Abstract
Differential Evolution (DE) is a global optimization process that uses population search to find the best solution. It offers characteristics such as fast convergence time, simple and understood algorithm, few parameters, and good stability. To improve its presentation, we propose a differential evolution algorithm based on subpopulation adaptive scale and multi-adjustment strategy (ASMSDE). The algorithm separates the population into three sub-populations based on fitness scores, and different operating tactics are used depending on their characteristics. The superior population uses Gaussian disturbance, while the inferior population uses Levy flights. The intermediate population is responsible for maintaining the population's overall variety. The sizes of the three sub-populations are adaptively changed in response to evolutionary results to account for changes in individual differences over time. With the number of iterations increases and the disparities between individuals reduce, adopt a single population model instead of multi-population model in the later stage of evolution. The ASMSDE algorithm's performance is evaluated by comparing it to other sophisticated algorithms that use benchmark function optimizations. Experimental results show that the ASMSDE algorithm outperforms the comparison algorithms in the majority of circumstances, demonstrating its effectiveness and capacity to manage local optimum situations.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Data availability
Enquiries about data availability should be directed to the authors.
References
Abbass HA, Sarker R, Newton C (2001) PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems. In: Proceedings of the 2001 congress on evolutionary computation (IEEE Cat. No. 01TH8546). IEEE, vol 2, pp 971–978
Abraham A, Jatoth RK, Rajasekhar A (2012) Hybrid differential artificial bee colony algorithm. J Comput Theor Nanosci 9(2):249–257
Brest J, Greiner S, Boskovic B et al (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(6):646–657
Cui L, Li G, Zhu Z et al (2018) A novel differential evolution algorithm with a self-adaptation parameter control method by differential evolution. Soft Comput 22:6171–6190
Das S, Konar A, Chakraborty UK (2005) Two improved differential evolution schemes for faster global search. In: Proceedings of the 7th annual conference on Genetic and evolutionary computation, pp 991–998
Deng L, Wang S, Qiao L, Zhang B (2018) DE-RCO: rotating crossover operator with multiangle searching strategy for adaptive differential evolution. IEEE Access 6:2970–2983
Deng L, Sun H, Li C (2020) JDF-DE: a differential evolution with Jrand number decreasing mechanism and feedback guide technique for global numerical optimization. Appl Intell 51:1–18
Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern Part B 26(1):29–41
Draa A, Bouzoubia S, Boukhalfa I (2015) A sinusoidal differential evolution algorithm for numerical optimisation. Appl Soft Comput 27:99–126
Draa A, Chettah K, Talbi H (2019) A compound Sinusoidal differential evolution algorithm for continuous optimization. Swarm Evol Comput 50:100450
Fan HY, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Glob Optim 27(1):105–129
Fu CM, Jiang C, Chen GS et al (2017) An adaptive differential evolution algorithm with an aging leader and challengers mechanism. Appl Soft Comput 57:60–73
Guo S, Yang C (2015) Enhancing differential evolution utilizing eigenvector-based crossover operator. IEEE Trans Evolut Comput 19(1):31–49
Guo S, Yang C, Hsu P, Tsai JS (2015) Improving differential evolution with a successful-parent-selecting framework. IEEE Trans Evol Comput 19(5):717
Holland JB, Holland J, Holland JH et al (1975) Adaption in natural and artificial systems. Ann Arbor 6(2):126–137
Ibrahim RA, Abd Elaziz M, Lu S (2018) Chaotic opposition-based grey-wolf optimization algorithm based on differential evolution and disruption operator for global optimization. Expert Syst Appl 108:1–2
Islam SM, Das S, Ghosh S, Roy S, Suganthan PN (2012) An adaptive differential evolution algorithm with novel mutation and crossover strategies for global numerical optimization. IEEE Trans Syst Man Cybern B 42(2):482
Ji J, Xiao H, Yang C (2021) HFADE-FMD: a hybrid approach of fireworks algorithm and differential evolution strategies for functional module detection in protein-protein interaction networks. Appl Intell 51(6788):1–15
Jiashan Z, Yingxian C, Xiaoqun L (2019) Hybrid bee colony Algorithm embedded with differential evolution operator and its application in VRPSDP. Pract Underst Math 049(004):117–123 (in Chinese)
Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: IEEE international conference on neural networks, pp 1942–1948
Leon M, Xiong N, Molina D, Herrera F (2019) A novel memetic framework for enhancing differential evolution algorithms via combination with Alopex local search. Int J Comput Intell Syst 12(2):795–808
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(C):577
Li X, Wang L, Jiang Q et al (2021) Differential evolution algorithm with multi-population cooperation and multi-strategy integration. Neurocomputing 421:285–302
Liang J, Wang P, Guo L, Qu B, Yue C, Yu K, Wang Y (2019) Multi-objective flow shop scheduling with limited buffers using hybrid self-adaptive differential evolution. Memet Comput 11:407–422
Lianghong Wu, Yaonan W, Shao Z et al (2007) Research and application of two-population pseudo-parallel differential evolution algorithm. Control Theory Appl 24(3):453–458 (in Chinese)
Lin W, Xiaoyu W, Jianchao W (2018) A differential hybrid leapfrog algorithm based on selection strategy. Comput Eng Sci 040(001):121–127 (in Chinese)
Liu Z, Wang Y, Yang S, Cai Z (2016) Differential evolution with a two-stage optimization mechanism for numerical optimization. In: 2016 IEEE congress on evolutionary computation (CEC), pp 3170–3177
Liu J, Lampinen J (2005) A fuzzy adaptive differential evolution algorithm. Soft Comput 9(6):448–462
Luo J, Shi B (2019) A hybrid whale optimization algorithm based on modified differential evolution for global optimization problems. Appl Intell 49:1982–2000
Min Z (2021) Research on improvement and application of differential evolution algorithm. Northern University for Nationalities, https://doi.org/10.27754/d.cnki.gbfmz (in chinese)
Mohamed AW, Mohamed AK (2019) Adaptive guided differential evolution algorithm with novel mutation for numerical optimization. Int J Mach Learn Cybern 10(2):253–277
Mohamed AW, Suganthan PN (2018) Real-parameter unconstrained optimization based on enhanced fitness-adaptive differential evolution algorithm with novel mutation. Soft Comput 22:3215–3235
Peng H, Guo Z, Deng C et al (2018) Enhancing differential evolution with random neighbors based strategy. J Comput Sci 26(5):501–511
Pengfei H (2017) Research on improvement and application of differential evolution algorithm. Xiangtan University, (in Chinese)
Potter MA, De Jong KA (1994) A cooperative coevolutionary approach to function optimization. In: International conference on parallel problem solving from nature. Berlin, Heidelberg: Springer Berlin Heidelberg, pp 249–257
Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417
Qing AY (2004) Electromagnetic inverse scattering of multiple perfectly conducting cylinders by differential evolution strategy with individuals in groups (GDES). IEEE Trans Antennas Propag 52(5):1223–1229
Sengupta R, Pal M, Saha S, Bandyopadhyay S (2020) Uniform distribution driven adaptive differential evolution. Appl Intell 50(11):3638–3659
Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Sun G, Yang B, Yang Z, Xu G (2020) An adaptive differential evolution with combined strategy for global numerical optimization. Soft Comput 24(9):6277–6296
Tanabe R, Fukunaga A (2013) Success-history based parameter adaptation for differential evolution. In: 2013 IEEE congress on evolutionary computation. IEEE, pp 71–78
Tanabe R, Fukunaga AS (2014) Improving the search performance of SHADE using linear population size reduction. In: 2014 IEEE congress on evolutionary computation (CEC). IEEE, 1658–1665
Tatsis VA, Parsopoulos KE (2017) Differential evolution with grid-based parameter adaptation. Soft Comput 21(8):2105–2127
Thangaraj R, Pant M, Abraham A et al (2011) Particle swarm optimization: hybridization perspectives and experimental illustrations. Appl Math Comput 217(12):5208–5226
Tian M, Gao X (2019) An improved differential evolution with information intercrossing and sharing mechanism for numerical optimization. Swarm Evolut Comput 50:100341
Van P, Aarts E (1987) Simulated annealing: theory and applications. D.Reidel Publishing Company
Wang Y, Cai Z, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15(1):55–66
Wang Y, Liu ZZ, Li J et al (2016) Utilizing cumulative population distribution information in differential evolution. Appl Soft Comput 48:329–346
Wu G, Mallipeddi R, Suganthan PN et al (2016) Differential evolution with multi-population based ensemble of mutation strategies. Inf Sci 329:329–345
Wu G, Xin S, Li H, Chen H, Suganthan PN (2017) Ensemble of differential evolution variants. Inf Sci 423:172
Wu X, Liu X, Zhao N (2019) An improved differential evolution algorithm for solving a distributed assembly flexible job shop scheduling problem. Memet Comput 11(4):335–355
Xueqing Y (2017) Improved differential evolution algorithm based on population classification. Shaanxi Normal University, (in Chinese)
Yan L, Xuan-yian B, Zong-ran D (2022) A discrete hybrid algorithm based on differential evolution and cuckoo search for optimizing the layout of ship pipe route. Ocean Eng 261:112164 (in Chinese)
Yang G (2022) Adaptive differential evolution algorithm based on neighborhood search. Comput Inf Technol 30(04):1–4. https://doi.org/10.19414/j.cnki.1005-1228.2022.04.002. (in Chinese)
Yang Z, Yao X, He J (2007) Making a difference to differential evolution. Advances in metaheuristics for hard optimization. Springer, Berlin, Heidelberg, pp 397–414
Yu W, Shen M, Chen W, Zhan Z, Gong Y, Lin Y, Liu O, Zhang J (2014) Differential evolution with two-level parameter adaptation. IEEE Trans Cybern 44(7):1080–1099
Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958
Zhao W, Liu E, Wang B, Gao S, Peng CE (2018) Differential evolutionary optimization of an equivalent dipole model for electromagnetic emission analysis. IEEE Trans Electromagn Compat 60(6):1635–1639
Zhi Z, Min Z, Haimiao M et al (2020) Bat differential hybrid algorithm for collaborative intelligence. Comput Eng Des 41(02):402–410 (in Chinese)
Zhu T, Hao Y, Luo W, Ning H (2018) Learning enhanced differential evolution for tracking optimal decisions in dynamic power systems. Appl Soft Comput 67:812–821
Zhu Peng D, Nisuo OZ (2022) Sparrow search algorithm combining differential evolution and mixed multi-strategy. Comput Eng Des 43(06):1609–1619. https://doi.org/10.16208/j.issn1000-7024.2022.06.014. (in Chinese)
Zixing C, Tao G (2004) Research progress of immune algorithms. Control Decis 08:841–846
Funding
This study was not funded by any grants or external funding sources.
Author information
Authors and Affiliations
Contributions
All authors contributed equally to the article.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no competing interests.
Ethical approval
Further, we would like to mention that this article does not contain any studies with animals and does not involve any studies over human being.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Xue, C., Liu, T., Deng, L. et al. Multi-population multi-strategy differential evolution algorithm with dynamic population size adjustment. Soft Comput 28, 9949–9963 (2024). https://doi.org/10.1007/s00500-024-09843-4
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-024-09843-4