Skip to main content

Advertisement

Springer Nature Link
Log in

A continuous approach to combinatorial optimization: application of water system pump operations

  • Review Article
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

In this paper, we have suggested a penalty method to modify the combinatorial optimization problem with the linear constraints to a global optimization problem with linear constraints. It also deals with a topic of vital significance of pump operation optimization in a water system. In this connection we have done a lot of work to formulate a model based on a simplified flow volume balance to resolve the problem of optimal pump operation settings of switching “ON” and “OFF” with the reduced gradient method. This global solution approach incorporates some benefits for practical application to a real system as is shown in the case study.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Similar content being viewed by others

References

  1. Acar Y., Kadipasaoglu S.N., Day J.M.: Incorporating uncertainty in optimal decision making: integrating mixed integer programming and simulation to solve combinatorial problems. Comput. Ind. Eng. 56, 106–112 (2009)

    Article  Google Scholar 

  2. Barán B., Lucken C., Soelo A.: Multi-objective pump scheduling optimisation using evolutionary strategies. Adv. Eng. Soft. 36, 39–47 (2005)

    Article  MATH  Google Scholar 

  3. Cunha M., Cunha M.: Tabu search algorithms for water network optimization. Eur. J. Oper. Res. 157, 746–758 (2004)

    Article  MATH  Google Scholar 

  4. El Mouatasim, A.: Stochastic perturbation on global optimization: analyses and application. Ph-D Thesis, Universty of Mohammed V, Engineering Mohammadia School, Rabat-Morocco (2007)

  5. El Mouatasim A., Al-Hossain A.: Reduced gradient method for minimax estimation of a bounded Poisson mean. J. Stat. Adv. Theory Appl. 2(2), 183–197 (2009)

    Google Scholar 

  6. El Mouatasim A., Ellaia R., Souzade Cursi J.E.: Random perturbation of variable metric method for unconstraint nonsmooth nonconvex optimization. Appl. Math. Comput. Sci. 16(4), 463–474 (2006)

    MATH  MathSciNet  Google Scholar 

  7. Glasnovic Z., Margeta J.: A model for optimal sizing of photovoltaic irrigation water pumping systems. Sol. Energy 81, 904–916 (2007)

    Article  Google Scholar 

  8. Ge R., Huang C.: A Continuous approach to nonlinear integer programming. Appl. Math. Comput. 34, 39–60 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  9. Giannessi, F., Niccolucci, F.: Connections between nonlinear and integer programming problems. Istituto Nazionale di Alta Matematica Symposia Mathematica Volume XIX (1976)

  10. Gisvold K.M., Moe J.: A Method for nonlinear mixed integer programming and its application to design problems. J. Eng. Ind. 94(2), 353–364 (1972)

    Article  Google Scholar 

  11. Harjunkoski I., Jain V., Grossmann I.E.: Hybrid mixed-integer/constraint logic programming strategies for solving scheduling and combinatorial optimization problems. Comput. Chem. Eng. 24, 337–343 (2000)

    Article  Google Scholar 

  12. Lauler E.L., Bell M.D.: A Method for solving discrete programming problems. Oper. Res. 14, 1098–1112 (1966)

    Article  Google Scholar 

  13. Loucks D.P., Stedinger J.R., Haith D.A.: Water Resource Systems Planning and Analysis. Prentice-Hall, Englewood Cliffs (1981)

    Google Scholar 

  14. Mays L.W.: Water Distribution Systems Handbook. McGraw-Hill, New York (2000)

    Google Scholar 

  15. Kaanodia K.K., Rizwanullah M.A.: comparative study of simulated vehicle routine problem and LINGO Software solution in LPG distribution system. J. Appl. Math. Stat. Inform. 5(2), 23–38 (2009)

    Google Scholar 

  16. Kasperski, A., Zieliński, P.: Solving combinatorial optimization problem with fuzzy weights. 2008 IEEE International Conference on Fuzzy Systems, pp. 318–323 (2008)

  17. Ormsbee L.E., Lansey K.E.: Optimal control of water supply pumping systems. J. Water. Res. Planing Manag. 120(2), 237–252 (1994)

    Article  Google Scholar 

  18. Pardalos P.M., Prokopyev O.A., Busygin S. et al.: Continuous approaches for solving discrete optimization problems. In: Appa, G. (eds) Handbook on Modelling for Discrete Optimization, pp. 39–60. Springer, New York (2006)

    Google Scholar 

  19. Pulido-Calvo I., Gutiérrez-Estrada J.C., Asensio-Fernández R.: Optimal design of pumping stations of inland intensive fishfarms. Aquac. Eng. 35, 283–291 (2006)

    Article  Google Scholar 

  20. Watters L.: Reduction of integer polynomial programming problems to zero-one linear programming problems. Oper. Res. 15, 1171–1174 (1967)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Jazan University, P.B. 2097, Jazan, Saudi Arabia

    A. El Mouatasim & A. Al-Hossain

  2. Laboratory of Study and Research for Applied Mathematics, Mohammed V University, Engineering Mohammadia School, Rabat, BP. 765, Ibn Sina avenue, Agdal, Morocco

    A. El Mouatasim & R. Ellaia

Authors
  1. A. El Mouatasim
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. R. Ellaia
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. A. Al-Hossain
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to A. El Mouatasim.

Rights and permissions

Reprints and permissions

About this article

Cite this article

El Mouatasim, A., Ellaia, R. & Al-Hossain, A. A continuous approach to combinatorial optimization: application of water system pump operations. Optim Lett 6, 177–198 (2012). https://doi.org/10.1007/s11590-010-0262-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-010-0262-2

Keywords