Tradeoff Analysis Index for Many-Objective Reservoir Optimization

  • Rong Tang
  • Wei Ding
  • Lei YeEmail author
  • Yuntao Wang
  • Huicheng Zhou


There exists complicated competitive and synergetic relationships among the objectives in the multi-objective problems, which is hard to quantify and brings difficulty for decision making. Existing studies focus on the tradeoff analysis qualitatively and are lack of quantitative calculation. This study proposes a tradeoff analysis index called Conflict Evaluation Index (CEI) for quantitative many-objective conflict evaluation and tradeoff analysis using Pareto optimal solutions. The index is applied into a six-objective reservoir operation problem. In the application, a reservoir operation optimization model including two electricity objectives and four water supply objectives is established and Pareto optimal solutions are obtained with ε-NSGAII. CEI values of any two objectives are calculated under four water demand scenarios. The results show that the conflict degrees among six objectives become more fierce with the increase of water demands and the major conflict is shifted from electricity objectives to water supply objectives. Besides, the CEI values are applied to determine the objective weights and recommend the best solutions. Objectives of intensive conflict are assigned a large weight, and solutions with better performance in those objectives are recommended. The application illustrates that the proposed index is rational and can be instrumental for insightful many-objective analysis and informed decision making.


Conflict evaluation Decision making Many-objective analysis Reservoir operation Tradeoff analysis 



This study was funded by the Supported by the National Key Research and Development Program of China (Grant No. 2016YFC0402203) and National Natural Science Foundation of China (Grant No. 51709036, 91647201, 91547116).


  1. Chandramouli S, Nanduri UV (2011) Comparison of stochastic and fuzzy dynamic programming models for the operation of a multipurpose reservoir. Water Environ J 25(4):547–554CrossRefGoogle Scholar
  2. Chang LC, Chang FJ (2009) Multi-objective evolutionary algorithm for operating parallel reservoir system. J Hydrol 377(1):12–20CrossRefGoogle Scholar
  3. Deb K, Saxena DK. (2005). On finding Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. KanGAL ReportGoogle Scholar
  4. Delipetrev B, Solomatine D. (2016). Multi-objective nested algorithms for optimal reservoir operation. Egu General Assembly ConferenceGoogle Scholar
  5. Engau A, Wiecek MM (2007) 2D decision-making for multicriteria design optimization. Struct Multidiscip Optim 34(4):301–315CrossRefGoogle Scholar
  6. Fu G, Kapelan Z, Kasprzyk JR, Reed P (2013) Optimal design of water distribution systems using many-objective visual analytics. J Water Resour Plan Manag ASCE 139(6):624–633CrossRefGoogle Scholar
  7. Giuliani M, Herman JD, Castelletti A, Reed P (2014a) Many-objective reservoir policy identification and refinement to reduce policy inertia and myopia in water management. Water Resour Res 50(4):3355–3377CrossRefGoogle Scholar
  8. Giuliani M, Galelli S, Soncini-Sessa R (2014b) A dimensionality reduction approach for many-objective Markov decision processes: application to a water reservoir operation problem. Environ Model Softw 57(3):101–114CrossRefGoogle Scholar
  9. Hurford AP, Huskova I, Harou JJ (2014) Using many-objective trade-off analysis to help dams promote economic development, protect the poor and enhance ecological health. Environ Sci Pol 38(38):72–86CrossRefGoogle Scholar
  10. Joeres EF, Seus G, Engelmann HM (1981) The linear decision rule (LDR) reservoir problem with correlated inflows: 1. Model development. Water Resour Res 17(1):18–24CrossRefGoogle Scholar
  11. Kollat JB, Reed P (2007) A framework for visually interactive decision-making and design using evolutionary multi-objective optimization (VIEO). Environ Model Softw 22(12):1691–1704CrossRefGoogle Scholar
  12. Kulturel-Konak S, Coit DW, Baheranwala F (2008) Pruned Pareto-optimal sets for the system redundancy allocation problem based on multiple prioritized objectives. J Heuristics 14(4):335–357CrossRefGoogle Scholar
  13. Leitner S, Wall F. (2014). Coordination mechanisms in multi objective setups: results of an agent-based simulation: Springer International PublishingGoogle Scholar
  14. Matrosov ES, Huskova I, Kasprzyk JR, Harou JJ, Lambert C, Reed PM (2015) Many-objective optimization and visual analytics reveal key trade-offs for London’s water supply. J Hydrol 531:1040–1053CrossRefGoogle Scholar
  15. Meng F, Fu G, Butler D (2016) Water quality permitting: from end-of-pipe to operational strategies. Water Res 101:114–126CrossRefGoogle Scholar
  16. Reddy MJ, Kumar DN (2006) Optimal reservoir operation using multi-objective evolutionary algorithm. Water Resour Manag 20(6):861–878CrossRefGoogle Scholar
  17. Smith R, Kasprzyk J, Zagona E (2016) Many-objective analysis to optimize pumping and releases in multireservoir water supply network. J Water Resour Plan Manag 142(2)CrossRefGoogle Scholar
  18. Triantaphyllou E, Baig K (2005) The impact of aggregating benefit and cost criteria in four MCDA methods. IEEE Trans Eng Manag 52(2):213–226CrossRefGoogle Scholar
  19. Yang G, Guo S, Liu P, Li L, Xu C (2017) Multiobjective reservoir operating rules based on cascade reservoir input variable selection method. Water Resour Res 53(4):3446–3363CrossRefGoogle Scholar
  20. Zhang C, Wang G, Peng Y, Tang G, Liang G (2012) A negotiation-based multi-objective, multi-party decision-making model for inter-basin water transfer scheme optimization. Water Resour Manag 26(14):4029–4038CrossRefGoogle Scholar
  21. Zhang C, Xu B, Li Y, Fu G (2017) Exploring the relationships among reliability, resilience, and vulnerability of water supply using many-objective analysis. J Water Resour Plan Manag 143(8):04017044CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Rong Tang
    • 1
  • Wei Ding
    • 1
  • Lei Ye
    • 1
    Email author
  • Yuntao Wang
    • 1
  • Huicheng Zhou
    • 1
  1. 1.School of Hydraulic EngineeringDalian University of TechnologyDalianPeople’s Republic of China

Personalised recommendations