Abstract
Differential evolution (DE) is a popular evolutionary technique which can be applied in various constrained and unconstrained optimization problems along with the real time problems by modifying its operators like mutation, crossover and selection. In this paper initialization process of population along with the mutation rate is modified using the concept of logistic map and wavelet transformation in DE respectively. This modification increases the convergence rate. The modified proposal is tested on various benchmark problems. Also the evaluated results are compared for performance with state of the art algorithms, along with three real time non linear engineering problems, which dictates that the modified DE is easily applicable to the real time optimization problems.
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Abderazek H, Ferhat D, Atanasovska I, Boualem K (2015) A differential evolution algorithm for tooth profile optimization with respect to balancing specific sliding coefficients of involute cylindrical spur and helical gears. Adv Mech Eng 7:1–11
Ali M, Pant M, Singh VP (2010) Two modified differential evolution algorithms and their applications to engineering design problems. World J Model Simul 6(1):72–80
Anh P (2016) Engineering optimization by constrained differential evolution with nearest neighbour comparison. Vietnam J Mech 38(2):89–101
Biswas P, Suganthan P, Mallipeddi R, Amaratunga G (2018) Optimal power flow solutions using differential evolution algorithm integrated with effective constraint handling techniques. Eng Appl Artif Intell 68:81–100
Brest J, Greiner S 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
Cai Y, Chen Y, Wang T, Tian H (2016) Improving differential evolution with a new selection method of parents for mutation. Front Comput Sci 10(2):246–269
Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: 6th international symposium on machine and human science, pp 39–43
Fu C, Xu Y, Jiang C, Han X, Huang Z (2017) Improved differential evolution with shrinking space technique for constrained optimization. Chin J Mech Eng 30(3):553–565
Hamza F, Abderazek H, Lakhdar S, Ferhat D, Yıldız A (2018) Optimum design of cam-roller follower mechanism using a new evolutionary algorithm. Int J Adv Manuf Technol 99(5–8):1267–1282
Holland JH (1975) Adaptive in natural and artificial systems. University of Michigan Press, Ann Arbor
Jigang H, Hui F, Jie W (2019) A PI controller optimized with modified differential evolution algorithm for speed control of BLDC motor. Automatika 60(2):135–148
Knobloch R, Mlýnek J, Srb R (2017) The classic differential evolution algorithm and its convergence properties. Appl Math 62(2):197–208
Kumar P, Pant M (2014) Modified random localization based DE for static economic power dispatch with generator constraints. Int J Bio-Inspired Comput 6(4):250–261
Kumar P, Pant M (2016) Recognition of noise source in multi sounds field by modified random localized based DE algorithm. Int J Syst Assur Eng Manag 9(1):245–261
Kumar P, Pant M (2012) Enhanced mutation strategy for differential evolution. In Proceedings of IEEE congress of evolutionary computing (CEC-12), pp 1–6.
Kumar S, Pant M, Ray AK (2018) DE-IE: differential evolution for color image enhancement. Int J Syst Assur Eng Manag 9(3):577–588
Kuo R, Zulvia F (2018) An improved differential evolution with cluster decomposition algorithm for automatic clustering. Soft Comput
Lei Y, Gou J, Wang C, Luo W, Cai Y (2017) Improved differential evolution with a modified orthogonal learning strategy. IEEE Access 5:9699–9716
Li X, Zhang H (2018) Enhanced differential evolution with modified parent selection technique for numerical optimisation. Int J Comput Sci Eng 17(1):98
Li Y, Zhan Z, Gong Y, Chen W, Zhang J, Li Y (2014) Differential evolution with an evolution path: A DEEP evolutionary algorithm. IEEE Trans Cybern 45(9):1798–1810
Mohamed A, Sabry H, Abd-Elaziz T (2013) Real parameter optimization by an effective differential evolution algorithm. Egypt Inf J 14:37–53
Price KV, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization Natural Computing Series. Springer, Berlin
Qin A, Huang V, Suganthan P (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417
Qiu X, Li B, Cui Z, Li J (2014) A fractal mutation factor modified differential evolution algorithm. Appl Mech Mater 598:418–423
Rahnamayan S, Tizhoosh HR, Salama MMA (2008) Opposition-based differential evolution. IEEE Trans Evol Comput 12(1):64–79
Rajpurohit J, Sharma TK, Abraham A, Vaishali A (2017) Glossary of metaheuristic algorithms. Int J Comput Inf Syst Ind Manag Applic 9:181–205
Rout BD, Pati BB, Panda S (2018) A hybrid modified differential evolution-pattern search approach for SSSC based damping controller design under communication constraints. Int J Syst Assur Eng Manag 9(4):962–971
Singh P, Chaturvedi P, Kumar P (2018) A novel differential evolution approach for constraint optimization. Int J Bio-Inspired Comput 12(4):254–265
Storn R, Price K (1995) Differential evolution: a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical report TR-95–012, International Computer Science Institute, Berkeley, USA
Suganthan PN, Hansen N, Liang JJ, Deb K, Chen YP, Auger A, Tiwari S (2005) Problem definition and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical report, Nanyang Technological University, Singapore
Vesterstrom J, Thomsen R (2004) A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. Proc Cong Evolut Comput 2:1980–1987
Yao X, Liu Y, Liang K-H, Lin G (2003) Fast evolutionary algorithms. In: Ghosh A, Tsutsui S (eds) Advances in Evolutionary Computing. Natural Computing Series. Springer, Berlin, Heidelberg, pp 45–94. https://doi.org/10.1007/978-3-642-18965-4_2
Yi W, Li X, Gao L, Zhou Y (2015) ε Constrained differential evolution algorithm with a novel local search operator for constrained optimization problems. In: Proceedings in adaptation, learning and optimization, pp 495–507
Zaheer H, Pant M, Kumar S (2018) A new guiding force strategy for differential evolution. Int J Syst Assur Eng Manag 8(4):2170–2183
Zhang J, Sanderson A (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958
Zou D, Wu J, Gao L, Li S (2013) A modified differential evolution algorithm for unconstrained optimization problems. Neurocomputing 120:469–481
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Kashyap, K., Sharma, T.K. & Rajpurohit, J. Logistic map and wavelet transform based differential evolution. Int J Syst Assur Eng Manag 11, 506–514 (2020). https://doi.org/10.1007/s13198-019-00920-8
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DOI: https://doi.org/10.1007/s13198-019-00920-8