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Decomposition-based constrained dominance principle NSGA-Ⅱ for constrained many-objective optimization problems

GU Qing-hua1,2 MO Ming-hui2 LU Cai-wu1 CHEN Lu2

(1.School of Resources Engineering, Xi’an University of Architecture and Technology, Xi’an, Shaanxi Province, China 710055)
(2.School of Management, Xi’an University of Architecture and Technology, Xi’an, Shaanxi Province, China 710055)

【Abstract】The distribution and convergence of solutions are poor when constrained many-objective optimization problems are solved with many-objective evolutionary algorithm, which tends to fall into local optimal solutions. We propose a decomposition-based constrained dominance principle NSGA-II (DBCDP–NSGA-II) based on the fusion of Pareto dominance, decomposition, and constraint dominance. In the study, based on retaining the fast non-dominant ranking in NSGA-II, Pareto dominance is employed firstly to dominate the population. Then according to the nature of the solution, the DBCDP is adopted to punish the equivalent solutions. The feasible and infeasible solutions in sparse regions are preserved to improve the distribution, diversity, and convergence of the population. Finally, the critical values are reordered by the vertical distance and the crowding distance from the individual to the weight vector until N optimal individuals are selected for the next iteration. With constrained DTLZ taken as an example, the algorithm is compared with C–NSGA-II, C–MOEA/D, C–MOEA/DD, and C–NSGA-Ⅲ. The results show that it has a more uniform distribution and better global convergence than the other four algorithms.

【Keywords】 constrained many-objective optimization; Deb constrained dominance; MOEA/D; NSGA-II; distribution; convergence;


【Funds】 National Natural Science Foundation of China (51774228, 51404182) Natural Science Foundation of Shaanxi Province (2017JM5043) Special Scientific Research Project of Shaanxi Provincial Department of Education (17JK0425)

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    [1] Li B, Li J, Tang K, et al. Many-objective evolutionary algorithms: A survey [J]. Acm Computing Surveys, 2015, 48 (1): 1–35.

    [2] Christian von Lücken, Benjamín Barán, Brizuela C. A survey on many-objective evolutionary algorithms for many-objective problems [J]. Computational Optimization and Applications, 2014, 58 (3): 707–756.

    [3] Mendes J B, Maia N A, Veloso R R. A hybrid many-objective evolutionary algorithm for truck dispatching in open-pit-mining [J]. IEEE Latin America Transactions, 2016, 14 (3): 1329–1334.

    [4] Matrosov E S, Huskova I, Kasprzyk J R, et al. Many-objective optimization and visual analytics reveal key trade-offs for London’s water supply [J]. Journal of Hydrology, 2015, 531: 1040–1053.

    [5] Fan Z, Li W, Cai X, et al. Push and pull search for solving constrained many-objective optimization problems [J]. Swarm and Evolutionary Computation, 2019, 44 (1): 665–679.

    [6] Zhang Q, Li H. MOEA/D: A many-objective evolutionary algorithm based on decomposition [J]. IEEE Transactions on Evolutionary Computation, 2008, 11 (6): 712–731.

    [7] Li H, Zhang Q. Many-objective optimization problems with complicated pareto sets, MOEA/D and NSGA-II [J]. IEEE Transactions on Evolutionary Computation, 2009, 13 (2): 284–302.

    [8] Deb K, Pratap A, Agarwal S, et al. A fast and elitist many-objective genetic algorithm: NSGA-II [J]. IEEE Transactions on Evolutionary Computation, 2002, 6 (2): 182–197.

    [9] Takahama T, Sakai S. Constrained optimization by epsilon constrained particle swarm optimizer with epsilon-level control [C]. Soft Computing as Transdisciplinary Science and Technology. Berlin, Heidelberg: Springer, 2005: 1019–1029.

    [10] Runarsson T P, Yao X. Stochastic ranking for constrained evolutionary optimization [J]. IEEE Transactions on Evolutionary Computation, 2000, 4 (3): 284–294.

    [11] Jain H, Deb K. An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, Part II [J]. IEEE Transactions on Evolutionary Computation, 2014, 18 (4): 602–622.

    [12] Li K, Deb K, Zhang Q, et al. An evolutionary many-objective optimization algorithm based on dominance and decomposition [J]. IEEE Transactions on Evolutionary Computation, 2015, 19 (5): 694–716.

    [13] Bi X J, Wang C. A reference point constrained dominance-based NSGA-III algorithm [J]. Control and Decision, 2019, 34 (2): 369–376 (in Chinese).

    [14] Liu J C, Li F, Wang H H, et al. Survey on evolutionary many-objective optimization algorithms [J]. Control and Decision, 2018, 33 (5): 114–122 (in Chinese).

    [15] Elarbi M, Bechikh S, Gupta A, et al. A new decomposition-based NSGA-II for many-objective optimization [J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017, 48 (7): 1191–1210.

    [16] Das I, Dennis J E. Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems [J]. Siam Journal on Optimization, 1998, 8 (3): 631–657.

    [17] Li Z Y, Huang T, Chen S M, et al. Overview of constrained optimization evolutionary algorithms [J]. Journal of Software, 2017, 28 (6): 1529–1546.

    [18] Deb K. An efficient constraint handling method for genetic algorithms [J]. Computer Methods in Applied Mechanics and Engineering, 2000, 186 (2/4): 311–338.

    [19] Deb K, Thiele L, Laumanns M, et al. Scalable test problems for evolutionary many-objective optimization [C]. Evolutionary Many-objective Optimization. London: Springer, 2005: 105–145.

    [20] Zitzler E, Thiele L, Laumanns M, et al. Performance assessment of multi objective optimizers: An analysis and review [J]. IEEE Transactions on Evolutionary Computation, 2003, 7 (2): 117–132.

    [21] Derrac J, García S, Molina D, et al. A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms [J]. Swarm & Evolutionary Computation, 2011, 1 (1): 3–18.

This Article


CN: 21-1124/TP

Vol 35, No. 10, Pages 2466-2474

October 2020


Article Outline


  • 0 Introduction
  • 1 Basic definitions
  • 2 DBCDP–NSGA-II algorithm
  • 3 Experimental simulation and analysis
  • 4 Conclusions
  • References