Water Resources Management

, Volume 22, Issue 7, pp 895–909 | Cite as

Optimizing Hydropower Reservoir Operation Using Hybrid Genetic Algorithm and Chaos

  • Chun-Tian Cheng
  • Wen-Chuan Wang
  • Dong-Mei Xu
  • K. W. Chau


Genetic algorithms (GA) have been widely applied to solve water resources system optimization. With the increase of the complexity and the larger problem scale of water resources system, GAs are most frequently faced with the problems of premature convergence, slow iterations to reach the global optimal solution and getting stuck at a local optimum. A novel chaos genetic algorithm (CGA) based on the chaos optimization algorithm (COA) and genetic algorithm (GA), which makes use of the ergodicity and internal randomness of chaos iterations, is presented to overcome premature local optimum and increase the convergence speed of genetic algorithm. CGA integrates powerful global searching capability of the GA with that of powerful local searching capability of the COA. Two measures are adopted in order to improve the performance of the GA. The first one is the adoption of chaos optimization of the initialization to improve species quality and to maintain the population diversity. The second is the utilization of annealing chaotic mutation operation to replace standard mutation operator in order to avoid the search being trapped in local optimum. The Rosenbrock function and Schaffer function, which are complex and global optimum functions and often used as benchmarks for contemporary optimization algorithms for GAs and Evolutionary computation, are first employed to examine the performance of the GA and CGA. The test results indicate that CGA can improve convergence speed and solution accuracy. Furthermore, the developed model is applied for the monthly operation of a hydropower reservoir with a series of monthly inflow of 38 years. The results show that the long term average annual energy based CGA is the best and its convergent speed not only is faster than dynamic programming largely, but also overpasses the standard GA. Thus, the proposed approach is feasible and effective in optimal operations of complex reservoir systems.


Chaos Genetic algorithm Optimization Hydropower system 


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  1. Ahmed JA, Sarma AK (2005) Genetic Algorithm for optimal operating policy of a multipurpose reservoir. Water Resour Manag 19(2):145–161CrossRefGoogle Scholar
  2. Chang L-C, Chang F-J (2001) Intelligent control for modeling of real time reservoir operation. Hydrol Process 15(9):1621–1634CrossRefGoogle Scholar
  3. Chang F-J, Lai J-S, Kao L-S (2003) Optimization of operation rule curves and flushing schedule in a reservoir. Hydrol Process 17(8):1623–1640CrossRefGoogle Scholar
  4. Chang J-X, Huang Q, Wang Y-M (2005a) Genetic algorithms for optimal reservoir dispatching. Water Resour Manag 19(4):321–331CrossRefGoogle Scholar
  5. Chang F-J, Chen L, Chang L-C (2005b) Optimizing the reservoir operating rule curves by genetic algorithms. Hydrol Process 19(11):2277–2289CrossRefGoogle Scholar
  6. Chau KW, Albermani F (2003) Knowledge-based system on optimum design of liquid retaining structures with genetic algorithms. J Struct Engi ASCE 129(10):1312–1321CrossRefGoogle Scholar
  7. Cheng C-T, Ou C-P, Chau KW (2002) Combining a fuzzy optimal model with a genetic algorithm to solve multiobjective rainfall-runoff model calibration. J Hydrol 268(1–4):72–86CrossRefGoogle Scholar
  8. Cheng C-T, Wu X-Y, Chau KW (2005) Multiple criteria rainfall-runoff model calibration using a parallel genetic algorithm in a cluster of computer. Hydrol Sci J 50(6):1069–1088CrossRefGoogle Scholar
  9. Cheng C-T, Zhao M-Y, Chau KW, Wu X-Y (2006). Using Genetic Algorithm and TOPSIS for xinanjing model calibration with a single procedure. J Hydrol 316(1–4):129–140CrossRefGoogle Scholar
  10. Goldberg DE (1989) Genetic algorithm in search, optimization and machine learning. Addison-Wesley Publishing Co., Inc., Reading, MAGoogle Scholar
  11. Labadie JW (2004) Optimal operation of multireservoir systems: State-of-the-art review. J Water Resour Plan Manage 130(2):93–111CrossRefGoogle Scholar
  12. Li B, Jiang W-S (1998) Optimizing complex functions by chaos search. Cybern Syst 29(4):409–419CrossRefGoogle Scholar
  13. Liao G-C (2006) Hybrid chaos search genetic algorithm and meta-heuristics method for short-term load forecasting. Electr Eng 88(3):265–276CrossRefGoogle Scholar
  14. Lü Q-Z, Shen G-L, Yu R-Q (2003) A chaotic approach to maintain the population diversity of genetic algorithm in network training. Computational Biology and Chemistry 27(3):363–371CrossRefGoogle Scholar
  15. May RM (1976) Simple mathematical models with very complicated dynamics. Nature 261:459–467CrossRefGoogle Scholar
  16. Oliveira R, Loucks DP (1997) Operating rules for multireservoir systems. Water Resour Res 33(4):839–852CrossRefGoogle Scholar
  17. Ohya M (1998) Complexities and their applications to characterization of chaos. Int J Theor Phys 37(1):495–505CrossRefGoogle Scholar
  18. Reis LFR, Walters GA, Savic D, Chaudhry FH (2005) Multi-reservoir operation planning using hybrid genetic algorithm and linear programming (GA-LP): An alternative stochastic approach. Water Resour Manag 19(6):831–848CrossRefGoogle Scholar
  19. Rosenbrock HH (1960) An automatic method for finding the greatest or least value of a function. Comput J 3:175–184CrossRefGoogle Scholar
  20. Sharif M, Wardlaw R (2000) Multireservoir systems optimization using genetic algorithm: Case study. J Comput Civ Eng 14(4):255–263CrossRefGoogle Scholar
  21. Siarry P, Petrowski A, Bessaou M (2002) A multipopulation genetic algorithm aimed at multimodal optimization. Adv Eng Softw 33(4):207–213CrossRefGoogle Scholar
  22. Wardlaw R, Sharif M (1999) Evaluation of genetic algorithms for optimal reservoir system operation. J Water Resour Plan Manage 125(1):25–33CrossRefGoogle Scholar
  23. Wang Z, Zhang T, Wang H (1999) Simulated annealing algorithm based on chaotic variable. Control and Decision 14(4):381–384Google Scholar
  24. Wurbs RA (1993) Reservoir-system simulation and optimization models. J Water Resour Plan Manage 119(4):455–472CrossRefGoogle Scholar
  25. Yeh WW-G (1985) Reservoir management and operation models: a state-of-the-art review. Water Resour Res 21(12):1797-1818CrossRefGoogle Scholar
  26. Wei G (2004) Fast immunized evolutionary programming. Evolutionary Computation 2004, CEC2004, Congress, 666–670Google Scholar
  27. Yan X, Chen D, Hu S (2003) Chaos-genetic algorithms for optimizing the operating conditions based on RBF-PLS model. Comput Chem Eng 27(10):1393–1404CrossRefGoogle Scholar
  28. Yuan X, Yuan Y, Zhang Y (2002) A hybrid chaotic genetic algorithm for short-term hydro system scheduling. Math Comput Simul 59(4):319–327CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  • Chun-Tian Cheng
    • 1
  • Wen-Chuan Wang
    • 1
  • Dong-Mei Xu
    • 2
  • K. W. Chau
    • 3
  1. 1.Institute of Hydropower System & HydroinformaticsDalian University of TechnologyDalianPeople’s Republic of China
  2. 2.Department of Water ConservancyNorth China Institute of Water Conservancy and Hydroelectric PowerZhengZhouPeople’s Republic of China
  3. 3.Department of Civil and Structural EngineeringHong Kong Polytechnic UniversityKowloonHong Kong

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