Abstract
Differential evolution (DE) algorithms tend to be limited to local optimization when solving complex optimization problems. Different iteration schemes lead to different convergence speeds. In this paper, we mainly use the dynamic mutation parameter \(\text {FS}\) to improve the DE algorithm. Based on two ideas, a total of seven DE schemes are proposed to optimize the DE algorithm. We test the performance of the improved DE scheme on 56 test functions. Experiments show that the improved DE algorithm is better than the baseline DE algorithm in terms of accuracy, convergence and8 convergence speed.



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
Abu KR, Aljarah I, Sharieh A, Abd EM, Damaševičius R, Krilavičius T (2022) A review of the modification strategies of the nature inspired algorithms for feature selection problem. Mathematics 10(3):464
Angeline PJ, Saunders GM, Pollack JB (1994) An evolutionary algorithm that constructs recurrent neural networks. IEEE Trans Neural Netw 5(1):54–65
Baatar N, Pham MT, Koh CS (2013) Multiguiders and nondominate ranking differential evolution algorithm for multiobjective global optimization of electromagnetic problems. IEEE Trans Magn 49(5):2105–2108
Bhandari AK (2020) A novel beta differential evolution algorithm-based fast multilevel thresholding for color image segmentation. Neural Comput Appl 32(9):4583–4613
Biedrzycki R, Arabas J, Jagodziński D (2019) Bound constraints handling in differential evolution: an experimental study. Swarm Evol Comput 50:100453
Cai X, Hu Z, Zhao P, Zhang W, Chen J (2020) A hybrid recommendation system with many-objective evolutionary algorithm. Expert Syst Appl 159:113648
Cheng MY, Tran DH (2014) Two-phase differential evolution for the multiobjective optimization of time-cost tradeoffs in resource-constrained construction projects. IEEE Trans Eng Manage 61(3):450–461
Chowdhury A, Ghosh A, Giri DS (2010) Optimization of antenna configuration with a fitness-adaptive differential evolution algorithm. Prog Electromagn Res B 26:291–319
Coelho LDS, Mariani VC, Da LMVF, Leite JV (2013) Novel gamma differential evolution approach for multiobjective transformer design optimization. IEEE Trans Magn 49(5):2121–2124
Cui R, Liu H, Zhang C (2019) A deep neural framework for continuous sign language recognition by iterative training. IEEE Trans Multimed 21(7):1880–1891
Daham HA, Mohammed HJ (2021) An evolutionary algorithm approach for vehicle routing problems with backhauls. Mater Today Proc 20:21
Deb K, Anand A, Joshi D (2002) A computationally efficient evolutionary algorithm for real-parameter optimization. Evol Comput 10(4):371–395
Deng W, Xu J, Song Y, Zhao H (2021) Differential evolution algorithm with wavelet basis function and optimal mutation strategy for complex optimization problem. Appl Soft Comput 100:106724
Deng W, Shang S, Cai X, Zhao H, Zhou Y, Chen H, Deng W (2021) Quantum differential evolution with cooperative coevolution framework and hybrid mutation strategy for large scale optimization. Knowl Based Syst 224:107080
Deng W, Shang S, Cai X, Zhao H, Song Y, Xu J (2021) An improved differential evolution algorithm and its application in optimization problem. Soft Comput 25(7):5277–5298
Deng W, Xu J, Song Y, Zhao H (2021) Differential evolution algorithm with wavelet basis function and optimal mutation strategy for complex optimization problem. Appl Soft Comput 100:106724
Famelis IT, Kaloutsa V (2021) Parameterized neural network training for the solution of a class of stiff initial value systems. Neural Comput Appl 33(8):3363–3370
Ghosh A, Das S, Chowdhury A, Giri R (2011) An improved differential evolution algorithm with fitness-based adaptation of the control parameters. Inform Sci 181(18):3749–3765
Gupta S, Su R (2022) An efficient differential evolution with fitness-based dynamic mutation strategy and control parameters. Knowl Based Syst 251:109280
Kang Y, Wang H, Pu B, Tao L, Chen J, Philip SY (2022) A hybrid two-stage teaching-learning-based optimization algorithm for feature selection in bioinformatics. IEEE ACM Trans Comput Biol 20:22
Mohamed AW, Suganthan PN (2018) Real-parameter unconstrained optimization based on enhanced fitness-adaptive differential evolution algorithm with novel mutation. Soft Comput 22(10):3215–3235
Nadimi-Shahraki MH, Taghian S, Mirjalili S, Faris H (2020) MTDE: an effective multi-trial vector-based differential evolution algorithm and its applications for engineering design problems. Appl Soft Comput 97:106761
Reddy SS (2019) Optimal power flow using hybrid differential evolution and harmony search algorithm. Int J Mach Learn Cybern 10(5):1077–1091
Shen X, Zou D, Duan N, Zhang Q (2019) An efficient fitness-based differential evolution algorithm and a constraint handling technique for dynamic economic emission dispatch. Energy 186:115801
Sikdar UK, Ekbal A, Saha S (2015) MODE: multiobjective differential evolution for feature selection and classifier ensemble. Soft Comput 19(12):3529–3549
Song Y, Wu D, Wagdy MA, Zhou X, Zhang B, Deng W (2021) Enhanced success history adaptive DE for parameter optimization of photovoltaic models. Complexity 2021:2021
Storn R, Price K (1995) Differential evolution-a simple efficient adaptive scheme for global optimization [R]. Tech. Rep. TR-95-012, ICSI, Berkeley, Calif, USA
Tenaglia GC, Lebensztajn L (2014) A multiobjective approach of differential evolution optimization applied to electromagnetic problems. IEEE Trans Magn 50(2):625–628
Tiwari S, Kumar A (2022) Optimal micro-PMUs placement with channel limits using dynamically controlled Taguchi binary particle swarm optimization. Electr Power Compos Syst 50(18):1072–1086
Tiwari S, Kumar A (2023) Advances and bibliographic analysis of particle swarm optimization applications in electrical power system: concepts and variants. Evol Intell 16(1):23–47
Tiwari S, Kumar A, Basetti V (2022) Multi-objective micro phasor measurement unit placement and performance analysis in distribution system using NSGA-II and PROMETHEE-II. Measurement 198:111443
Wang Y, Yu Y, Gao S, Pan H, Yang G (2019) A hierarchical gravitational search algorithm with an effective gravitational constant. Swarm Evol Comput 46:118–139
Wu L, Wang Y, Yuan X, Chen Z (2011) Multiobjective optimization of HEV fuel economy and emissions using the self-adaptive differential evolution algorithm. IEEE Trans Veh Technol 60(6):2458–2470
Xue X, Zhang J (2021) Matching large-scale biomedical ontologies with central concept based partitioning algorithm and adaptive compact evolutionary algorithm. Appl Soft Comput 106:107343
Xue Y, Cai X, Neri F (2022) A multi-objective evolutionary algorithm with interval based initialization and self-adaptive crossover operator for large-scale feature selection in classification. Appl Soft Comput 127:109420
Zeng Z, Zhang M, Chen T, Hong Z (2021) A new selection operator for differential evolution algorithm. Knowl Based Syst 226:107150
Zhan ZH, Shi L, Tan KC, Zhang J (2022) A survey on evolutionary computation for complex continuous optimization. Artif Intell Rev 55(1):59–110
Zhang Q, Zou D, Duan N, Shen X (2019) An adaptive differential evolutionary algorithm incorporating multiple mutation strategies for the economic load dispatch problem. Appl Soft Comput 78:641–669
Zhang Y, Gong D, Gao X, Tian T, Sun X (2020) Binary differential evolution with self-learning for multi-objective feature selection. Inform Sci 507:67–85
Zhang Y, Li S, Xu B (2021) Convergence analysis of beetle antennae search algorithm and its applications. Soft Comput 25(16):10595–10608
Zhao W, Yang Y, Lu Z (2022) Interval short-term traffic flow prediction method based on CEEMDAN-SE noise reduction and LSTM optimized by GWO. WCMC 2022:2022
Funding
This work is supported in part by the National Natural Science Foundation of China under Grant 62206109 and the Innovation and Entrepreneurship Training Program for Undergraduate under Grant CX22356.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Human and animal rights
This article does not contain any studies with human participants or animals performed by any of the authors.
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
Lin, Y., Yang, Y. & Zhang, Y. Improved differential evolution with dynamic mutation parameters. Soft Comput 27, 17923–17941 (2023). https://doi.org/10.1007/s00500-023-09080-1
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-023-09080-1