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Reference Point Based Multi-Objective Optimization of Reservoir Operation: a Comparison of Three Algorithms

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Abstract

Traditional multi-objective evolutionary algorithms treat each objective equally and search randomly in all solution spaces without using preference information. This might reduce the search efficiency and quality of solutions preferred by decision makers, especially when solving problems with complicated properties or many objectives. Three reference point based algorithms which adopt preference information in optimization progress, e.g., R-NSGA-II, r-NSGA-II and g-NSGA-II, have been shown to be effective in finding more preferred solutions in theoretical test problems. However, more efforts are needed to test their effectiveness in real-world problems. This study conducts a comparison of the above three algorithms with a standard algorithm NSGA-II on a reservoir operation problem to demonstrate their performance in improving the search efficiency and quality of preferred solutions. Under the same calculation times of the objective functions, Pareto optimal solutions of the four algorithms are used in the empirical comparison in terms of the approximation to the preferred solutions. Three performance indicators are then adopted for further comparison. Results show that R-NSGA-II and r-NSGA-II can improve the search efficiency and quality of preferred solutions. The convergence and diversity of their solutions in the concerned region are better than NSGA-II, and the closeness degree to the reference point can be increased by 42.8%, and moreover the number of preferred solutions can be increased by more than 3 times when part of objectives are preferred. By contrast, g-NSGA-II shows worse performance. This study exhibits the performance of three reference point based algorithms and provides insights in algorithm selection for multi-objective reservoir optimization problems.

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References

  • Barati R (2011) Parameter estimation of nonlinear Muskingum models using Nelder-Mead simplex algorithm. J Hydrol Eng 16(11):946–954

    Article  Google Scholar 

  • Barati R, Neyshabouri SAAS, Ahmadi G (2014) Development of empirical models with high accuracy for estimation of drag coefficient of flow around a smooth sphere: an evolutionary approach. Powder Technol 257:11–19

    Article  Google Scholar 

  • Bechikh S, Kessentini M, Said LB, Ghédira K (2015) Preference incorporation in evolutionary multiobjective optimization: a survey of the state-of-the-art. Adv Comput 98:141–207

    Article  Google Scholar 

  • Branke J, Kaussler T, Schmeck H (2001) Guidance in evolutionary multiobjective optimization. Adv Eng Softw 32(6):499–507

    Article  Google Scholar 

  • Chou FNF, Wu CW (2014) Determination of cost coefficients of priority-based water allocation linear programming model - a network flow approach. Hydrol Earth Syst Sci 18(5):1857–1872

    Article  Google Scholar 

  • Chu JG, Zhang C, Fu GT, Li Y, Zhou HC (2015) Improving multi-objective reservoir operation optimization with sensitivity-informed problem decomposition. Hydrol Earth Syst Sci 19(8):3557–3570

    Article  Google Scholar 

  • Deb K, Kumar A. (2007). Interactive evolutionary multiobjective optimization and decision making using reference direction method. Genetic and evolutionary computation conference, 781–788, GECCO 2007, proceedings, London, England, UK, July 7-11, 2007 ACM

  • Deb K, Sundar J. (2006). Reference point based multi-objective optimization using evolutionary algorithms. Conference on genetic and evolutionary computation, 635-642

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

    Article  Google Scholar 

  • Fonseca CM, Fleming PJ (1998) Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I. a unified formulation. IEEE Trans Syst Man Cybern Syst Hum 28(1):26–27

    Article  Google Scholar 

  • Giuliani M, Herman JD, Castelletti A, Reed P (2014) Many-objective reservoir policy identification and refinement to reduce policy inertia and myopia in water management. Water Resour Res 50(4):3355–3377

    Article  Google Scholar 

  • Hosseini K, Nodoushan E, Barati R, Shahheydari H (2016) Optimal design of labyrinth spillways using meta-heuristic algorithms. J Civ Eng 20(1):468–477

    Google Scholar 

  • Israel MS, Lund JR (2008) Priority preserving unit penalties in network flow modeling. J Water Resour Plan Manag 125(4):205–214

    Article  Google Scholar 

  • Li K, Deb K, Yao X (2018) R-metric: evaluating the performance of preference-based evolutionary multi-objective optimization using reference points. IEEE Trans Evol Comput 22(6):821–835

    Article  Google Scholar 

  • Liu Y, Gong D, Sun X, Zhang Y. (2014). A reference points-based evolutionary algorithm for many-objective optimization. Companion publication of the 2014 conference on genetic and evolutionary computation, 1053-1056

  • Luo J, Chen C, Xie J (2015) Multi-objective immune algorithm with preference-based selection for reservoir flood control operation. Water Resour Manag 29(5):1447–1466

    Article  Google Scholar 

  • Mohammadi A, Omidvar MN, Li X. (2012). Reference point based multi-objective optimization through decomposition. Evolutionary computation, 1-8

  • Molinac J, Hernández-Díaz AG, Coello CAC, Caballero R (2009) G-dominance: reference point based dominance for multiobjective metaheuristics. Eur J Oper Res 197(2):685–692

    Article  Google Scholar 

  • Said LB, Bechikh S, Ghedira K (2010) The r-dominance: a new dominance relation for interactive evolutionary multicriteria decision making. IEEE Trans Evol Comput 14(5):801–818

    Article  Google Scholar 

  • Tang R, Ding W, Ye L, Wang Y, Zhou H (2019) Tradeoff analysis index for many-objective reservoir optimization. Water Resour Manag 33(13):4637–4651

    Article  Google Scholar 

  • Thiele L, Miettinen K, Korhonen PJ, Molina J (2009) A preference-based evolutionary algorithm for multi-objective optimization. Evol Comput 17(3):411–436

    Article  Google Scholar 

  • Zarei A, Mousavi SF, Eshaghi Gordji M, Karami H (2019) Optimal reservoir operation using bat and particle swarm algorithm and game theory based on optimal water allocation among consumers. Water Resour Manag 33(9):3071–3093

    Article  Google Scholar 

  • Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195

    Article  Google Scholar 

Download references

Acknowledgements

This study is supported by the National Natural Science Foundation of China (Grant No. 91747102, 51709036, 91647201, 51579027) and the last author’s Royal Society Industry Fellowship (Ref: IF160108). K. Li is supported by UKRI Future Leaders Fellowship (Ref: MR/S017062/1).

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Correspondence to Wei Ding.

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Tang, R., Li, K., Ding, W. et al. Reference Point Based Multi-Objective Optimization of Reservoir Operation: a Comparison of Three Algorithms. Water Resour Manage 34, 1005–1020 (2020). https://doi.org/10.1007/s11269-020-02485-9

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