Abstract
In this work, a novel operator-based differential evolution (DE) algorithm has been proposed. The proposed approach has been inspired by the internal adaption (environment) of the search space. Therefore, maintaining environment (vectors) for the search space can be achieved by introducing the better fitness of candidate solution. In the proposed approach, candidate solutions are multiplied with the different parameter values, which depend on the nature of the problem and available counterbalancing resources. The proposed variant termed an internal adaption-based environment is considered in the existing mutation and crossover operators to provide more diversity for selecting the effective mutant solutions. In the experimental analysis, the proposed approach is compared with the five modern DE variants and tested on benchmark function (f1 to f24) on 20, and 40 dimensions. In addition, it is also verified by hypothesis testing in terms of the minimum error. From the obtained results, it is observed that the proposed algorithm is found to be a better target value in terms of the minimum number of function evaluation and statistical functions. It also validates that the proposed algorithm has achieved a reasonable convergence rate and diversity on 20 and 40 dimensions.
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References
R. Storn, K. Price, Differential Evolution–A Simple and Efficient Adaptive Scheme for Global Optimization Over Continuous Spaces (International Computer Science Institute, Berkeley, 1995)
M.G.H. Omran, A. Salman, A.P. Engelbrecht, Self-adaptive differential evolution, in Proceedings of the International Conference on Computational Intelligence and Security, Xi’an, China, pp. 192-199, 15–19 Dec 2005
E. Mezura-Montes, J. Vel azquez-Reyes, C.A. Coello, A comparative study of differential evolution variants for global optimization, in Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation (2006), pp. 485–492
H.-Y. Fan, J. Lampinen, A trigonometric mutation operation to differential evolution. J. Global Opt. 27(1), 105–129 (2003)
A.K. Qin, V.L. Huang, P.N. Suganthan, Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans. Evol. Comput. 13(2), 398–417 (2009)
M.M. Ali, A. Torn, Population set based global optimization algorithms: some modifications and numerical studies. Comput. Oper. Res. 31(10), 1703–1725 (2004)
J. Brest, S. Greiner, B. Boskovic, M. Mernik, V. Zumer, Self adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans. Evol. Comput. 10, 646–657 (2006)
V.L. Huang, S.Z. Zhao, R. Mallipeddi, P.N. Suganthan, Multi-objective optimization using self-adaptive differential evolution algorithm, in Proceedings of the 11th Conference on Evolutionary Computation,Trondheim, Norway, pp. 190-194, 18–21 May 2009
R. Mallipeddi, P.N. Suganthan, Empirical study on the effect of population size on differential evolution algorithm, in Proceedings of the IEEE Congress on Evolutionary Computation, Hong Kong, pp. 3663-3670, 1–6 June 2008
S. Das, A. Konar, U.K. Chakraborty, wo improved differential evolution schemes for faster global search, in Proceedings of the Genetic Evolution Computing Conference, Washington DC, USA (2005), pp. 991-998
D.K. Tasoulis, N.G. Pavlidis, V.P. Plagianakos, M.N. Vrahatis, Parallel differential evolution, in Proceedings of the 2004 Congress on Evolutionary Computation (2004), pp. 2023–2029
N. Noman, H. Iba, Accelerating differential evolution using an adaptive local search. IEEE Trans. Evol. Comput. 12(1), 107–125 (2008)
Radha Thangaraj, Millie Pant, Ajith Abraham, New mutation schemes for differential evolution algorithm and their application to the optimization of directional over-current relay settings. Appl. Math. Comput. 216(2), 532–544 (2010)
I. Fajfar, J. Puhan, S. Tomazic, A. Burmen, On Selection in Differential Evolution, English Edition. (Elektrotehniki Vestnik, 2011), pp. 275–280
Y. Wang, Z. Cai, Q. Zhang, Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans. Evol. Comput. 15, 55–66 (2011)
S.M. Islam, S. Das, S. Ghosh, S. Roy, P.N. Suganthan, An adaptive differential evolution algorithm with novel mutation and crossover strategies for global numerical optimization, IEEE Trans. Syst. MAN Cyber. Part B Cyber. 42(2), 482–500 (2012)
Ruhul A. Sarker, Saber M. Elsayed, Tapabrata Ray, Differential evolution with dynamic parameters selection for optimization problems. IEEE Trans. Evol. Comput. 18(5), 689–707 (2014)
W. Gong, Z. Cai, Y. Wang, Repairing the Crossover Rate in Adaptive Differential Evolution Applied soft commuting, (Elsevier, Feb 2014), pp. 149–168
Xinyu Zhou, Wu. Zhijian, Hui Wang, Shahryar Rahnamayan, Enhancing differential evolution with role assignment scheme. Soft Comput. 18, 2209–2225 (2014)
Wenchao Yi, Liang Gao, Xinyu Li, Yinzhi Zhou, A new differential evolution algorithm with a hybrid mutation operator and self-adapting control parameters for global optimization problems. ApplIntell 42, 642–660 (2015)
Qinqin Fan, Xuefeng Yan, Self-adaptive differential evolution algorithm with discrete mutation control parameters. Exp. Syst. Appl. 42, 1551–1572 (2015)
Rainer Storn, Kenneth Price, Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Global Opt. 11(4), 341–359 (1997)
Jingqiao Zhang, Arthur C. Sanderson, JADE: adaptive differential evolution with optional external archive. IEEE Trans. Evol. Comput. 13(5), 945–958 (2009)
N. Hansen et al., Real-parameter black-box optimization benchmarking 2009: noiseless functions definitions (2009)
S. Finck, N. Hansen, R. Ros, A. Auger, Real-parameter black-box optimization benchmarking 2009: presentation of the noiseless functions, in Technical Report 2009/20, Research Center PPE, 2009. Updated February, (2010)
S. Finck, N. Hansen, R. Ros, A. Auger, Real-parameter black-box optimization benchmarking2010: presentation of the noiseless functions. http://coco.lri.fr/downloads/download15.02/bbobdocfunctions.pdf
N. Hansen, A. Auger, S. Finck, R. Ros, Real-parameter black-box optimization benchmarking 2010: Experimental Setup, in Technical Report, RR-7215, INRIA (2010)
S. Das, P.N. Suganthan, Differential evolution: a survey of the state-of-the-art. IEEE Trans. Evol. Comput. 15(1), 4–31 (2011)
P. Posik, V. Klems, JADE, an adaptive differential evolution algorithm, benchmarked on the BBOB noiseless testbed. GECCO’12, Philadelphia, PA, USA, (2012)
L. Pal, Benchmarking a Hybrid Multi Level Single Linkage Algorithm on the BBOB Noiseless Testbed, GECCO’13, Amsterdam, Netherlands, (2013)
G.H. Wu, R. Mallipeddi, P.N. Suganthan, R. Wang, H.K. Chen, Differential evolution with multi-population based ensemble of mutation strategies. Inf. Sci. 329, 329–345 (2016). https://doi.org/10.1016/j.ins.2015.09.009
Y. Wang, Z.Z. Liu, J. Li, H.X. Li, G.G. Yen, Utilizing cumulative population distribution information in differential evolution. Appl. Soft Comput. 48, 329–346 (2016)
Y. Wang, B. Xu, G. Sun, S. Yang, A two-phase differential evolution for uniform designs in constrained experimental domains. IEEE Trans. Evol. Comput., (in press). https://doi.org/10.1109/TEVC.2017.2669098
Z. Z. Liu, Y. W. S. Yang, Z. Cai, Differential evolution with a two-stage optimization mechanism for numerical optimization, in 2016 IEEE Congress on Evolutionary Computation (CEC) (Vancouver, BC, 2016), pp. 3170–3177
Shailendra Pratap Singh, Anoj Kumar, Homeostasis mutation based differential evolution algorithm. J. Intell. Fuzzy Syst. 32(5), 3525–3537 (2017)
Hu. Zhongbo, Su. Qinghua, Xianshan Yang, Zenggang Xiong, Not guaranteeing convergence of differential evolution on a class of multimodal functions. Appl. Soft Comput. 41, 479–487 (2016)
Y. Wang, Z. Z. Liu, J. Li, H. X. Li, J. Wang, On the selection of solutions for mutation in differential evolution. Front. Comput. Sci. 12, 297–315. (2016)
Yong Wang, Zhi-Zhong. Liu, Jianbin Li, Han-Xiong. Li, Gery G. Yen, Utilizing cumulative population distribution information in differential evolution. Appl. Soft Comput. 48, 329–346 (2016)
Yong Wang, Han-Xiong. LI, Tingwen Huang, Long Li, Differential evolution based on covariance matrix learning and bimodal distribution parameter setting. Appl. Soft Comput. 18, 232–247 (2014)
S.P. Singh, A. Kumar, Multiobjective differential evolution using homeostasis based mutation for application in software cost estimation. Appl. Intell. 48(3), 628–650 (2018)
S.P. Singh, A. Kumar, Software cost estimation using homeostasis mutation based differential evolution, in 2017 11th International Conference on Intelligent Systems and Control (ISCO), (2017), pp. 173–181
S.P. Singh, V.P. Singh, A.K. Mehta, Differential evolution using homeostasis adaption based mutation operator and its application for software cost estimation, J. King Saud Univ. Comput. Inf. Sci., (2018)
S. P. Singh, Cost estimation model using enhance based differential evolution algorithm, Iran J. Comput. Sci. (Springer), (2019), pp. 1–12
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Singh, S.P. Improved based Differential Evolution Algorithm using New Environment Adaption Operator. J. Inst. Eng. India Ser. B 103, 107–117 (2022). https://doi.org/10.1007/s40031-021-00645-y
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DOI: https://doi.org/10.1007/s40031-021-00645-y