 users manual. U.S Environmental Protection Agency, CincinnatiGoogle Scholar
  51. Savic DA, Walters GA (1997) Genetic algorithms for least-cost design of water distribution networks. J Water Resour Plann Manag 123(2):67–77Google Scholar
  52. Shin S, Lee S, Judi DR, Parvania M, Goharian E, McPherson T, Burian SJ (2018) A systematic review of quantitative resilience measures for water infrastructure systems. Water 10(2):164Google Scholar
  53. Skworcow P, Paluszczyszyn D, Ulanicki B (2014) Pump schedules optimisation with pressure aspects in complex large-scale water distribution systems. Drink Water Eng Sci 7:53–62Google Scholar
  54. Spurk J, Aksel N (2008) Fluid mechanics. Springer, BerlinzbMATHGoogle Scholar
  55. Tawarmalani M, Sahinidis NV (2005) A polyhedral branch-and-cut approach to global optimization. Math Program 103:225–249MathSciNetzbMATHGoogle Scholar
  56. Todini E (2000) Looped water distribution networks design using a resilience index based heuristic approach. Urban Water 2(2):115–122Google Scholar
  57. Ulanicki B, Kahler J, Coulbeck B (2008) Modeling the efficiency and power characteristics of a pump group. J Water Resour Plann Manag 134(1):88–93Google Scholar
  58. Varma KVK, Narasimhan S, Bhallamudi SM (1997) Optimal design of water distribution systems using an NLP method. J Environ Eng 123(4):381–388Google Scholar
  59. Verleye D, Aghezzaf EH (2013) Optimising production and distribution operations in large water supply networks: a piecewise linear optimisation approach. Int J Prod Res 51(23–24):7170–7189Google Scholar
  60. Vielma JP, Nemhauser GL (2011) Modeling disjunctive constraints with a logarithmic number of binary variables and constraints. Math Program 128(1–2):49–72MathSciNetzbMATHGoogle Scholar
  61. Wächter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program 106(1):25–57MathSciNetzbMATHGoogle Scholar
  62. Yates D, Templeman A, Boffey T (1984) The computational complexity of the problem of determining least capital cost designs for water supply networks. Eng Optim 7(2):143–155Google Scholar
  63. Yu G, Powell RS, Sterling MJH (1994) Optimized pump scheduling in water distribution systems. J Optim Theory Appl 83(3):463–488MathSciNetzbMATHGoogle Scholar
  64. Zessler U, Shamir U (1989) Optimal operation of water distribution systems. J Water Resour Plann Manag 115(6):735–752Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Lena C. Altherr
    • 1
  • Philipp Leise
    • 1
  • Marc E. Pfetsch
    • 2
    Email author
  • Andreas Schmitt
    • 2
  1. 1.Chair of Fluid Systems, Department of Mechanical EngineeringTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Research Group Optimization, Department of MathematicsTechnische Universität DarmstadtDarmstadtGermany

Personalised recommendations