Skip to main content
Springer Nature Link
Account
Menu
Find a journal Publish with us Track your research
Search
Cart
  1. Home
  2. Machine Intelligence Research
  3. Article

Evolutionary Computation for Expensive Optimization: A Survey

  • Review
  • Open access
  • Published: 21 January 2022
  • Volume 19, pages 3–23, (2022)
  • Cite this article
Download PDF

You have full access to this open access article

Machine Intelligence Research Aims and scope Submit manuscript
Evolutionary Computation for Expensive Optimization: A Survey
Download PDF
  • Jian-Yu Li  ORCID: orcid.org/0000-0002-6143-92071,2,
  • Zhi-Hui Zhan  ORCID: orcid.org/0000-0003-0862-05141,2 &
  • Jun Zhang3 

  • 4003 Accesses

  • 11 Altmetric

  • 1 Mention

  • Explore all metrics

Abstract

Expensive optimization problem (EOP) widely exists in various significant real-world applications. However, EOP requires expensive or even unaffordable costs for evaluating candidate solutions, which is expensive for the algorithm to find a satisfactory solution. Moreover, due to the fast-growing application demands in the economy and society, such as the emergence of the smart cities, the internet of things, and the big data era, solving EOP more efficiently has become increasingly essential in various fields, which poses great challenges on the problem-solving ability of optimization approach for EOP. Among various optimization approaches, evolutionary computation (EC) is a promising global optimization tool widely used for solving EOP efficiently in the past decades. Given the fruitful advancements of EC for EOP, it is essential to review these advancements in order to synthesize and give previous research experiences and references to aid the development of relevant research fields and real-world applications. Motivated by this, this paper aims to provide a comprehensive survey to show why and how EC can solve EOP efficiently. For this aim, this paper firstly analyzes the total optimization cost of EC in solving EOP. Then, based on the analysis, three promising research directions are pointed out for solving EOP, which are problem approximation and substitution, algorithm design and enhancement, and parallel and distributed computation. Note that, to the best of our knowledge, this paper is the first that outlines the possible directions for efficiently solving EOP by analyzing the total expensive cost. Based on this, existing works are reviewed comprehensively via a taxonomy with four parts, including the above three research directions and the real-world application part. Moreover, some future research directions are also discussed in this paper. It is believed that such a survey can attract attention, encourage discussions, and stimulate new EC research ideas for solving EOP and related real-world applications more efficiently.

Article PDF

Download to read the full article text

Similar content being viewed by others

A survey on evolutionary computation for complex continuous optimization

Article Open access 27 July 2021

Evolutionary constrained multi-objective optimization: a review

Article Open access 04 July 2024

A comparative study of the evolutionary many-objective algorithms

Article 04 March 2019

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.
  • Artificial Intelligence
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

References

  1. Y. Jin. A comprehensive survey of fitness approximation in evolutionary computation. Soft Computing, vol.9, no. 1, pp. 3–12, 2005. DOI: https://doi.org/10.1007/s00500-003-0328-5.

    Article  Google Scholar 

  2. S. Q. Shan, G. G. Wang. Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions. Structural and Multidisciplinary Optimization, vol.41, no. 2, pp. 219–241, 2010. DOI: https://doi.org/10.1007/s00158-009-0420-2.

    Article  MathSciNet  MATH  Google Scholar 

  3. Y. Tenne, C. K. Goh. Computational Intelligence in Expensive Optimization Problems, Berlin, Germany: Springer, 2010. DOI: https://doi.org/10.1007/978-3-642-10701-6.

    Book  MATH  Google Scholar 

  4. K. Tunyasuvunakool, J. Adler, Z. Wu, T. Green, M. Zielinski, A. Žídek, A. Bridgland, A. Cowie, C. Meyer, A. Laydon, S. Velankar, G. J. Kleywegt, A. Bateman, R. Evans, A. Pritzel, M. Figurnov, O. Ronneberger, R. Bates, S. A. A. Kohl, A. Potapenko, A. J. Ballard, B. Romera-Paredes, S. Nikolov, R. Jain, E. Clancy, D. Reiman, S. Petersen, A. W. Senior, K. Kavukcuoglu, E. Birney, P. Kohli, J. Jumper, D. Hassabis. Highly accurate protein structure prediction for the human proteome. Nature, vol.596, no. 7873, pp.590–596, 2021. DOI: https://doi.org/10.1038/s41586-021-03828-l.

    Article  Google Scholar 

  5. J. Jumper, R. Evans, A. Pritzel, T. Green, M. Figurnov, O. Ronneberger, K. Tunyasuvunakool, R. Bates, A. Žídek, A. Potapenko, A. Bridgland, C. Meyer, S. A. A. Kohl, A. J. Ballard, A. Cowie, B. Romera-Paredes, S. Nikolov, R. Jain, J. Adler, T. Back, S. Petersen, D. Reiman, E. Clancy, M. Zielinski, M. Steinegger, M. Pacholska, T. Berghammer, S. Bodenstein, D. Silver, O. Vinyals, A. W. Senior, K. Kavukcuoglu, P. Kohli, D. Hassabis. Highly accurate protein structure prediction with AlphaFold. Nature, vol.596, no. 7873, pp.583–589, 2021. DOI: https://doi.org/10.1038/s41586-021-03819-2.

    Article  Google Scholar 

  6. A. Mirhoseini, A. Goldie, M. Yazgan, J. W. Jiang, E. Songhori, S. Wang, Y. J. Lee, E. Johnson, O. Pathak, A. Nazi, J. Pak, A. Tong, K. Srinivasa, W. Hang, E. Tuncer, Q. V. Le, J. Laudon, R. Ho, R. Carpenter, J. Dean. A graph placement methodology for fast chip design. Nature, vol.594, no. 7862, pp. 207–212, 2021. DOI: https://doi.org/10.1038/s41586-021-03544-w.

    Article  Google Scholar 

  7. T. H. Zhao, W. Tu, Z. X. Fang, X. F. Wang, Z. D. Huang, S. W. Xiong, M. Zheng. Optimizing living material delivery during the COVID-19 Outbreak. IEEE Transactions on Intelligent Transportation Systems, to be published. DOI: https://doi.org/10.1109/TITS.2021.3061076.

  8. Y. C. Jin. Surrogate-assisted evolutionary computation: Recent advances and future challenges. Swarm and Evolutionary Computation, vol. 1, no. 2, pp. 61–70, 2011. DOI: https://doi.org/10.1016/j.swevo.2011.05.001.

    Article  Google Scholar 

  9. Y. C. Jin, H. D. Wang, T. Chugh, D. Guo, K. Miettinen. Data-driven evolutionary optimization: An overview and case studies. IEEE Transactions on Evolutionary Computation, vol.23, no.3, pp.442–458, 2019. DOI: https://doi.org/10.1109/TEVC.2018.2869001.

    Article  Google Scholar 

  10. Y. C. Jin, H. D. Wang, C. L. Sun. Data-driven Evolutionary Optimization, Cham, Germany: Springer, 2021. DOI: https://doi.org/10.1007/978-3-030-74640-7.

    Book  Google Scholar 

  11. S. Nguyen, M. J. Zhang, K. C. Tan. Surrogate-assisted genetic programming with simplified models for automated design of dispatching rules. IEEE Transactions on Cybernetics, vol.47, no. 9, pp. 2951–2965, 2017. DOI: https://doi.org/10.1109/TCYB.2016.2562674.

    Article  Google Scholar 

  12. W. J. Hong, P. Yang, K. Tang. Evolutionary computation for large-scale multi-objective optimization: A decade of progresses. International Journal of Automation and Computing, vol.18, no. 2, pp. 155–169, 2021. DOI: https://doi.org/10.1007/s11633-020-1253-0.

    Article  Google Scholar 

  13. T. F. Zhao, W. N. Chen, X. X. Ma, X. K. Wu. Evolutionary computation in social propagation over complex networks: A survey. International Journal of Automation and Computing, vol.18, no. 4, pp. 503–520, 2021. DOI: https://doi.org/10.1007/S11633-021-1302-3.

    Article  Google Scholar 

  14. J. H. Holland. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, Cambridge, USA: MIT Press, 1992.

    Book  Google Scholar 

  15. H. Zhao, Z. H. Zhan, Y. Lin, X. F. Chen, X. N. Luo, J. Zhang, S. Kwong, J. Zhang. Local binary pattern-based adaptive differential evolution for multimodal optimization problems. IEEE Transactions on Cybernetics, vol.50, no.7, pp.3343–3357, 2020. DOI: https://doi.org/10.1109/TCYB.2019.2927780.

    Article  Google Scholar 

  16. Z. J. Wang, Z. H. Zhan, Y. Lin, W. J. Yu, H. Wang, S. Kwong, J. Zhang. Automatic niching differential evolution with contour prediction approach for multimodal optimization problems. IEEE Transactions on Evolutionary Computation, vol.24, no. 1, pp. 114–128, 2020. DOI: https://doi.org/10.1109/TEVC.2019.2910721.

    Article  Google Scholar 

  17. X. H. Qiu, Y. T. Hu, B. Li. Sequential fault diagnosis using an inertial velocity differential evolution algorithm. International Journal of Automation and Computing, vol.16, no.3, pp.389–397, 2019. DOI: https://doi.org/10.1007/s11633-016-1008-0.

    Article  Google Scholar 

  18. J. Kennedy, R. Eberhart. Particle swarm optimization. In Proceedings of International Conference on Neural Networks, IEEE, Perth, Australia, pp. 1942–1948, 1995. DOI: https://doi.org/10.1109/ICNN.1995.488968.

    Chapter  Google Scholar 

  19. G. H. Lin, J. Zhang, Z. H. Liu. Hybrid particle swarm optimization with differential evolution for numerical and engineering optimization. International Journal of Automation and Computing, vol.15, no. 1, pp. 103–114, 2018. DOI: https://doi.org/10.1007/s11633-016-0990-6.

    Article  Google Scholar 

  20. X. Zhang, K. J. Du, Z. H. Zhan, S. Kwong, T. L. Gu, J. Zhang. Cooperative coevolutionary bare-bones particle swarm optimization with function independent decomposition for large-scale supply chain network design with uncertainties. IEEE Transactions on Cybernetics, vol.50, no. 10, pp. 4454–4468, 2020. DOI: https://doi.org/10.1109/TCYB.2019.2937565.

    Article  Google Scholar 

  21. H. Zhao, Z. G. Chen, Z. H. Zhan, S. Kwong, J. Zhang. Multiple populations co-evolutionary particle swarm optimization for multi-objective cardinality constrained portfolio optimization problem. Neurocomputing, vol. 430, pp. 58–70, 2021. DOI: https://doi.org/10.1016/j.neucom.2020.12.022.

    Article  Google Scholar 

  22. J. R. Jian, Z. G. Chen, Z. H. Zhan, J. Zhang. Region encoding helps evolutionary computation evolve faster: A new solution encoding scheme in particle swarm for large-scale optimization. IEEE Transactions on Evolutionary Computation, vol.25, no. 4, pp. 779–793, 2021. DOI: https://doi.org/10.1109/TEVC.2021.3065659.

    Article  Google Scholar 

  23. Z. G. Chen, Z. H. Zhan, Y. Lin, Y. J. Gong, T. L. Gu, F. Zhao, H. Q. Yuan, X. Chen, Q. Li, J. Zhang. Multiobjective cloud workflow scheduling: A multiple populations ant colony system approach. IEEE Transactions on Cybernetics, vol.49, no. 8, pp. 2912–2926, 2019.

    Article  Google Scholar 

  24. S. Z. Zhou, Z. H. Zhan, Z. G. Chen, S. Kwong, J. Zhang. A multi-objective ant colony system algorithm for airline crew rostering problem with fairness and satisfaction. IEEE Transactions on Intelligent Transportation Systems, to be published. DOI: https://doi.org/10.1109/TITS.2020.2994779.

  25. D. Liang, Z. H. Zhan, Y. C. Zhang, J. Zhang. An efficient ant colony system approach for new energy vehicle dispatch problem. IEEE Transactions on Intelligent Transportation Systems, vol.21, no. 11, pp.4784–4797, 2020. DOI: https://doi.org/10.1109/TITS.2019.2946711.

    Article  Google Scholar 

  26. Z. H. Zhan, L. Shi, K. C. Tan, J. Zhang. A survey on evolutionary computation for complex continuous optimization. Artificial Intelligence Review, to be published. DOI: https://doi.org/10.1007/s10462-021-10042-y.

  27. K. C. Tan, L. Feng, M. Jiang. Evolutionary transfer optimization-a new frontier in evolutionary computation research. IEEE Computational Intelligence Magazine, vol.16, no. 1, pp. 22–33, 2021. DOI: https://doi.org/10.1109/MCI.2020.3039066.

    Article  Google Scholar 

  28. J. R. Jian, Z. H. Zhan, J. Zhang. Large-scale evolutionary optimization: A survey and experimental comparative study. International Journal of Machine Learning and Cybernetics, vol.11, no. 3, pp. 729–745, 2020. DOI: https://doi.org/10.1007/s13042-019-01030-4.

    Article  Google Scholar 

  29. Z. H. Zhan, J. Zhang, Y. Lin, J. Y. Li, T. Huang, X. Q. Guo, F. F. Wei, S. Kwong, X. Y. Zhang, R. You. Matrix-based evolutionary computation. IEEE Transactions on Emerging Topics in Computational Intelligence, to be published. DOI: https://doi.org/10.1109/TETCI.2020.3047410.

  30. S. Rahnamayan, S. J. Mousavirad. Towards Solving large-scale expensive optimization problems efficiently using coordinate descent algorithm. In Proceedings of IEEE International Conference on Systems, Man, and Cybernetics, IEEE, Toronto, Canada, pp. 2506–2513, 2020. DOI: https://doi.org/10.1109/SMC42975.2020.9283224.

  31. C. He, R. Cheng, C. J. Zhang, Y. Tian, Q. Chen, X. Yao. Evolutionary large-scale multiobjective optimization for ratio error estimation of voltage transformers. IEEE Transactions on Evolutionary Computation, vol.24, no. 5, pp. 868–881, 2020. DOI: https://doi.org/10.1109/TEVC.2020.2967501.

    Article  Google Scholar 

  32. I. Voutchkov, A. J. Keane, A. Bhaskar, T. M. Olsen. Weld sequence optimization: The use of surrogate models for solving sequential combinatorial problems. Computer Methods in Applied Mechanics and Engineering, vol.194, no. 30–33, pp. 3535–3551, 2005. DOI: https://doi.org/10.1016/J.CMA.2005.02.003.

    Article  MATH  Google Scholar 

  33. Y. C. Jin, B. Sendhoff. A systems approach to evolutionary multiobjective structural optimization and beyond. IEEE Computational Intelligence Magazine, vol.4, no.3, pp. 62–76, 2009. DOI: https://doi.org/10.1109/MCI.2009.933094.

    Article  Google Scholar 

  34. Z. Zhou, Y. S. Ong, M. H. Nguyen, D. Lim. A study on polynomial regression and Gaussian process global surrogate model in hierarchical surrogate-assisted evolutionary algorithm. In Proceedings of IEEE Congress on Evolutionary Computation, IEEE, Edinburgh, UK, pp. 2832–2839, 2005. DOI: https://doi.org/10.1109/CEC.2005.1555050.

    Google Scholar 

  35. T. Chugh, Y. C. Jin, K. Miettinen, J. Hakanen, K. Sindhya. A surrogate-assisted reference vector guided evolutionary algorithm for computationally expensive many-objective optimization. IEEE Transactions on Evolutionary Computation, vol.22, no. 1, pp. 129–142, 2018. DOI: https://doi.org/10.1109/TEVC.2016.2622301.

    Article  Google Scholar 

  36. J. Tian, Y. Tan, J. C. Zeng, C. L. Sun, Y. C. Jin. Multiobjective infill criterion driven Gaussian process-assisted particle swarm optimization of high-dimensional expensive problems. IEEE Transactions on Evolutionary Computation, vol.23, no.3, pp.459–472, 2019. DOI: https://doi.org/10.1109/TEVC.2018.2869247.

    Article  Google Scholar 

  37. Z. S. Song, H. D. Wang, C. He, Y. C. Jin. A Kriging-assisted two-archive evolutionary algorithm for expensive many-objective optimization. IEEE Transactions on Evolutionary Computation, to be published. DOI: https://doi.org/10.1109/TEVC.2021.3073648.

  38. J. P. Luo, A. Gupta, Y. S. Ong, Z. K. Wang. Evolutionary optimization of expensive multiobjective problems with Co-sub-Pareto front Gaussian process surrogates. IEEE Transactions on Cybernetics, vol.49, no. 5, pp. 1708–1721, 2019. DOI: https://doi.org/10.1109/TCYB.2018.2811761.

    Article  Google Scholar 

  39. J. P. Luo, L. Chen, X. Li, Q. F. Zhang. Novel multitask conditional neural-network surrogate models for expensive optimization. IEEE Transactions on Cybernetics, to be published. DOI: https://doi.org/10.1109/TCYB.2020.3014126.

  40. T. Janus, A. Lüubbers, S. Engell. Neural networks for surrogate-assisted evolutionary optimization of chemical processes. In proceedings of IEEE Congress on Evolutionary Computation, pp. 1–8, 2020. DOI: https://doi.org/10.1109/CEC48606.2020.9185781.

  41. S. Zapotecas Martínez, C. A. Coello Coello. MOEA/D assisted by RBF networks for expensive multi-objective optimization problems. In Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, ACM, Amsterdam, The Netherlands, pp. 1405–1412, 2013. DOI: https://doi.org/10.1145/2463372.2465805.

    Chapter  Google Scholar 

  42. D. Lim, Y. Jin, Y. S. Ong, B. Sendhoff. Generalizing surrogate-assisted evolutionary computation. IEEE Transactions on Evolutionary Computation, vol. 14, no. 3, pp. 329–355, 2010. DOI: https://doi.org/10.1109/TEVC.2009.2027359.

    Article  Google Scholar 

  43. C. L. Sun, Y. C. Jin, R. Cheng, J. L. Ding, J. C. Zeng. Surrogate-assisted cooperative swarm optimization of high-dimensional expensive problems. IEEE Transactions on Evolutionary Computation, vol.21, no. 4, pp. 644–660, 2017. DOI: https://doi.org/10.1109/TEVC.2017.2675628.

    Article  Google Scholar 

  44. R. G. Regis. Evolutionary programming for high-dimensional constrained expensive black-box optimization using radial basis functions. IEEE Transactions on Evolutionary Computation, vol.18, no. 3, pp. 326–347, 2014. DOI: https://doi.org/10.1109/TEVC.2013.2262111.

    Article  Google Scholar 

  45. H. D. Wang, Y. C. Jin. A Random forest-assisted evolutionary algorithm for data-driven constrained multiobjective combinatorial optimization of trauma systems. IEEE Transactions on Cybernetics, vol.50, no. 2, pp. 536–549, 2020. DOI: https://doi.org/10.1109/TCYB.2018.2869674.

    Article  Google Scholar 

  46. L. Han, H. D. Wang. A random forest assisted evolutionary algorithm using competitive neighborhood search for expensive constrained combinatorial optimization. Memetic Computing, vol. 13, no. 1, pp. 19–30, 2021. DOI: https://doi.org/10.1007/s12293-021-00326-9.

    Article  MathSciNet  Google Scholar 

  47. Y. N. Sun, H. D. Wang, B. Xue, Y. C. Jin, G. G. Yen, M. J. Zhang. Surrogate-assisted evolutionary deep learning using an end-to-end random forest-based performance predictor. IEEE Transactions on Evolutionary Computation, vol. 24, no. 2, pp. 350–364, 2020. DOI: https://doi.org/10.1109/TEVC.2019.2924461.

    Article  Google Scholar 

  48. H. D. Wang, Y. C. Jin, J. Doherty. Committee-based active learning for surrogate-assisted particle swarm optimization of expensive problems. IEEE Transactions on Cybernetics, vol.47, no.9, pp. 2664–2677, 2017. DOI: https://doi.org/10.1109/TCYB.2017.2710978.

    Article  Google Scholar 

  49. H. D. Wang, Y. C. Jin, C. L. Sun, J. Doherty. Offline data-driven evolutionary optimization using selective surrogate ensembles. IEEE Transactions on Evolutionary Computation, vol.23, no. 2, pp. 203–216, 2019. DOI: https://doi.org/10.1109/TEVC.2018.2834881.

    Article  Google Scholar 

  50. F. F. Wei, W. N. Chen, Q. Yang, J. Deng, X. N. Luo, H. Jin, J. Zhang. A classifier-assisted level-based learning swarm optimizer for expensive optimization. IEEE Transactions on Evolutionary Computation, vol.25, no. 2, pp. 219–233, 2021. DOI: https://doi.org/10.1109/TEVC.2020.3017865.

    Article  Google Scholar 

  51. J. Y. Li, Z. H. Zhan, C. Wang, H. Jin, J. Zhang. Boosting data-driven evolutionary algorithm with localized data generation. IEEE Transactions on Evolutionary Computation, vol.24, no.5, pp.923–937, 2020. DOI: https://doi.org/10.1109/TEVC.2020.2979740.

    Article  Google Scholar 

  52. J. Y. Li, Z. H. Zhan, H. Wang, J. Zhang. Data-driven evolutionary algorithm with perturbation-based ensemble surrogates. IEEE Transactions on Cybernetics, vol.51, no.8, pp.3925–3937, 2021. DOI: https://doi.org/10.1109/TCYB.2020.3008280.

    Article  Google Scholar 

  53. M. Salami, T. Hendtlass. A fast evaluation strategy for evolutionary algorithms. Applied Soft Computing, vol.2, no. 3, pp. 156–173, 2003. DOI: https://doi.org/10.1016/S1568-4946(02)00067-4.

    Article  Google Scholar 

  54. C. L. Sun, J. C. Zeng, J. Pan, S. D. Xue, Y. C. Jin. A new fitness estimation strategy for particle swarm optimization. Information Sciences, vol. 221, pp. 355–370, 2013. DOI: https://doi.org/10.1016/j.ins.2012.09.030.

    Article  MathSciNet  MATH  Google Scholar 

  55. J. Tian, Y. Tan, C. L. Sun, J. C. Zeng, Y. C. Jin. A self-adaptive similarity-based fitness approximation for evolutionary optimization. In Proceedings of IEEE Symposium Series on Computational Intelligence, IEEE, Athens, Greece, pp. 1–8, 2016. DOI: https://doi.org/10.1109/SSCI.2016.7850209.

    Google Scholar 

  56. H. S. Kim, S. B. Cho. An efficient genetic algorithm with less fitness evaluation by clustering. In Proceedings of IEEE Congress on Evolutionary Computation, IEEE, Seoul, Korea, pp. 887–894, 2001. DOI: https://doi.org/10.1109/CEC.2001.934284.

    Google Scholar 

  57. Y. C. Jin, B. Sendhoff. Reducing fitness evaluations using clustering techniques and neural network ensembles. In Proceedings of Genetic and Evolutionary Computation Conference, Springer, Seattle, USA, pp. 688–699, 2004. DOI: https://doi.org/10.1007/978-3-540-24854-5_71.

    Google Scholar 

  58. P. F. Huang, H. D. Wang. Comparative empirical study on constraint handling in offline data-driven evolutionary optimization. Applied Soft Computing, vol. 110, Article number 107603, 2021. DOI: https://doi.org/10.1016/j.asoc.2021.107603.

  59. K. Deb, R. Hussein, P. C. Roy, G. Toscano-Pulido. A taxonomy for metamodeling frameworks for evolutionary multiobjective optimization. IEEE Transactions on Evolutionary Computation, vol.23, no. 1, pp. 104–116, 2019. DOI: https://doi.org/10.1109/TEVC.2018.2828091.

    Article  Google Scholar 

  60. G. H. Li, Q. F. Zhang. Multiple penalties and multiple local surrogates for expensive constrained optimization. IEEE Transactions on Evolutionary Computation, vol. 25, no. 4, pp. 769–778, 2021. DOI: https://doi.org/10.1109/TEVC.2021.3066606.

    Article  Google Scholar 

  61. Y. Wang, D. Q. Yin, S. X. Yang, G. Y. Sun. Global and local surrogate-assisted differential evolution for expensive constrained optimization problems with inequality constraints. IEEE Transactions on Cybernetics, vol.49, no. 5, pp. 1642–1656, 2019. DOI: https://doi.org/10.1109/TCYB.2018.2809430.

    Article  Google Scholar 

  62. B. C. Wang, H. X. Li, Q. F. Zhang, Y. Wang. Decomposition-based multiobjective optimization for constrained evolutionary optimization. IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol.51, no. 1, pp. 574–587, 2021. DOI: https://doi.org/10.1109/TSMC.2018.2876335.

    Article  Google Scholar 

  63. A. Habib, H. K. Singh, T. Chugh, T. Ray, K. Miettinen. A multiple surrogate assisted decomposition-based evolutionary algorithm for expensive multi/many-objective optimization. IEEE Transactions on Evolutionary Computation, vol. 23, no. 6, pp. 1000–1014, 2019. DOI: https://doi.org/10.1109/TEVC.2019.2899030.

    Article  Google Scholar 

  64. M. Asafuddoula, T. Ray, R. Sarker. Evaluate till you violate: A differential evolution algorithm based on partial evaluation of the constraint set. In Proceedings of IEEE Symposium on Differential Evolution, IEEE, Singapore, pp. 31–37, 2013. DOI: https://doi.org/10.1109/SDE.2013.6601439.

    Google Scholar 

  65. M. Asafuddoula, T. Ray, R. Sarker. A self-adaptive differential evolution algorithm with constraint sequencing. In Proceedings of the 25th Australasian Joint Conference on Artificial Intelligence, Springer, Sydney, Australia, pp. 182–193, 2012. DOI: https://doi.org/10.1007/978-3-642-35101-3_16.

    Google Scholar 

  66. M. Asafuddoula, T. Ray, R. Sarker. A differential evolution algorithm with constraint sequencing: An efficient approach for problems with inequality constraints. Applied Soft Computing, vol.36, pp. 101–113, 2015. DOI: https://doi.org/10.1016/j.asoc.2015.07.007.

    Article  Google Scholar 

  67. M. Asafuddoula, T. Ray, R. Sarker. An improved self-adaptive constraint sequencing approach for constrained optimization problems. Applied Mathematics and Computation, vol.253, pp. 23–39, 2015. DOI: https://doi.org/10.1016/j.amc.2014.12.032.

    Article  MathSciNet  MATH  Google Scholar 

  68. K. H. Rahi, H. K. Singh, T. Ray. Partial evaluation strategies for expensive evolutionary constrained optimization. IEEE Transactions on Evolutionary Computation, to be published. DOI: https://doi.org/10.1109/TEVC.2021.3078486.

  69. H. D. Wang, Y. C. Jin, J. Doherty. A generic test suite for evolutionary multifidelity optimization. IEEE Transactions on Evolutionary Computation, vol.22, no. 6, pp. 836–850, 2018. DOI: https://doi.org/10.1109/TEVC.2017.2758360.

    Article  Google Scholar 

  70. N. M. Alexandrov, R. M. Lewis, C. R. Gumbert, L. L. Green, P. A. Newman. Optimization with variable-fidelity models applied to wing design. In Proceedings of the 38th AIAA Aerospace Sciences Meeting and Exhibit, AIAA, Reno, USA, 2000.

    Google Scholar 

  71. J. Zheng, H. B. Qiu, H. Y. Feng. The variable fidelity optimization for simulation-based design: A review. In Proceedings of the 16th IEEE International Conference on Computer Supported Cooperative Work in Design, IEEE, Wuhan, China, pp. 289–294, 2012. DOI: https://doi.org/10.1109/CSCWD.2012.6221832.

    Google Scholar 

  72. D. Lim, Y. S. Ong, Y. Jin, B. Sendhoff. Evolutionary optimization with dynamic fidelity computational models. In Proceedings of the 4th International Conference on Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence, Springer, Shanghai, China, pp. 235–242, 2008. DOI: https://doi.org/10.1007/978-3-540-85984-0_29.

    Google Scholar 

  73. S. Koziel. Multi-fidelity multi-grid design optimization of planar microwave structures with sonnet. In Proceedings of the 26th Annual Review of Progress in Applied Computational Electromagnetics, Tampere, Finland, pp. 719–724, 2010.

  74. S. H. Wu, Z. H. Zhan, J. Zhang. SAFE: Scale-adaptive fitness evaluation method for expensive optimization problems. IEEE Transactions on Evolutionary Computation, vol. 25, no. 3, pp. 478–491, 2021. DOI: https://doi.org/10.1109/TEVC.2021.3051608.

    Article  Google Scholar 

  75. J. Y. Li, Z. H. Zhan, J. Xu, S. Kwong, J. Zhang. Surrogate-assisted hybrid-model estimation of distribution algorithm for mixed-variable hyperparameters optimization in convolutional neural networks. IEEE Transactions on Neural Networks and Learning System, to be published. DOI: https://doi.org/10.1109/TNNLS.2021.3106399.

  76. D. J. J. Toal. Some considerations regarding the use of multi-fidelity kriging in the construction of surrogate models. Structural and Multidisciplinary Optimization, vol.51, no.6, pp. 1223–1245, 2015. DOI: https://doi.org/10.1007/s00158-014-1209-5.

    Article  Google Scholar 

  77. G. H. Li, Q. F. Zhang, Q. Z. Lin, W. F. Gao. A three-level radial basis function method for expensive optimization. IEEE Transactions on Cybernetics, to be published. DOI: https://doi.org/10.1109/TCYB.2021.3061420.

  78. Z. H. Han, S. Görtz, R. Zimmermann. Improving variable-fidelity surrogate modeling via gradient-enhanced kriging and a generalized hybrid bridge function. Aerospace Science and Technology, vol. 25, no. 1, pp. 177–189, 2013. DOI: https://doi.org/10.1016/j.ast.2012.01.006.

    Article  Google Scholar 

  79. N. Courrier, P. A. Boucard, B. Soulier. Variable-fidelity modeling of structural analysis of assemblies. Journal of Global Optimization, vol.64, no.3, pp.577–613, 2016. DOI: https://doi.org/10.1007/s10898-015-0345-9.

    Article  MathSciNet  MATH  Google Scholar 

  80. C. Smith, J. Doherty, Y. C. Jin. Multi-objective evolutionary recurrent neural network ensemble for prediction of computational fluid dynamic simulations. In Proceedings of IEEE Congress on Evolutionary Computation, IEEE, Beijing, China, pp. 2609–2616, 2014. DOI: https://doi.org/10.1109/CEC.2014.6900552.

    Google Scholar 

  81. G. Y. Sun, G. Y. Li, S. W. Zhou, W. Xu, X. J. Yang, Q. Li. Multi-fidelity optimization for sheet metal forming process. Structural and Multidisciplinary Optimization, vol.44, no. 1, pp. 111–124, 2011. DOI: https://doi.org/10.1007/s00158-010-0596-5.

    Article  Google Scholar 

  82. E. Y. Li, H. Wang, F. Ye. Two-level multi-surrogate assisted optimization method for high dimensional nonlinear problems. Applied Soft Computing, vol.46, pp. 26–36, 2016. DOI: https://doi.org/10.1016/j.asoc.2016.04.035.

    Article  Google Scholar 

  83. X. F. Ji, Y. Zhang, D. W. Gong, X. Y. Sun. Dual-surrogate-assisted cooperative particle swarm optimization for expensive multimodal problems. IEEE Transactions on Evolutionary Computation, vol.25, no. 4, pp. 794–808, 2021. DOI: https://doi.org/10.1109/TEVC.2021.3064835.

    Article  Google Scholar 

  84. J. Liu, Y. Wang, G. Y. Sun, T. Pang. Multisurrogate-assisted ant colony optimization for expensive optimization problems with continuous and categorical variables. IEEE Transactions on Cybernetics, to be published. DOI: https://doi.org/10.1109/TCYB.2021.3064676.

  85. X. W. Cai, L. Gao, X. Y. Li. Efficient generalized surrogate-assisted evolutionary algorithm for high-dimensional expensive problems. IEEE Transactions on Evolutionary Computation, vol.24, no. 2, pp. 365–379, 2020. DOI: https://doi.org/10.1109/TEVC.2019.2919762.

    Article  Google Scholar 

  86. Z. X. Li, V. Tam, L. K. Yeung, Z. L. Li. Applying an adaptive multi-population optimization algorithm to enhance machine learning models for computational finance. In Proceedings of the 22nd IEEE International Conference on High Performance Computing and Communications, the 18th IEEE International Conference on Smart City, the 6th IEEE International Conference on Data Science and Systems, IEEE, Yanuca Island, Fiji, pp. 1322–1329, 2020. DOI: https://doi.org/10.1109/HPCC-SmartCity-DSS50907.2020.00170.

    Google Scholar 

  87. J. J. Zhou, X. F. Yao, Y. Z. Lin, F. T. S. Chan, Y. Li. An adaptive multi-population differential artificial bee colony algorithm for many-objective service composition in cloud manufacturing. Information Sciences, vol.456, pp. 50–82, 2018. DOI: https://doi.org/10.1016/j.ins.2018.05.009.

    Article  MathSciNet  Google Scholar 

  88. J. Blanchard, C. Beauthier, T. Carletti. A surrogate-assisted cooperative Co-evolutionary algorithm for solving high dimensional, expensive and black box optimization problems. In Proceedings of the 6th International Conference on Engineering Optimization, Springer, Cham, Germany, pp. 41–52, 2018. DOI: https://doi.org/10.1007/978-3-319-97773-7_4.

    Google Scholar 

  89. A. Zychowski, A. Gupta, J. Mańdziuk, Y. S. Ong. Addressing expensive multi-objective games with postponed preference articulation via memetic co-evolution. Knowledge-Based Systems, vol.154, pp. 17–31, 2018. DOI: https://doi.org/10.1016/j.knosys.2018.05.012.

    Article  Google Scholar 

  90. M. Neshat, B. Alexander, M. Wagner. A hybrid cooperative co-evolution algorithm framework for optimising power take off and placements of wave energy converters. Information Sciences, vol.534, pp. 218–244, 2020. DOI: https://doi.org/10.1016/j.ins.2020.03.112.

    Article  MathSciNet  Google Scholar 

  91. Q. F. Zhang, W. D. Liu, E. Tsang, B. Virginas. Expensive multiobjective optimization by MOEA/D with Gaussian process model. IEEE Transactions on Evolutionary Computation, vol.14, no. 3, pp. 456–474, 2010. DOI: https://doi.org/10.1109/TEVC.2009.2033671.

    Article  Google Scholar 

  92. T. Akhtar, C. A. Shoemaker. Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection. Journal of Global Optimization, vol.64, no. 1, pp. 17–32, 2016. DOI: https://doi.org/10.1007/s10898-015-0270-y.

    Article  MathSciNet  MATH  Google Scholar 

  93. J. Y. Zhang, A. M. Zhou, G. X. Zhang. A classification and Pareto domination based multiobjective evolutionary algorithm. In Proceedings of IEEE Congress on Evolutionary Computation, IEEE, Sendai, Japan, pp.2883–2890, 2015. DOI: https://doi.org/10.1109/CEC.2015.7257247.

    Google Scholar 

  94. J. Knowles. ParEGO: A hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Transactions on Evolutionary Computation, vol.10, no. 1, pp. 50–66, 2006. DOI: https://doi.org/10.1109/TEVC.2005.851274.

    Article  Google Scholar 

  95. L. Q. Pan, C. He, Y. Tian, H. D. Wang, X. Y. Zhang, Y. C. Jin. A classification-based surrogate-assisted evolutionary algorithm for expensive many-objective optimization. IEEE Transactions on Evolutionary Computation, vol.23, no.1, pp. 74–88, 2019. DOI: https://doi.org/10.1109/TEVC.2018.2802784.

    Article  Google Scholar 

  96. T. Chugh, K. Sindhya, K. Miettinen, J. Hakanen, Y. C. Jin. On constraint handling in surrogate-assisted evolutionary many-objective optimization. In Proceedings of the 14th International Conference on Parallel Problem Solving from Nature, Springer, Edinburgh, UK, pp. 214–224, 2016. DOI: https://doi.org/10.1007/978-3-319-45823-6_20.

    Google Scholar 

  97. M. Herrera, A. Guglielmetti, M. Y. Xiao, R. F. Coelho. Metamodel-assisted optimization based on multiple kernel regression for mixed variables. Structural and Multidisciplinary Optimization, vol.49, no.6, pp.979–991, 2014. DOI: https://doi.org/10.1007/s00158-013-1029-z.

    Article  Google Scholar 

  98. H. C. Dong, B. W. Song, P. Wang, Z. M. Dong. Surrogate-based optimization with clustering-based space exploration for expensive multimodal problems. Structural and Multidisciplinary Optimization, vol.57, no. 4, pp. 1553–1577, 2018. DOI: https://doi.org/10.1007/s00158-017-1826-x.

    Article  Google Scholar 

  99. Y. Guo, J. Y. Li, Z. H. Zhan. Efficient hyperparameter optimization for convolution neural networks in deep learning: A distributed particle swarm optimization approach. Cybernetics and Systems, vol. 52, no. 1, pp. 36–57, 2021. DOI: https://doi.org/10.1080/01969722.2020.1827797.

    Article  Google Scholar 

  100. J. L. Ding, C. E. Yang, Y. C. Jin, T. Y. Chai. Generalized multitasking for evolutionary optimization of expensive problems. IEEE Transactions on Evolutionary Computation, vol.23, no.1, pp.44–58, 2019. DOI: https://doi.org/10.1109/TEVC.2017.2785351.

    Article  Google Scholar 

  101. S. Huang, J. Zhong, W. Yu. Surrogate-assisted evolutionary framework with adaptive knowledge transfer for multi-task optimization. IEEE Transactions on Emerging Topics in Computing, to be published. DOI: https://doi.org/10.1109/TETC.2019.2945775.

  102. Z. H. Han, F. Liu, C. Z. Xu, K. S. Zhang, Q. F. Zhang. Efficient multi-objective evolutionary algorithm for constrained global optimization of expensive functions. In Proceedings of IEEE Congress on Evolutionary Computation, IEEE, Wellington, New Zealand, pp. 2026–2033, 2019. DOI: https://doi.org/10.1109/CEC.2019.8789986.

    Google Scholar 

  103. P. Liao, C. L. Sun, G. C. Zhang, Y. C. Jin. Multi-surrogate multi-tasking optimization of expensive problems. Knowledge-based Systems, vol. 205, Article number 106262, 2020. DOI: https://doi.org/10.1016/J.KNOSYS.2020.106262.

  104. X. W. Cai, L. Gao, X. Y. Li, H. B. Qiu. Surrogate-guided differential evolution algorithm for high dimensional expensive problems. Swarm and Evolutionary Computation, vol.48, pp. 288–311, 2019. DOI: https://doi.org/10.1016/j.swevo.2019.04.009.

    Article  Google Scholar 

  105. Q. H. Gu, Q. Wang, N. N. Xiong, S. Jiang, L. Chen. Surrogate-assisted evolutionary algorithm for expensive constrained multi-objective discrete optimization problems. Complex & Intelligent Systems, to be published. DOI: https://doi.org/10.1007/S40747-020-00249-X.

  106. F. Zhang, X. Y. Cai, Z. Fan. A batched expensive multiobjective optimization based on constrained decomposition with grids. In Proceedings of IEEE Symposium Series on Computational Intelligence, IEEE, Xiamen, China, pp. 2081–2087, 2019. DOI: https://doi.org/10.1109/SSCI44817.2019.9002765.

    Google Scholar 

  107. L. Han, H. Wang. A random forest assisted evolutionary algorithm using competitive neighborhood search for expensive constrained combinatorial optimization. Memetic Computing, vol. 13, no. 1, pp. 19–30, 2021.

    Article  MathSciNet  Google Scholar 

  108. Z. Yang, H. B. Qiu, L. Gao, C. Jiang, L. M. Chen, X. W. Cai. A novel surrogate-assisted differential evolution for expensive optimization problems with both equality and inequality constraints. In Proceedings of IEEE Congress on Evolutionary Computation, IEEE, Wellington, New Zealand, pp. 1688–1695, 2019. DOI: https://doi.org/10.1109/CEC.2019.8790113.

    Google Scholar 

  109. P. S. Palar, T. Tsuchiya, G. T. Parks. A comparative study of local search within a surrogate-assisted multi-objective memetic algorithm framework for expensive problems. Applied Soft Computing, vol.43, pp. 1–19, 2016. DOI: https://doi.org/10.1016/j.asoc.2015.12.039.

    Article  Google Scholar 

  110. R. E. Smith, B. A. Dike, S. A. Stegmann. Fitness inheritance in genetic algorithms. In Proceedings of ACM Symposium on Applied Computing, ACM, Nashville, USA, pp. 345–350, 1995. DOI: https://doi.org/10.1145/315891.316014.

    Google Scholar 

  111. J. H. Chen, D. E. Goldberg, S. Y. Ho, K. Sastry. Fitness inheritance in multi-objective optimization. In Proceedings of Genetic and Evolutionary Computation Conference, New York, USA, pp. 319–326, 2002.

  112. Y. Zheng, B. A. Julstrom, W. D. Cheng. Design of vector quantization codebooks using a genetic algorithm. In Proceedings of IEEE International Conference on Evolutionary Computation, IEEE, Indianapolis, USA, pp. 525–529, 1997. DOI: https://doi.org/10.1109/ICEC.1997.592366.

    Google Scholar 

  113. K. Sastry, D. E. Goldberg, M. Pelikan. Don’t evaluate, inherit. In Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation, ACM, San Francisco, USA, pp. 551–558, 2001.

    Google Scholar 

  114. Z. H. Zhan, X. F. Liu, H. X. Zhang, Z. T. Yu, J. Weng, Y. Li, T. L. Gu, J. Zhang. Cloudde: A heterogeneous differential evolution algorithm and its distributed cloud version. IEEE Transactions on Parallel and Distributed Systems, vol.28, no.3, pp.704–716, 2017. DOI: https://doi.org/10.1109/TP-DS.2016.2597826.

    Article  Google Scholar 

  115. H. X. Zhen, W. Y. Gong, L. Wang. Data-driven evolutionary sampling optimization for expensive problems. Journal of Systems Engineering and Electronics, vol. 32, no. 2, pp. 318–330, 2021. DOI: https://doi.org/10.23919/JSEE.2021.000027.

    Article  Google Scholar 

  116. İ. B. Aydilek. A hybrid firefly and particle swarm optimization algorithm for computationally expensive numerical problems. Applied Soft Computing, vol.66, pp. 232–249, 2018. DOI: https://doi.org/10.1016/j.asoc.2018.02.025.

    Article  Google Scholar 

  117. E. Ampellio, L. Vassio. A hybrid ABC for expensive optimizations: CEC 2016 competition benchmark. In Proceedings of IEEE Congress on Evolutionary Computation, IEEE, Vancouver, Canada, pp. 1157–1164, 2016. DOI: https://doi.org/10.1109/CEC.2016.7743918.

    Google Scholar 

  118. Q. Q. Kong, X. J. He, C. L. Sun. A surrogate-assisted hybrid optimization algorithms for computational expensive problems. In Proceedings of the 12th World Congress on Intelligent Control and Automation, IEEE, Guilin, China, pp. 2126–2130, 2016. DOI: https://doi.org/10.1109/WCICA.2016.7578825.

    Google Scholar 

  119. M. K. Karakasis, A. P. Giotis, K. C. Giannakoglou. Inexact information aided, low-cost, distributed genetic algorithms for aerodynamic shape optimization. International Journal for Numerical Methods in Fluids, vol.43, no. 10–11, pp. 1149–1166, 2003. DOI: https://doi.org/10.1002/fld.575.

    Article  MATH  Google Scholar 

  120. M. O. Akinsolu, B. Liu, V. Grout, P. I. Lazaridis, M. E. Mognaschi, P. Di Barba. A parallel surrogate model assisted evolutionary algorithm for electromagnetic design optimization. IEEE Transactions on Emerging Topics in Computational Intelligence, vol.3, no. 2, pp. 93–105, 2019. DOI: https://doi.org/10.1109/TETCI.2018.2864747.

    Article  Google Scholar 

  121. M. K. Karakasis, D. G. Koubogiannis, K. C. Giannakoglou. Hierarchical distributed metamodel-assisted evolutionary algorithms in shape optimization. International Journal for Numerical Methods in Fluids, vol.53, no.3, pp.455–469, 2007. DOI: https://doi.org/10.1002/fld.1288.

    Article  MATH  Google Scholar 

  122. Y. Z. Sun, J. Wang, Z. H. Lu. Asynchronous parallel surrogate optimization algorithm based on ensemble surrogating model and stochastic response surface method. In Proceedings of the 5th International Conference on Big Data Security on Cloud, IEEE International Conference on High Performance and Smart Computing, and IEEE International Conference on Intelligent Data and Security, IEEE, Washington, USA, pp. 74–84, 2019. DOI: https://doi.org/10.1109/BIGDATASECURITY-HPSC-IDS.2019.00024.

    Google Scholar 

  123. Y. J. Gong, W. N. Chen, Z. H. Zhan, J. Zhang, Y. Li, Q. F. Zhang, J. J. Li. Distributed evolutionary algorithms and their models: A survey of the state-of-the-art. Applied Soft Computing, vol.34, pp. 286–300, 2015. DOI: https://doi.org/10.1016/j.asoc.2015.04.061.

    Article  Google Scholar 

  124. X. F. Liu, Z. H. Zhan, J. H. Lin, J. Zhang. Parallel differential evolution based on distributed cloud computing resources for power electronic circuit optimization. In Proceedings of Genetic and Evolutionary Computation Conference Companion, ACM, Denver, USA, pp. 117–118, 2016. DOI: https://doi.org/10.1145/2908961.2908972.

    Google Scholar 

  125. N. Ma, X. F. Liu, Z. H. Zhan, J. H. Zhong, J. Zhang. Load balance aware distributed differential evolution for computationally expensive optimization problems. In Proceedings of Genetic and Evolutionary Computation Conference Companion, ACM, Berlin, Germany, pp. 209–210, 2017. DOI: https://doi.org/10.1145/3067695.3075602.

    Chapter  Google Scholar 

  126. Z. H. Zhan, Z. J. Wang, H. Jin, J. Zhang. Adaptive distributed differential evolution. IEEE Transactions on Cybernetics, vol.50, no. 11, pp. 4633–4647, 2020. DOI: https://doi.org/10.1109/TCYB.2019.2944873.

    Article  Google Scholar 

  127. X. F. Liu, Z. H. Zhan, J. Zhang. Resource-aware distributed differential evolution for training expensive neural-network-based controller in power electronic circuit. IEEE Transactions on Neural Networks and Learning Systems, to be published. DOI: https://doi.org/10.1109/TNNLS.2021.3075205.

  128. J. Y. Li, Z. H. Zhan, R. D. Liu, C. Wang, S. Kwong, J. Zhang. Generation-level parallelism for evolutionary computation: A pipeline-based parallel particle swarm optimization. IEEE Transactions on Cybernetics, vol.51, no. 10, pp. 4848–4859, 2021. DOI: https://doi.org/10.1109/TCYB.2020.3028070.

    Article  Google Scholar 

  129. Y. F. Ge, W. J. Yu, Y. Lin, Y. J. Gong, Z. H. Zhan, W. N. Chen, J. Zhang. Distributed differential evolution based on adaptive mergence and split for large-scale optimization. IEEE Transactions on Cybernetics, vol.48, no. 7, pp. 2166–2180, 2018. DOI: https://doi.org/10.1109/TCYB.2017.2728725.

    Article  Google Scholar 

  130. Z. J. Wang, Z. H. Zhan, W. J. Yu, Y. Lin, J. Zhang, T. L. Gu, J. Zhang. Dynamic group learning distributed particle swarm optimization for large-scale optimization and its application in cloud workflow scheduling. IEEE Transactions on Cybernetics, vol. 50, no. 6, pp. 2715–2729, 2020. DOI: https://doi.org/10.1109/TCYB.2019.2933499.

    Article  Google Scholar 

  131. Z. J. Wang, Z. H. Zhan, S. Kwong, H. Jin, J. Zhang. Adaptive granularity learning distributed particle swarm optimization for large-scale optimization. IEEE Transactions on Cybernetics, vol.51, no.3, pp. 1175–1188, 2021. DOI: https://doi.org/10.1109/TCYB.2020.2977956.

    Article  Google Scholar 

  132. M. N. Omidvar, X. D. Li, X. Yao. Smart use of computational resources based on contribution for cooperative co-evolutionary algorithm. In Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation Conference, ACM, Dublin, Ireland, pp. 1115–1122, 2011. DOI: https://doi.org/10.1145/2001576.2001727.

    Google Scholar 

  133. Z. G. Ren, Y. S. Liang, A. M. Zhang, Y. Yang, Z. R. Feng, L. Wang. Boosting cooperative coevolution for large scale optimization with a fine-grained computation resource allocation strategy. IEEE Transactions on Cybernetics, vol. 49, no. 12, pp. 4180–4193, 2019. DOI: https://doi.org/10.1109/TCYB.2018.2859635.

    Article  Google Scholar 

  134. M. N. Omidvar, B. Kazimipour, X. D. Li, X. Yao. CB-CC3—A contribution-based cooperative co-evolutionary algorithm with improved exploration/exploitation balance. In Proceedings of IEEE Congress on Evolutionary Computation, IEEE, Vancouver, Canada, pp. 3541–3548, 2016. DOI: https://doi.org/10.1109/CEC.2016.7744238.

    Google Scholar 

  135. M. Yang, M. N. Omidvar, C. H. Li, X. D. Li, Z. H. Cai, B. Kazimipour, X. Yao. Efficient resource allocation in cooperative co-evolution for large-scale global optimization. IEEE Transactions on Evolutionary Computation, vol. 21, no. 4, pp. 493–505, 2017. DOI: https://doi.org/10.1109/TEVC.2016.2627581.

    Article  Google Scholar 

  136. B. Kazimipour, M. N. Omidvar, A. K. Qin, X. D. Li, X. Yao. Bandit-based cooperative coevolution for tackling contribution imbalance in large-scale optimization problems. Applied Soft Computing, vol.76, pp. 265–281, 2019. DOI: https://doi.org/10.1016/j.asoc.2018.12.007.

    Article  Google Scholar 

  137. S. Mahdavi, S. Rahnamayan, M. E. Shiri. Cooperative Co-evolution with sensitivity analysis-based budget assignment strategy for large-scale global optimization. Applied Intelligence, vol.47, no.3, pp.888–913, 2017. DOI: https://doi.org/10.1007/s10489-017-0926-z.

    Article  Google Scholar 

  138. A. Song, W. N. Chen, P. T. Luo, Y. J. Gong, J. Zhang. Overlapped cooperative co-evolution for large scale optimization. In Proceedings of IEEE International Conference on Systems, Man, and Cybernetics, IEEE, Banff, Canada, pp. 3689–3694, 2017. DOI: https://doi.org/10.1109/SMC.2017.8123206.

    Google Scholar 

  139. G. A. Trunfio. Adaptation in cooperative coevolutionary optimization. In Proceedings of Adaptation and Hybridization in Computational Intelligence, Springer, Cham, Germany, pp. 91–109, 2015. DOI: https://doi.org/10.1007/978-3-319-14400-9_4.

    Chapter  Google Scholar 

  140. X. G. Peng, Y. P. Wu. Large-scale cooperative co-evolution with bi-objective selection based imbalanced multimodal optimization. In Proceedings of IEEE Congress on Evolutionary Computation, IEEE, Donostia, Spain, pp. 1527–1532, 2017. DOI: https://doi.org/10.1109/CEC.2017.7969484.

    Google Scholar 

  141. H. D. Wang, Y. C. Jin, J. O. Jansen. Data-driven surrogate-assisted multiobjective evolutionary optimization of a trauma system. IEEE Transactions on Evolutionary Computation, vol.20, no.6, pp.939–952, 2016. DOI: https://doi.org/10.1109/TEVC.2016.2555315.

    Article  Google Scholar 

  142. D. Guo, T. Y. Chai, J. L. Ding, Y. C. Jin. Small data driven evolutionary multi-objective optimization of fused magnesium furnaces. In Proceedings of IEEE Symposium Series on Computational Intelligence, IEEE, Athens, Greece, pp. 1–8, 2016. DOI: https://doi.org/10.1109/SSCI.2016.7850211.

    Google Scholar 

  143. T. Chugh, K. Sindhya, K. Miettinen, Y. C. Jin, T. Kratky, P. Makkonen. Surrogate-assisted evolutionary multiobjective shape optimization of an air intake ventilation system. In Proceedings of IEEE Congress on Evolutionary Computation, IEEE, Donostia, Spain, pp. 1541–1548, 2017. DOI: https://doi.org/10.1109/CEC.2017.7969486.

    Google Scholar 

  144. T. Chugh, N. Chakraborti, K. Sindhya, Y. C. Jin. A data-driven surrogate-assisted evolutionary algorithm applied to a many-objective blast furnace optimization problem. Materials and Manufacturing Processes, vol.32, no. 10, pp. 1172–1178, 2017. DOI: https://doi.org/10.1080/10426914.2016.1269923.

    Article  Google Scholar 

  145. H. D. Wang, L. Feng, Y. C. Jin, J. Doherty. Surrogate-assisted evolutionary multitasking for expensive minimax optimization in multiple scenarios. IEEE Computational Intelligence Magazine, vol. 16, no. 1, pp. 34–48, 2021. DOI: https://doi.org/10.1109/MCI.2020.3039067.

    Article  Google Scholar 

  146. C. He, Y. Tian, H. D. Wang, Y. C. Jin. A repository of real-world datasets for data-driven evolutionary multi-objective optimization. Complex & Intelligent Systems, vol.6, no.1, pp. 189–197, 2020. DOI: https://doi.org/10.1007/s40747-019-00126-2.

    Article  Google Scholar 

  147. C. Picard, J. Schiffmann. Realistic constrained multiobjective optimization benchmark problems from design. IEEE Transactions on Evolutionary Computation, vol. 25, no. 2, pp. 234–246, 2021. DOI: https://doi.org/10.1109/TEVC.2020.3020046.

    Article  Google Scholar 

  148. C. Lu, L. Gao, W. Y. Gong, C. Y. Hu, X. S. Yan, X. Y. Li. Sustainable scheduling of distributed permutation flow-shop with non-identical factory using a knowledge-based multi-objective memetic optimization algorithm. Swarm and Evolutionary Computation, vol. 60, Article number 100803, 2021. DOI: https://doi.org/10.1016/J.SWEVO.2020.100803.

  149. Z. G. Chen, Y. Lin, Y. J. Gong, Z. H. Zhan, J. Zhang. Maximizing lifetime of range-adjustable wireless sensor networks: A neighborhood-based estimation of distribution algorithm. IEEE Transactions on Cybernetics, to be published. DOI: https://doi.org/10.1109/TCYB.2020.2977858.

  150. Y. F. Ge, W. J. Yu, J. L. Cao, H. Wang, Z. H. Zhan, Y. C. Zhang, J. Zhang. Distributed memetic algorithm for outsourced database fragmentation. IEEE Transactions on Cybernetics, vol.51, no. 10, pp.4808–4821, 2021. DOI: https://doi.org/10.1109/TCYB.2020.3027962.

    Article  Google Scholar 

  151. J. Y. Li, K. J. Du, Z. H. Zhan, H. Wang, J. Zhang. Multi-criteria differential evolution: Treating multitask optimization as multi-criteria optimization. In Proceedings of Genetic and Evolutionary Computation Conference Companion, ACM, Lille, France, pp. 183–184, 2021. DOI: https://doi.org/10.1145/3449726.3459456.

    Chapter  Google Scholar 

  152. X. F. Liu, Z. H. Zhan, T. L. Gu, S. Kwong, Z. Y. Lu, H. B. L. Duh, J. Zhang. Neural network-based information transfer for dynamic optimization. IEEE Transactions on Neural Networks and Learning Systems, vol.31, no.5, pp. 1557–1570, 2020. DOI: https://doi.org/10.1109/TNNLS.2019.2920887.

    Article  Google Scholar 

  153. S. C. Liu, Z. H. Zhan, K. C. Tan, J. Zhang. A multiobjective framework for many-objective optimization. IEEE Transactions on Cybernetics, to be published. DOI: https://doi.org/10.1109/TCYB.2021.3082200.

  154. X. F. Liu, Z. H. Zhan, Y. Gao, J. Zhang, S. Kwong, J. Zhang. Coevolutionary particle swarm optimization with bottleneck objective learning strategy for many-objective optimization. IEEE Transactions on Evolutionary Computation, vol.23, no.4, pp.587–602, 2019. DOI: https://doi.org/10.1109/TEVC.2018.2875430.

    Article  Google Scholar 

  155. S. J. Li, W. Y. Gong, Q. Gu. A comprehensive survey on meta-heuristic algorithms for parameter extraction of photovoltaic models. Renewable and Sustainable Energy Reviews, vol.141, Article number 110828, 2021. DOI: https://doi.org/10.1016/J.RSER.2021.110828.

  156. W. Y. Gong, Z. W. Liao, X. Y. Mi, L. Wang, Y. Y. Guo. Nonlinear equations solving with intelligent optimization algorithms: A survey. Complex System Modeling and Simulation, vol.1, no.1, pp. 15–32, 2021. DOI: https://doi.org/10.23919/CSMS.2021.0002.

    Article  Google Scholar 

  157. Z. G. Chen, Z. H. Zhan, H. Wang, J. Zhang. Distributed individuals for multiple peaks: A novel differential evolution for multimodal optimization problems. IEEE Transactions on Evolutionary Computation, vol.24, no.4, pp. 708–719, 2020. DOI: https://doi.org/10.1109/TEVC.2019.2944180.

    Article  Google Scholar 

  158. X. Y. Cai, M. Hu, D. W. Gong, Y. N. Guo, Y. Zhang, Z. Fan, Y. H. Huang. A decomposition-based coevolutionary multiobjective local search for combinatorial multiobjective optimization. Swarm and Evolutionary Computation, vol. 49, pp. 178–193, 2019. DOI: https://doi.org/10.1016/j.swevo.2019.05.007.

    Article  Google Scholar 

  159. X. Zhang, Z. H. Zhan, W. Fang, P. J. Qian, J. Zhang. Multi population ant colony system with knowledge based local searches for multiobjective supply chain configuration. IEEE Transactions on Evolutionary Computation, to be published, DOI: https://doi.org/10.1109/TEVC.2021.3097339.

  160. Z. W. Ma, Y. Wang, W. Song. A new fitness function with two rankings for evolutionary constrained multiobjective optimization. IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol.51, no. 8, pp. 5005–5016, 2021. DOI: https://doi.org/10.1109/TSMC.2019.2943973.

    Article  Google Scholar 

  161. Y. Wang, J. P. Li, X. H. Xue, B. C. Wang. Utilizing the correlation between constraints and objective function for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation, vol.24, no.1, pp. 29–43, 2020. DOI: https://doi.org/10.1109/TEVC.2019.2904900.

    Article  Google Scholar 

  162. Z. Z. Liu, Y. Wang. Handling constrained multiobjective optimization problems with constraints in both the decision and objective spaces. IEEE Transactions on Evolutionary Computation, vol.23, no.5, pp.870–884, 2019. DOI: https://doi.org/10.1109/TEVC.2019.2894743.

    Article  Google Scholar 

  163. Z. Tan, H. D. Wang. A kriging-assisted evolutionary algorithm using feature selection for expensive sparse multi-objective optimization. In Proceedings of IEEE Congress on Evolutionary Computation, IEEE, Glasgow, UK, pp. 1–8, 2020. DOI: https://doi.org/10.1109/CEC48606.2020.9185825.

    Google Scholar 

  164. Z. Tan, H. D. Wang, S. L. Liu. Multi-stage dimension reduction for expensive sparse multi-objective optimization problems. Neurocomputing, vol.440, pp. 159–174, 2021. DOI: https://doi.org/10.1016/j.neucom.2021.01.115.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by National Key Research and Development Program of China (No. 2019YFB2102102), the Outstanding Youth Science Foundation (No. 61822602), National Natural Science Foundations of China (Nos. 62176094, 61772207 and 61873097), the Key-Area Research and Development of Guangdong Province (No. 2020B010166002), Guangdong Natural Science Foundation Research Team (No. 2018B030312003), and National Research Foundation of Korea (No. NRF-2021H1D3A2A01082705).

Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, South China University of Technology, Guangzhou, 510006, China

    Jian-Yu Li & Zhi-Hui Zhan

  2. Pazhou Laboratory, Guangzhou, 510330, China

    Jian-Yu Li & Zhi-Hui Zhan

  3. Victoria University, Melbourne, 8001, Australia

    Jun Zhang

Authors
  1. Jian-Yu Li
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Zhi-Hui Zhan
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Jun Zhang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Zhi-Hui Zhan.

Additional information

Colored figures are available in the online version at https://link.springer.com/journal/11633

Jian-Yu Li received the B. Sc. degree in computer science and technology from South China University of Technology, China in 2018, where he is currently pursuing the Ph. D. degree in computer science and technology with School of Computer Science and Engineering. He has been invited as a reviewer of IEEE Transactions on Evolutionary Computation and the Neurocomputing.

His research interests include computational intelligence, data-driven optimization, machine learning (deep learning, and their applications in real-world problems, and in environments of distributed computing and big data). E-mail: jianyulics@qq.com ORCID iD: 0000-0002-6143-9207

Zhi-Hui Zhan received the B. Sc. and the Ph. D. degrees in computer science from the Sun Yat-sen University, China in 2007 and 2013, respectively. He is currently the Changjiang Scholar Young Professor with School of Computer Science and Engineering, South China University of Technology, China. He was a recipient of the IEEE Computational Intelligence Society (CIS) Outstanding Early Career Award in 2021, the Outstanding Youth Science Foundation from National Natural Science Foundations of China (NSFC) in 2018, and the Wu Wen-Jun Artificial Intelligence Excellent Youth from the Chinese Association for Artificial Intelligence in 2017. His doctoral dissertation was awarded the IEEE Computational Intelligence Society (CIS) Outstanding Ph.D. Dissertation and the China Computer Federation (CCF) Outstanding Ph.D. Dissertation. He is listed as one of the Highly Cited Chinese Researchers in Computer Science. He is currently an Associate Editor of IEEE Transactions on Evolutionary Computation, Neurocomputing, and Memetic Computing.

His research interests include evolutionary computation algorithms, swarm intelligence algorithms, deep learning, and their applications in real-world problems, and in environments of cloud computing and big data. E-mail: zhanapollo@163.com (Corresponding author) ORCID iD: 0000-0003-0862-0514

Jun Zhang received the Ph.D. degree in electronic engineering from City University of Hong Kong, China in 2002. He is currently a Korea Brain Pool Fellow Professor with Hanyang University, Republic of Korea, a visiting professor with Victoria University, Australia, and a visiting professor with Chaoyang University of Technology, China. He has published over more than 150 IEEE Transactions papers in his research areas. He was a recipient of the Changjiang Chair Professor from the Ministry of Education, China in 2013, the National Science Fund for Distinguished Young Scholars of China in 2011, and the First-Grade Award in Natural Science Research from the Ministry of Education, China in 2009. He is currently an Associate Editor of IEEE Transactions on Evolutionary Computation and IEEE Transactions on Cybernetics.

His research interests include computational intelligence, cloud computing, operations research, and power electronic circuits. E-mail: junzhang@ieee.org

Rights and permissions

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, JY., Zhan, ZH. & Zhang, J. Evolutionary Computation for Expensive Optimization: A Survey. Mach. Intell. Res. 19, 3–23 (2022). https://doi.org/10.1007/s11633-022-1317-4

Download citation

  • Received: 03 August 2021

  • Accepted: 09 October 2021

  • Published: 21 January 2022

  • Issue Date: February 2022

  • DOI: https://doi.org/10.1007/s11633-022-1317-4

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Expensive optimization problem
  • evolutionary computation
  • evolutionary algorithm
  • swarm intelligence
  • particle swarm optimization
  • differential evolution
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us
  • Track your research

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Journal finder
  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our brands

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Discover
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support
  • Legal notice
  • Cancel contracts here

Not affiliated

Springer Nature

© 2025 Springer Nature

pFad - Phonifier reborn

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.


Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy