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Large-scale evolutionary optimization: a survey and experimental comparative study

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Abstract

In the last decades, global optimization problems are very common in many research fields of science and engineering and lots of evolutionary computation algorithms have been used to deal with such problems, such as differential evolution (DE) and particle swarm optimization (PSO). However, the algorithms performance rapidly decreases as the increasement of the problem dimension. In order to solve large-scale global optimization problems more efficiently, a lot of improved evolutionary computation algorithms, especially the improved DE or improved PSO algorithms have been proposed. In this paper, we want to analyze the differences and characteristics of various large-scale evolutionary optimization (LSEO) algorithms on some benchmark functions. We adopt the CEC2010 and the CEC2013 large-scale optimization benchmark functions to compare the performance of seven well-known LSEO algorithms. Then, we try to figure out which algorithms perform better on different types of benchmark functions based on simulation results. Finally, we give some potential future research directions of LSEO algorithms and make a conclusion.

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References

  1. Shi GY, Dong JL (2002) Optimization methods. Higher Education Press, Beijing

    Google Scholar 

  2. Fletcher R (1987) Practical methods of optimization. Wiley-Interscience, New York

    MATH  Google Scholar 

  3. Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–72

    Article  Google Scholar 

  4. Storn R, Price K (1997) Differential evolution: a simple and efficient heuristic for global optimization over continuous spaces. J Global Opt 11(4):341–359

    Article  MathSciNet  MATH  Google Scholar 

  5. Storn R (1996) On the usage of differential evolution for function optimization. In: 1996 biennial conference of the North American fuzzy information processing, pp 519–523

  6. Cui L, Li G, Lin Q, Chen J, Lu N (2016) Adaptive differential evolution algorithm with novel mutation strategies in multiple sub-populations. Comput Oper Res 67:155–173

    Article  MathSciNet  MATH  Google Scholar 

  7. Li G, Lin Q, Cui L, Du Z, Liang Z, Chen J, Lu N, Ming Z (2016) A novel hybrid differential evolution algorithm with modified CoDE and JADE. Appl Soft Comput 47:577–599

    Article  Google Scholar 

  8. Muhlenbein H (1996) From recombination of genes to the estimation of distributions I. binary parameters. In: International Conference on Parallel Problem Solving from Nature. Springer, Berlin, Heidelberg, pp 178–187

    Chapter  Google Scholar 

  9. Zhang QF, Sun JY, Tsang E, Ford J (2004) Hybrid estimation of distribution algorithm for global optimization. Eng Comput 21(1):91–107

    Article  MATH  Google Scholar 

  10. Kennedy J, Eberhart RC (1995) Particle swarm optimization. IEEE Int. Conf. Neural Netw, Perth, pp 1942–1948

    Google Scholar 

  11. Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. In: the 6th Int. Symp. Micromachine Human Sci. Nagoya, pp 39–43

  12. Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern B Cybern 26(1):29–41

    Article  Google Scholar 

  13. Cui L, Li G, Luo Y, Chen F, Ming Z, Lu N, Lu J (2018) An enhanced artificial bee colony algorithm with dual-population framework. Swarm Evol Comput 43:184–206

    Article  Google Scholar 

  14. Yang ZY, Tang K, Yao X (2008) Large scale evolutionary optimization using cooperative coevolution. Inf Sci 178(15):2985–2999

    Article  MathSciNet  MATH  Google Scholar 

  15. Liu Y, Yao X, Zhao Q, Higuchi T (2001) Scaling up fast evolutionary programming with cooperative coevolution. In: IEEE Congr. Evol. Comput., pp 1101–1108

  16. Descartes R (1956) Discourse on method, 1st edn. Perentice Hall, Upper Saddle River

  17. Potter MA, Jong KAD (1994) A cooperative coevolutionary approach to function optimization. In: International Conference on Parallel Problem Solving from Nature, pp 249–257

    Chapter  Google Scholar 

  18. Bergh FV, Engelbrecht AP (2004) A cooperative approach to particle swarm optimization. IEEE Trans Evol Comput 8(3):225–239

    Article  Google Scholar 

  19. Li X, Yao X (2012) Cooperatively coevolving particle swarms for large scale optimization. IEEE Trans Evol Comput 16(2):210–224

    Article  Google Scholar 

  20. Yang Z, Tang K, Yao X (2008) Large scale evolutionary optimization using cooperative coevolution. Inf Sci 178(15):2985–2999

    Article  MathSciNet  MATH  Google Scholar 

  21. Shi Y, Teng H, Li Z (2005) Cooperative co-evolutionary differential evolution for function optimization. In: International Conference on Natural Computation, pp 1080–1088

    Google Scholar 

  22. Yang Z, Tang K, Yao X (2008) Multilevel cooperative coevolution for large scale optimization. In: IEEE Congr. Evol. Comput., pp 1663–1670

  23. Omidvar MN, Li X, Yao X (2010) Cooperative co-evolution with delta grouping for large scale non-separable function optimization. In: IEEE Congr. Evol. Comput., pp 1762–1769

  24. Omidvar M, Li X, Mei Y, Yao X (2014) Cooperative co-evolution with differential grouping for large scale optimization. IEEE Trans Evol Comput 18(3):378–393

    Article  Google Scholar 

  25. Ling YB, Li HJ, Cao B (2016) Cooperative co-evolution with graph-based differential grouping for large scale global optimization. In: IEEE International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery, pp 95–102

  26. Takahama T, Sakai S (2012) Large scale optimization by differential evolution with landscape modality detection and a diversity archive. In: IEEE Congr. Evol. Comput., pp 2842–2849

  27. Kushida J, Hara A, Takahama T (2015) Rank-based differential evolution with multiple mutation strategies for large scale global optimization. In: IEEE Congr. Evol. Comput., pp 353–360

  28. Ran C, Jin YC (2015) A competitive swarm optimizer for large scale optimization. IEEE Trans Cybern 45(2):191–204

    Article  Google Scholar 

  29. Ran C, Jin YC (2015) A social learning particle swarm optimization algorithm for scalable optimization. Inf Sci 291:43–60

  30. Yang Q, Xie HY, Chen WN, Zhang J (2016) Multiple parents guided differential evolution for large scale optimization. In: IEEE Congr. Evol. Comput., pp 3549–3556

  31. Zhao SZ, Liang JJ, Suganthan PN, Tasgetiren MF (2008) Dynamic multi-swarm particle swarm optimizer with local search for large scale global optimization. In: IEEE Congr. Evol. Comput., pp 3845–3852

  32. Molina D, Herrera F (2015) Iterative hybridization of DE with local search for the cec2015 special session on large scale global optimization. In: IEEE Congr. Evol. Comput., pp 1974–1978

  33. Ge YF, Yu WJ, Lin Y, Gong YJ, Zhan ZH, Chen WN, Zhang J (2018) Distributed differential evolution based on adaptive mergence and split for large-scale optimization. IEEE Trans Cybern 48(7):2166–2180

    Article  Google Scholar 

  34. Weber M, Neri F, Tirronen V (2011) Shuffle or update parallel differential evolution for large-scale optimization. Appl Soft Comput 15(11):2089–2107

    Article  Google Scholar 

  35. Wang H, Rahnamayan S, Wu ZJ (2013) Parallel differential evolution with self-adapting control parameters and generalized opposition-based learning for solving high-dimensional optimization problems. J Parallel Distrib Comput 73(1):62–73

    Article  Google Scholar 

  36. Liang JJ, Suganthan PN (2005) Dynamic multi-swarm particle swarm optimizer. In: IEEE Int. Swarm Intelligence Symposium, pp 124–129

  37. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82

    Article  Google Scholar 

  38. Tang K, Li X, Suganthan P, Yang Z, Weise T (2009) Benchmark functions for the cec 2010 special session and competition on large scale global optimization. In: Technical Report, Nature Inspired Computation and Applications Laboratory, USTC, China

  39. Li X, Tang K, Omidvar MN, Yang Z, Qin K (2013) Benchmark functions for the cec 2013 special session and competition on large scale global optimization. In: Evol. Comput. Mach. Learn. Subpopulation, Tech. Rep. RMIT University, Melbourne

  40. Shi Y, Eberhart RC (1998) A modified particle swarm optimizer. In: IEEE World Congr. Comput. Intell., pp 69–73

  41. Yang Z, Tang K, Yao X (2007) Differential evolution for high-dimensional function optimization In: IEEE Congr. Evol. Comput., pp 3523–3530

  42. Zhang X, Du KJ, Zhan ZH, Kwong S, Gu TL, Zhang J (2019) Cooperative co-evolutionary bare-bones particle swarm optimization with function independent decomposition for large-scale supply chain network design with uncertainties. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2019.2933499

    Article  Google Scholar 

  43. Omidvar MN, Li X, Yao X (2011) Smart use of computational resources based on contribution for cooperative co-evolutionary algorithms. In: Conference on Genetic and Evolutionary Computation, pp 1115–1122

  44. Omidvar MN, Kazimipour B, Li X, Yao X (2016) CBCC3—a contribution-based cooperative co-evolutionary algorithm with improved exploration/exploitation balance. In: IEEE Congr. Evol. Comput., pp 3541–3548

  45. Wang ZJ, Zhan ZH, Yu WJ, Lin Y, Zhang J, Gu TL, Zhang J (2019) Dynamic group learning distributed particle swarm optimization for large-scale optimization and its application in cloud workflow scheduling. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2019.2933499

    Article  Google Scholar 

  46. Wu G, Mallipeddi R, Suganthan PN, Wang R, Chen H (2016) Differential evolution with multi-population based ensemble of mutation strategies. Inf Sci 329:329–345

    Article  Google Scholar 

  47. Glotic A, Glotic A, Kitak P, Pihler J, Ticar I (2014) Parallel self-adaptive differential evolution algorithm for solving short-term hydro scheduling problem. IEEE Trans Power Syst 29(5):2347–2358

    Article  Google Scholar 

  48. Zhan ZH, Liu X, Zhang H, Yu Z, Weng J, Li Y, Gu T, Zhang J (2017) Cloudde: a heterogeneous differential evolution algorithm and its distributed cloud version. IEEE Trans Parallel Distrib Syst 28(3):704–716

    Article  Google Scholar 

  49. Liu XF, Zhan ZH, Gu TL, Kwong S, Lu Z, Duh HBL, Zhang J (2019) Neural network-based information transfer for dynamic optimization. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2019.2920887

    Article  Google Scholar 

  50. Liu XF, Zhan ZH, Zhang J (2018) Neural network for change direction prediction in dynamic optimization. IEEE Access 6:72649–72662

    Article  Google Scholar 

  51. Zhao H, Zhan ZH, Lin Y, Chen X, Luo XN, Zhang J, Kwong S, Zhang J (2019) Local binary pattern-based adaptive differential evolution for multimodal optimization problems. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2019.2927780

    Article  Google Scholar 

  52. Wang ZJ, Zhan ZH, Lin Y, Yu WJ, Wang H, Kwong S, Zhang J (2019) Automatic niching differential evolution with contour prediction approach for multimodal optimization problems. IEEE Trans Evol Comput. https://doi.org/10.1109/tevc.2019.2910721

    Article  Google Scholar 

  53. Wang ZJ, Zhan ZH, Lin Y, Yu WJ, Yuan HQ, Gu TL, Kwong S, Zhang J (2018) Dual-strategy differential evolution with affinity propagation clustering for multimodal optimization problems. IEEE Trans Evol Comput 22(6):894–908

    Article  Google Scholar 

  54. Zhan ZH, Li J, Cao J, Zhang J, Chung H, Shi YH (2013) Multiple populations for multiple objectives: a coevolutionary technique for solving multiobjective optimization problems. IEEE Trans Cybern 43(2):445–463

    Article  Google Scholar 

  55. Liu XF, Zhan ZH, Gao Y, Zhang J, Kwong S, Zhang J (2019) Coevolutionary particle swarm optimization with bottleneck objective learning strategy for many-objective optimization. IEEE Trans Evol Comput 23(4):587–602

    Article  Google Scholar 

  56. Chen ZG, Zhan ZH, Lin Y, Gong YJ, Yuan HQ, Gu TL, Kwong S, Zhang J (2019) Multiobjective cloud workflow scheduling: a multiple populations ant colony system approach. IEEE Trans Cybern 49(8):2912–2926

    Article  Google Scholar 

  57. Zhan ZH, Liu XF, Gong YJ, Zhang J, Chung HSH, Li Y (2015) Cloud computing resource scheduling and a survey of its evolutionary approaches. ACM Comput Surv 47(4):1–33

    Article  Google Scholar 

  58. Liu XF, Zhan ZH, Deng D, Li Y, Gu TL, Zhang J (2018) An energy efficient ant colony system for virtual machine placement in cloud computing. IEEE Trans Evol Comput 22(1):113–128

    Article  Google Scholar 

  59. Ma L, Gong M, Liu J, Cai Q, Jiao L (2014) Multi-level learning based memetic algorithm for community detection. Appl Soft Comput. 19:121–133

    Article  Google Scholar 

  60. Ma L, Li J, Lin Q, Gong M, Coello CAC, Ming Z (2019) Reliable link inference for network data with community structure. IEEE Trans Cybern 49(9):3347–3361

    Article  Google Scholar 

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Acknowledgements

This work was supported in part by the Outstanding Youth Science Foundation under Grant 61822602, in part by the National Natural Science Foundations of China (NSFC) under Grant 61772207 and Grant 61873097, in part by the Guangdong Natural Science Foundation Research Team under Grant 2018B030312003, and in part by the Guangdong-Hong Kong Joint Innovation Platform under Grant 2018B050502006.

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Correspondence to Zhi-Hui Zhan.

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Jian, JR., Zhan, ZH. & Zhang, J. Large-scale evolutionary optimization: a survey and experimental comparative study. Int. J. Mach. Learn. & Cyber. 11, 729–745 (2020). https://doi.org/10.1007/s13042-019-01030-4

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