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Preference-inspired coevolutionary algorithm based on differentiated space for many-objective problems

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Abstract

The preference-inspired coevolutionary algorithm (PICEAg) is an effective method for solving many-objective optimization problems. But PICEAg cannot identify the quality of non-dominated solutions, which have a similar fitness value, and lacks an effective diversity maintenance mechanism. Meanwhile, owing to the different preference space dominated by individuals, there are significant differences in the search ability of individuals, which makes the allocation of computing resources unreasonable. To address the above issues, in this paper, a neighbor selection strategy is first proposed, by which excellent individuals are selected from the neighboring individuals in a layer-by-layer manner. Next, a dynamic allocation of the preference strategy based on a differential space is proposed. By combining a decomposition-based method, a reference vector is used to divide an objective space into several subspaces, where the number of non-dominated solutions is used to evaluate the selection pressure. The smaller the number of non-dominated solutions, the larger the selection pressure is within the subspaces, and the larger the number of preferences that should be allocated. Finally, the improved algorithm is compared against eight state-of-the-art algorithms on the WFG and ZDT test suites. The experimental results show the effectiveness of the improved algorithm in tackling most many-objective problems.

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References

  • Asafuddoula M, ray T, sarker R, (2015) A decomposition based evolutionary algorithm for many objective optimization. IEEE Trans Evolut Comput 19(3):445–460

  • Bader J, Zitzler E (2011) Hype: an algorithm for fast hypervolume-based many-objective optimization. Evol Comput 19(1):45–76

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Bosman P, Thierens D (2003) The balance between proximity and diversity in multiobjective evolutionary algorithms, vol 7

  • Brockhoff D, Wagner T, Trautmann H (2012) On the properties of the r2 indicator. In: Conference on Genetic and Evolutionary Computation

  • Cheng R, Jin Y, Olhofer M, Sendhoff B (2016) A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 20(5):773–791

    Article  Google Scholar 

  • Deb K, Jain H (2014) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part i: Solving problems with box constraints. IEEE Trans Evol Comput 18(4):577–601

    Article  Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: Nsga-ii, ieee trans. on evol. IEEE Transactions on Evolutionary Computation 6

  • Farina M, Amato P (2002) On the optimal solution definition for many-criteria optimization problems. pp 233–238

  • Freitas ARRD, Fleming PJ, Guimarães FG (2015) Aggregation trees for visualization and dimension reduction in many-objective optimization. Inf Sci 298(298):288–314

    Article  Google Scholar 

  • Gu F, Cheung YM (2018) Self-organizing map-based weight design for decomposition-based many-objective evolutionary algorithm. IEEE Trans Evol Comput 22(2):211–225

    Article  Google Scholar 

  • He Z, Yen GG, Zhang J (2014) Fuzzy-based pareto optimality for many-objective evolutionary algorithms. IEEE Trans Evol Comput 18(2):269–285

    Article  Google Scholar 

  • Hu J, Guo Y, Zheng J, Zou J (2016) A preference-based multi-objective evolutionary algorithm using preference selection radius. Soft Comput 21(17):1–27

    Google Scholar 

  • Ishibuchi H, Tsukamoto N, Nojima Y (2008) Evolutionary many-objective optimization: A short review. In: 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence), pp 2419–2426

  • Ishibuchi H, Yu S, Masuda H, Nojima Y (2017) Performance of decomposition-based many-objective algorithms strongly depends on pareto front shapes. IEEE Trans Evol Comput 21(2):169–190

    Article  Google Scholar 

  • Li K, Deb K, Zhang Q, Kwong S (2015) An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans Evol Comput 19(5):694–716

    Article  Google Scholar 

  • Molina J, Santana LV, Hernáindez-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 

  • Murata T, Taki A (2010) Examination of the performance of objective reduction using correlation-based weighted-sum for many objective knapsack problems. In: International Conference on Hybrid Intelligent Systems

  • Purshouse RC, Jalbă C, Fleming PJ (2011) Preference-driven co-evolutionary algorithms show promise for many-objective optimisation. In: Proceedings of the 6th International Conference on Evolutionary Multi-criterion Optimization, Springer-Verlag, Berlin, Heidelberg, EMO’11, pp 136–150

  • Qiu F, Wu Y, Qiu Q, Wang L (2013) Many-objective evolutionary algorithm based on bipolar preferences dominance. J Softw 3:476–489

    MATH  Google Scholar 

  • Sudeng S, Wattanapongsakorn N (2015) Post pareto-optimal pruning algorithm for multiple objective optimization using specific extended angle dominance. Eng Appl Artif Intell 38:221–236

    Article  Google Scholar 

  • Trivedi A, Srinivasan D, Sanyal K, Ghosh A (2017) A survey of multiobjective evolutionary algorithms based on decomposition. IEEE Trans Evol Comput 21(3):440–462

    Google Scholar 

  • Veldhuizen DAV, Lamont GB (1999) Evolutionary computation and convergence to a pareto front. Stanford University California pp 221–228

  • Veldhuizen DAV, Lamont GB (2000) On measuring multiobjective evolutionary algorithm performance. In: Congress on Evolutionary Computation

  • Wang L, Du J, Qiu F, Jing B (2017) Preference-inspired co-evolutionary algorithm based on hybrid domination strategy. Pattern Recognit Artif Intell 30(6):509–519

    Google Scholar 

  • Wang R, Purshouse RC, Fleming PJ (2013) Preference-inspired coevolutionary algorithms for many-objective optimization. IEEE Trans Evol Comput 17(4):474–494

    Article  Google Scholar 

  • Wang R, Purshouse RC, Fleming PJ (2015) Preference-inspired co-evolutionary algorithms using weight vectors. Eur J Oper Res 243(2):423–441

    Article  MathSciNet  Google Scholar 

  • Yang S, Li M, Liu X, Zheng J (2013) A grid-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 17(5):721–736

    Article  Google Scholar 

  • Yuan Y, Ong YS, Gupta A, Hua X (2018) Objective reduction in many-objective optimization: Evolutionary multiobjective approaches and comprehensive analysis. IEEE Trans Evol Comput 22(2):189–210

    Article  Google Scholar 

  • Zheng J, Xie C (2014) A study on how to use angle information to include decision maker\(^{\prime }\)s preferences. Acta Electron Sinica 42(11):2239–2246

    Google Scholar 

  • Zhou A, Qu BY, Li H, Zhao SZ, Suganthan PN, Zhang Q (2011) Multiobjective evolutionary algorithms: A survey of the state of the art. Swarm Evol Comput 1(1):32–49

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (61472366, 61379077), in part by the Natural Science Foundation of Zhejiang Province ( LY17F020022), in part by Key Projects of Science and Technology Development Plan of Zhejiang Province (2018C01080).

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Authors and Affiliations

  1. College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou, 310023, China

    Liping Wang, Yu Ren, Jiafeng Lu & Pan Fu

  2. College of Business Administration, Zhejiang University of Technology, Hangzhou, 310023, China

    Wei Yu

  3. College of Education Science and Technology, Zhejiang University of Technology, Hangzhou, 310023, China

    Feiyue Qiu

  4. Key Laboratory of Visual Media Intelligent Processing Technology of Zhejiang Province, Hangzhou, 310023, China

    Liping Wang

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  1. Liping Wang
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  2. Wei Yu
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Correspondence to Liping Wang.

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Communicated by A. Di Nola.

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Wang, L., Yu, W., Qiu, F. et al. Preference-inspired coevolutionary algorithm based on differentiated space for many-objective problems. Soft Comput 25, 819–833 (2021). https://doi.org/10.1007/s00500-020-05369-7

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