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An adaptive evolutionary algorithm with coordinated selection strategies for many-objective optimization

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Abstract

Striking a balance between convergence and diversity matters considerably for evolutionary algorithms in solving many-objective optimization problems. The performance of these algorithms depends on their capability of obtaining a set of uniformly distributed solutions as close to the Pareto optimal front as possible. However, most existing evolutionary algorithms encounter challenges in solving many-objective optimization problems. Thus, in this paper, an adaptive many-objective evolutionary algorithm with coordinated selection strategies, labeled ACS-MOEA, is proposed to balance the convergence and diversity. The coordinated selection strategies include three selection strategies, i.e., the selection based on shifted-dominated distance, the selection based on objective vector angle, and the selection based on Non-Euclidean geometry distance. The first is used in the mating selection process to select high-quality parents for the generation of good offspring. Both the second and the third selection strategies are employed in the environmental selection process to delete poor solutions one by one for preserving the elitist solutions of the next generation. The performance of ACS-MOEA is verified by comparing it with six state-of-the-art algorithms on several well-known benchmark test suites with up to 10 objectives. Experimental results have fully demonstrated the competitiveness of ACS-MOEA in balancing convergence and diversity. Moreover, the proposed ACS-MOEA has also been verified to be effective in solving constrained many-objective optimization problems.

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References

  1. Li K, Yan X, Han Y, Ge F, Jiang Y (2022) Many-objective optimization based path planning of multiple UAVs in oilfield inspection. Appl Intell 1–16. https://doi.org/10.1007/s10489-021-02977-0

  2. Qu M, Zuo Y, Xiang F, Tao F (2022) An improved electromagnetism-like mechanism algorithm for energy-aware many-objective flexible job shop scheduling. Int J Adv Manuf Technol 119(7–8):4265–4275

    Google Scholar 

  3. Zhu S, Xu L, Goodman ED, Lu Z (2022) A new many-objective evolutionary algorithm based on generalized pareto dominance. IEEE Trans Cyber 52(8):7776–7790

  4. Liu Y, Zhu N, Li K, Li M, Li K (2019) An angle dominance criterion for evolutionary many-objective optimization. Inf Sci 509:376–399

    MathSciNet  MATH  Google Scholar 

  5. Zhou C, Dai G, Wang M (2018) Enhanced theta dominance and density selection based evolutionary algorithm for many-objective optimization problems. Appl Intell 48(4):992–1012

    Google Scholar 

  6. Gu Q, Chen H, Chen L, Li X, Xiong NN (2020) A many-objective evolutionary algorithm with reference points-based strengthened dominance relation. Inf Sci 554:236–255

    MathSciNet  Google Scholar 

  7. Khan B, Hanoun S, Johnstone M, Lim CP, Creighton D, Nahavandi S (2019) A scalarization-based dominance evolutionary algorithm for many-objective optimization. Inf Sci 474:236–252

    MathSciNet  MATH  Google Scholar 

  8. Tian Y, Cheng R, Zhang X, Su Y, Jin Y (2019) A strengthened dominance relation considering convergence and diversity for evolutionary many-objective optimization. IEEE Trans Evol Comput 23(2):331–345

    Google Scholar 

  9. Yang F, Xu L, Chu X, Wang S (2021) A new dominance relation based on convergence indicators and niching for many-objective optimization. Appl Intell 51(8):5525–5542

    Google Scholar 

  10. Shen J, Wang P, Wang X (2022) A Controlled Strengthened Dominance Relation for Evolutionary Many-Objective Optimization. IEEE Trans Cybern 5(52):3645–3657

  11. Yi X, Zhou Y, Li M, Chen Z (2017) A vector angle-based evolutionary algorithm for unconstrained many-objective optimization. IEEE Trans Evol Comput 21(1):131–152

    Google Scholar 

  12. He C, Tian Y, Jin Y, Zhang X, Pan L (2017) A radial space division based evolutionary algorithm for many-objective optimization. Appl Soft Comput 61:603–621

    Google Scholar 

  13. Sun Y, Bing X, Zhang M, Yen GG (2019) A new two-stage evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 23(5):748–761

  14. Chen H, Cheng R, Pedrycz W, Jin Y (2021) Solving many-objective optimization problems via multistage evolutionary search. IEEE Transactions on Systems Man Cybernetics-Systems 51(6):3552–3564

    Google Scholar 

  15. Ming F, Gong W, Wang L (2022) A two-stage evolutionary algorithm with balanced convergence and diversity for many-objective optimization. IEEE Trans Syst Man Cybern Syst 1–13. https://doi.org/10.1109/TSMC.2022.3143657

  16. Tian Y, Cheng H, Cheng R, Zhang X (2019) A multi-stage evolutionary algorithm for better diversity preservation in multi-objective optimization. IEEE Transactions on Systems, Man, and Cybernetics: Systems 51(9):5880–5894

    Google Scholar 

  17. Dhiman G, Kumar V (2019) KnRVEA: a hybrid evolutionary algorithm based on knee points and reference vector adaptation strategies for many-objective optimization. Appl Intell 49(7):2434–2460

    Google Scholar 

  18. Liu S, Lin Q, Wong KC, Coello Coello CA, Li J, Ming Z, Zhang J (2022) A self-guided reference vector strategy for many-objective optimization. IEEE Transactions on Cybernetics 52(2):1164–1178

    Google Scholar 

  19. Mz A, Lei WA, Wl B, Bo HA, Dl A, Qw A (2021) Many-objective evolutionary algorithm with adaptive reference vector. Inf Sci 563(2):70–90

    MathSciNet  Google Scholar 

  20. Zhang Q, Hui L (2008) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731

    Google Scholar 

  21. Yuan Y, Xu H, Wang B, Zhang B, Yao X (2016) Balancing convergence and diversity in decomposition-based many-objective optimizers. IEEE Trans Evol Comput 20(2):180–198

    Google Scholar 

  22. Chen J, Ding J, Tan KC, Chen Q (2021) A decomposition-based evolutionary algorithm for scalable multi/many-objective optimization. Memetic Computing 13(3):413–432

    Google Scholar 

  23. Zhao C, Zhou Y, Chen Z (2021) Decomposition-based evolutionary algorithm with automatic estimation to handle many-objective optimization problem. Inf Sci 546:1030–1046

    MathSciNet  MATH  Google Scholar 

  24. 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

    Google Scholar 

  25. Zou J, Zhang Z, Zheng J, Yang S (2021) A many-objective evolutionary algorithm based on dominance and decomposition with reference point adaptation. Knowl-Based Syst 231:912–931

    Google Scholar 

  26. Hla B, Wei DC, Zga D (2019) A multi-population evolutionary algorithm with single-objective guide for many-objective optimization. Inf Sci 503:39–60

    MathSciNet  Google Scholar 

  27. Han D, Du W, Du W, Jin Y, Wu C (2019) An adaptive decomposition-based evolutionary algorithm for many-objective optimization. Inf Sci 491:204–222

    MathSciNet  MATH  Google Scholar 

  28. Zhou J, Yao X, Chan FTS, Gao L, Jing X, Li X, Lin Y, Li Y (2019) A decomposition based evolutionary algorithm with direction vector adaption and selection enhancement. Inf Sci 501:248–271

    MathSciNet  MATH  Google Scholar 

  29. Yi J, Zhang W, Bai J, Zhou W, Yao L (2022) Multifactorial evolutionary algorithm based on improved dynamical decomposition for many-objective optimization problems. IEEE Trans Evol Comput 26(2):334–348

    Google Scholar 

  30. Sun Y, Yen GG, Yi Z (2018) IGD indicator-based evolutionary algorithm for many-objective optimization problems. IEEE Transaction on Evolutionary Computation 23(2):173–187

    Google Scholar 

  31. Cai X, Xiao Y, Li M, Hu H, Ishibuchi H, Li X (2021) A grid-based inverted generational distance for multi/many-objective optimization. IEEE Trans Evol Comput 25(1):21–34

    Google Scholar 

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

    Google Scholar 

  33. Zhou J, Yao X, Gao L, Hu C (2021) "An indicator and adaptive region division based evolutionary algorithm for many-objective optimization," Appl Soft Comput, vol. 99

  34. Chen G, Li J, Li M, Chen H (2021) An R2 Indicator and reference vector based many-objective optimization evolutionary algorithm. Acta Automat Sin 47(11):2675–2690

    MathSciNet  Google Scholar 

  35. Deb K, Thiele L, Laumanns M, Zitzler E (2006) Scalable test problems for evolutionary multi-objective optimization. Evolutionary Multiobjective Optimization:105–145

  36. Cheng R, Li M, Tian Y, Zhang X, Su Y (2017) A benchmark test suite for evolutionary many-objective optimization. Complex & Intelligent Systems 3(1):67–81

    Google Scholar 

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

    Google Scholar 

  38. Li K, Chen R, Fu G, Yao X (2019) Two-archive evolutionary algorithm for constrained multiobjective optimization. Evolutionary Computation, IEEE Transactions on 23(2):303–315

    Google Scholar 

  39. Zhou J, Zou J, Yang S, Zheng J, Pei T (2021) Niche-based and angle-based selection strategies for many-objective evolutionary optimization. Inf Sci 571:133–153

    MathSciNet  Google Scholar 

  40. Panichella A (2019) An adaptive evolutionary algorithm based on non-Euclidean geometry for many-objective optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO '19). Association for Computing Machinery, New York, pp 595–603

  41. Deb K, Agarwal S, Meyarivan T (2002) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Google Scholar 

  42. Zhang X, Tian Y, Cheng R, Jin Y (2015) An efficient approach to nondominated sorting for evolutionary multiobjective optimization. IEEE Trans Evol Comput 19(2):201–213

  43. 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

    Google Scholar 

  44. Shang K, Ishibuchi H, He L, Pang LM (2021) A survey on the Hypervolume Indicator in evolutionary multiobjective optimization. IEEE Trans Evol Comput 25(1):1–20

    Google Scholar 

  45. Tian Y, Cheng R, Zhang X, Jin Y (2017) PlatEMO: a MATLAB platform for evolutionary multi-objective optimization. IEEE Comput Intell Mag 12(4):73–87

    Google Scholar 

  46. Carrasco J, García S, Rueda MM, Das S, Herrera F (2020) Recent trends in the use of statistical tests for comparing swarm and evolutionary computing algorithms: practical guidelines and a critical review. Swarm and Evolutionary Computation 54:1006–1062

    Google Scholar 

  47. Yuan J, Liu HL, Gu F, Zhang Q, He Z (2020) Investigating the properties of indicators and an evolutionary many-objective algorithm based on a promising region. IEEE Trans Evol Comput 25(1):75–86

    Google Scholar 

  48. Agrawal RB, Deb K (1995) Simulated binary crossover for continuous search space. Complex Systems 9(3):115–148

    MathSciNet  MATH  Google Scholar 

  49. Deb K, Goyal M (1996) A combined genetic adaptive search (GeneAS) for engineering design. Computer Science and Informatics 26(4):30–45

    Google Scholar 

  50. Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 182(2):311–338

    MATH  Google Scholar 

  51. Jain H, Deb K (2014) An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: handling constraints and extending to an adaptive approach. IEEE Trans Evol Comput 18(4):602–622

    Google Scholar 

  52. Liao X, Li Q, Yang X, Zhang W, Li W (2008) Multiobjective optimization for crash safety design of vehicles using stepwise regression model. Struct Multidiscip Optim 35(6):561–569

    Google Scholar 

  53. Gu QH, Zhang XY, Chen L, Xiong NX (2022) An improved bagging ensemble surrogate-assisted evolutionary algorithm for expensive many-objective optimization. Appl Intell 52(6):5949–5965

    Google Scholar 

  54. Wang Q, Low SY, Li Z, Yiu K (2022) Sensor placement optimization of blind source separation in a wireless acoustic sensor network via hybrid descent methods. Appl Acoust 188:10859–10865

    Google Scholar 

  55. Li WF, He LJ, Cao YL (2021) Many-objective evolutionary algorithm with reference point-based fuzzy correlation entropy for energy-efficient job shop scheduling with limited workers. IEEE Transactions on Cybernetics:1–14

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Acknowledgements

This work is supported by the National Natural Science Foundation of China [grant number 52074205]; Natural Science Foundation of Shaanxi Province of China [grant number 2020JC-44].

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Authors and Affiliations

  1. School of Management, Xi’an University of Architecture and Technology, Xi’an, 710055, Shaanxi, China

    Qinghua Gu, Jiale Luo & Xuexian Li

  2. School of Resources Engineering, Xi’an University of Architecture and Technology, Xi’an, 710055, Shaanxi, China

    Qinghua Gu & Caiwu Lu

  3. Xi’an Key Laboratory for Intelligent Industrial Perception, Calculation and Decision, Xi’an University of Architecture and Technology, Xi’an, 710055, China

    Jiale Luo, Xuexian Li & Caiwu Lu

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  1. Qinghua Gu
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  2. Jiale Luo
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Correspondence to Qinghua Gu.

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Gu, Q., Luo, J., Li, X. et al. An adaptive evolutionary algorithm with coordinated selection strategies for many-objective optimization. Appl Intell 53, 9368–9395 (2023). https://doi.org/10.1007/s10489-022-03982-7

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