Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Improved Understanding on the Searching Behavior of NSGA-II Operators Using Run-Time Measure Metrics with Application to Water Distribution System Design Problems


In recent years, multi-objective evolutionary algorithms (MOEAs) have been widely used to handle various water resources problems. One challenge within MOEAs’ applications is a lack of understanding on how various operators alter a MOEA’s behavior to achieve its final performance (i.e., MOEAs are black-boxes to practitioners), and hence it is difficult to select the most appropriate operators to ensure the MOEA’s best performance for a given real-world problem. To address this issue, this study proposes the use of the run-time measure metrics to reveal the underlying searching behavior of the MOEA’s operators. The proposed methodology is demonstrated by the non-dominated sorting genetic algorithm II (NSGA-II, a widely used MOEA in water resources) with five commonly used crossover operators applied to six water distribution system design problems. Results show that the simulated binary crossover (SBX) and the simplex crossover (SPX) operators possess great ability in extending the front and finding Pareto-front solutions, respectively, while the naive crossover (NVX) strategy exhibits the overall worst performance in identifying optimal fronts. The obtained understanding on the operators’ searching behavior not only offers guidance for selecting appropriate operators for real-world water resources problems, but also builds fundamental knowledge for developing more advanced MOEAs in future.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7


  1. Artita KS, Kaini P, Nicklow JW (2013) Examining the possibilities: generating alternative watershed-scale BMP designs with evolutionary algorithms. Water Resour Manag 27(11):3849–3863

  2. Bi W, Dandy GC, Maier HR (2015) Improved genetic algorithm optimization of water distribution system design by incorporating domain knowledge. Environ Model Softw 69(0):370–381

  3. Chau KW, Wu CL (2010) A hybrid model coupled with singular spectrum analysis for daily rainfall prediction. J Hydroinf 12(4):458–473

  4. Chen XY, Chau KW, Busari AO (2015) A comparative study of population-based optimization algorithms for downstream river flow forecasting by a hybrid neural network model. Eng Appl Artif Intell 46(PA):258–268

  5. Deb K, Agrawal RB (2000) Simulated binary crossover for continuous search space. Comput Syst 9(3):1–15

  6. Deb K, Pratap A, Agarwal S, Meyarivan T (2002a) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

  7. Deb K, Anand A, Joshi D (2002b) A computationally efficient evolutionary algorithm for real-parameter optimization. Evol Comput 10(4):371–395

  8. Gholami V, Chau KW, Fadaee F, Torkaman J, Ghaffari A (2015) Modeling of groundwater level fluctuations using dendrochronology in alluvial aquifers. J Hydrol 529:1060–1069

  9. Hadka D, Reed P (2012) Diagnostic assessment of search controls and failure modes in many-objective evolutionary optimization. Evol Comput 20(3):423–452

  10. Higuchi, T., Tsutsui, S. and Yamamura, M. (2000). Theoretical analysis of simplex crossover for real-coded genetic algorithms. Proceedings of the 6th International Conference on Parallel Problem Solving from Nature, pp. 365–374

  11. Karamouz M, Nazif S, Sherafat MA, Zahmatkesh Z (2014) Development of an optimal reservoir operation scheme using extended evolutionary computing algorithms based on conflict resolution approach: a case study. Water Resour Manag 28(11):3539–3554

  12. Kollat JB, Reed PM (2007) A computational scaling analysis of multiobjective evolutionary algorithms in long-term groundwater monitoring applications. Adv Water Resour 30(3):408–419

  13. Maier HR et al (2014) Evolutionary algorithms and other metaheuristics in water resources: current status, research challenges and future directions. Environ Model Softw 62:271–299

  14. Nicklow J, Reed P, Savic D, Dessalegne T, Harrell L, Chan-Hilton A, Karamouz M, Minsker B, Ostfeld A, Singh A (2010) State of the art for genetic algorithms and beyond in water resources planning and management. J Water Resour Plan Manag 136(4):412–432

  15. Ono, I. and Kobayashi, S. (1997). A real coded genetic algorithm for function optimization using unimodal normal distributed crossover. Proceedings of the 7th International Conference on Genetic Algorithms, East Lansing, MI, USA, July 19–23, 1997, pp. 246–253

  16. Taormina R, Chau KW (2015) Data-driven input variable selection for rainfall–runoff modeling using binary-coded particle swarm optimization and extreme learning machines. J Hydrol 529:1617–1632

  17. Wang WC, Chau KW, Xu DM, Chen XY (2015a) Improving forecasting accuracy of annual runoff time series using ARIMA based on EEMD decomposition. Water Resour Manag 29(8):2655–2675

  18. Wang Q, Guidolin M, Savic D, Kapelan Z (2015b) Two-objective design of benchmark problems of a water distribution system via MOEAs: towards the best-known approximation of the true Pareto front. J Water Resour Plan Manag 141(3):04014060

  19. Yazdi J (2016) Decomposition based multi objective evolutionary algorithms for Design of Large-Scale Water Distribution Networks. Water Resour Manag 30(8):2749–2766

  20. Zecchin AC, Simpson AR, Maier HR, Marchi A, Nixon JB (2012) Improved understanding of the searching behavior of ant colony optimization algorithms applied to the water distribution design problem. Water Resour Res 48(9):W09505

  21. Zheng F, Zecchin A, Simpson A (2013) Self-adaptive differential evolution algorithm applied to water distribution system optimization. J Comput Civ Eng 27(2):148–158

  22. Zheng F, Zecchin A, Maier H, Simpson A (2016) Comparison of the searching behavior of NSGA-II, SAMODE, and Borg MOEAs applied to water distribution system design problems. J Water Resour Plan Manag 142(7):04016017

  23. Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271

Download references

Author information

Correspondence to Tingchao Yu.

Additional information


• Proposed metrics successfully reveal the underlying searching behavior of NSGA-II’s operators

• NSGA-II operators efficiently drive the fronts initially, followed by slow improvements.

• SBX and SPX are robust in finding the fronts for WDS design problems

• SBX possess great ability in extending the front and NVX showed overall worst performance

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zheng, F., Qi, Z., Bi, W. et al. Improved Understanding on the Searching Behavior of NSGA-II Operators Using Run-Time Measure Metrics with Application to Water Distribution System Design Problems. Water Resour Manage 31, 1121–1138 (2017). https://doi.org/10.1007/s11269-016-1564-7

Download citation


  • Searching behavior
  • Multi-objective optimization
  • Operators
  • Water distribution system