banner
Home > Open Journal Systems

Enhancing differential evolution through a modified mutation strategy for unimodal and multimodal problem optimization

Pooja Tiwari, Vishnu Narayan Mishra, Raghav Prasad Parouha

Abstract


Amid a lot of evolutionary methods (EMs), differential evolution (DE) is broadly used for various optimization issues. Though, it has rare shortcomings such as slow convergence, stagnation etc. Likewise, mutation and its control factor choice for DE is extremely inspiring for enhanced optimization. To increase the exploration competence of DE, a modified-DE (M-DE) is advised in this paper. It implemented a new mutation system, thru the perception of particle swarm optimization, to further trade off the population diversity. Meanwhile, centered on time-varying structure, new mutant control parameters incorporated with the suggested mutation scheme, to escaping local optima and keep evolving. Using the features of memory and robustly altered control parameters, exploitation and exploration ability of M-DE is well-adjusted. Also, admitted features of M-DE algorithm follows to speeding up convergence significantly. Finally, to verify the effectiveness of M-DE, groups of assessments have been piloted on six unimodal and seven multimodal benchmark suites. Performance of M-DE compared with different peer DE algorithms. According the investigational results, efficiency of the suggested M-DE technique has been confirmed.


Keywords


evolutionary algorithm; differential evolution; mutation operation; crossover; unimodal and multimodal

Full Text:

PDF

References


1. Parouha RP, Das KN. Parallel hybridization of differential evolution and particle swarm optimization for constrained optimization with its application. International Journal of System Assurance Engineering and Management 2016; 7(S1): 143–162. doi: 10.1007/s13198-015-0354-6

2. Storn R, Price K. Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 1997; 11(2): 341–359. doi: 10.1023/A:1008202821328

3. Dhanalakshmy DM, Jeyakumar G, Velayutham CS. Empirical investigations on evolution strategies to self-adapt the mutation and crossover parameters of differential evolution algorithm. International Journal of Intelligent Systems Technologies and Applications 2021; 20(2): 103–125. doi: 10.1504/ijista.2021.119028

4. Wang Y, Li B, Weise T. Estimation of distribution and differential evolution cooperation for large scale economic load dispatch optimization of power systems. Information Sciences 2010; 180(12): 2405–2420. doi: 10.1016/j.ins.2010.02.015

5. Dragoi EN, Curteanu S, Galaction AI, Cascaval D. Optimization methodology based on neural networks and self-adaptive differential evolution algorithm applied to an aerobic fermentation process. Applied Soft Computing 2013; 13(1): 222–238. doi: 10.1016/j.asoc.2012.08.004

6. Mesejo P, Ugolotti R, Di Cunto F, et al. Automatic hippocampus localization in histological images using differential evolution-based deformable models. Pattern Recognition Letters 2013; 34(3): 299–307. doi: 10.1016/j.patrec.2012.10.012

7. Li X, Hu C, Yan X. Chaotic differential evolution algorithm based on competitive coevolution and its application to dynamic optimization of chemical processes. Intelligent Automation & Soft Computing 2013; 19(1): 85–98. doi: 10.1080/10798587.2013.771437

8. Das KN, Parouha RP. Optimization with a novel hybrid algorithm and applications. OPSEARCH 2016; 53(3): 443–473. doi: 10.1007/s12597-015-0240-7

9. Parouha RP, Das KN. Economic load dispatch using memory based differential evolution. International Journal of Bio-Inspired Computation 2018; 11(3): 159–170. doi: 10.1504/ijbic.2018.091700

10. Neri F, Tirronen V. Recent advances in differential evolution: A survey and experimental analysis. Artificial Intelligence Review 2010; 33(1–2): 61–106. doi: 10.1007/s10462-009-9137-2

11. Das S, Suganthan PN. Differential evolution: A survey of the state-of-the-art. IEEE Transactions on Evolutionary Computation 2011; 15(1): 4–31. doi: 10.1109/tevc.2010.2059031

12. Das S, Mullick SS, Suganthan PN. Recent advances in differential evolution—An updated survey. Swarm and Evolutionary Computation 2016; 27: 1–30. doi: 10.1016/j.swevo.2016.01.004

13. Eltaei T, Mahmood A. Differential evolution: A survey and analysis. Applied Sciences 2018; 8(10): 1945. doi: 10.3390/app8101945

14. Opara KR, Arabas J. Differential evolution: A survey of theoretical analyses. Swarm and Evolutionary Computation 2019; 44: 546–558. doi: 10.1016/j.swevo.2018.06.010

15. Bilal, Pant M, Zaheer H, et al. Differential evolution: A review of more than two decades of research. Engineering Applications of Artificial Intelligence 2020; 90: 103479. doi: 10.1016/j.engappai.2020.103479

16. Ahmad MF, Isa NAM, Lim WH, Ang KM. Differential evolution: A recent review based on state-of-the-art works. Alexandria Engineering Journal 2022; 61(5): 3831–3872. doi: 10.1016/j.aej.2021.09.013

17. Lampinen J, Zelinka I. On stagnation of the differential evolution algorithm. In: Proceedings of MENDEL 2000, 6th International Mendel Conference on Soft Computing; 7–9 June 2000; Brno, Czech Republic. pp. 76–83.

18. Coelho L dos S, Souza RCT, Mariani VC. Improved differential evolution approach based on cultural algorithm and diversity measure applied to solve economic load dispatch problems. Mathematics and Computers in Simulation 2009; 79(10): 3136–3147. doi: 10.1016/j.matcom.2009.03.005

19. Mallipeddi R, Suganthan PN, Pan QK, Tasgetiren MF. Differential evolution algorithm with ensemble of parameters and mutation strategies. Applied Soft Computing 2011; 11(2): 1679–1696. doi: 10.1016/j.asoc.2010.04.024

20. Wang Y, Cai Z, Zhang Q. Differential evolution with composite trial vector generation strategies and control parameters. IEEE Transactions on Evolutionary Computation 2011; 15(1): 55–66. doi: 10.1109/tevc.2010.2087271

21. Gong W, Fialho A, Cai Z, Li H. Adaptive strategy selection in differential evolution for numerical optimization: An empirical study. Information Sciences 2011; 181(24): 5364–5386. doi: 10.1016/j.ins.2011.07.049

22. Gong W, Zhou A, Cai Z. A multioperator search strategy based on cheap surrogate models for evolutionary optimization. IEEE Transactions on Evolutionary Computation 2015; 19(5): 746–758. doi: 10.1109/tevc.2015.2449293

23. Wu G, Mallipeddi R, Suganthan PN, et al. Differential evolution with multipopulation based ensemble of mutation strategies. Information Sciences 2016; 329: 329–345. doi: 10.1016/j.ins.2015.09.009

24. Zou D, Li S, Wang GG, et al. An improved differential evolution algorithm for the economic load dispatch problems with or without valve-point effects. Applied Energy 2016; 181: 375–390. doi: 10.1016/j.apenergy.2016.08.067

25. Neto JXV, Reynoso-Meza G, Ruppel TH, et al. Solving non-smooth economic dispatch by a new combination of continuous GRASP algorithm and differential evolution. International Journal of Electrical Power & Energy Systems 2017; 84: 13–24. doi: 10.1016/j.ijepes.2016.04.012

26. Zhang Q, Zou D, Duan N, Shen X. An adaptive differential evolutionary algorithm incorporating multiple mutation strategies for the economic load dispatch problem. Applied Soft Computing 2019; 78: 641–669. doi: 10.1016/j.asoc.2019.03.019

27. Ma H, Shen S, Yu M, et al. Multi-population techniques in natureinspired optimization algorithms: A comprehensive survey. Swarm and Evolutionary Computation 2019; 44: 365–387. doi: 10.1016/j.swevo.2018.04.011

28. Noman N, Iba H. Accelerating differential evolution using an adaptive local search. IEEE Transactions on Evolutionary Computation 2008; 12(1): 107–125. doi: 10.1109/tevc.2007.895272

29. Kennedy J, Eberhart R. Particle swarm optimization. Proceedings of IEEE İnternational Conference on Neural Networks 1995; 4: 1942–1948.

30. Jia D, Zheng G, Khan MK. An effective memetic differential evolution algorithm based on chaotic local search. Information Sciences 2011; 181(15): 3175–3187. doi: 10.1016/j.ins.2011.03.018

31. Dhaliwal JS, Dhillon J. Profit based unit commitment using memetic binary differential evolution algorithm. Applied Soft Computing 2019; 81: 105502. doi: 10.1016/j.asoc.2019.105502

32. Zuo M, Dai G, Peng L, et al. A case learning-based differential evolution algorithm for global optimization of interplanetary trajectory design. Applied Soft Computing 20220; 94: 106451. doi: 10.1016/j.asoc.2020.106451

33. Parouha RP, Verma P. State-of-the-art reviews of meta-heuristic algorithms with their novel proposal for unconstrained optimization and applications. Archives of Computational Methods in Engineering 2021; 28(5): 4049–4115. doi: 10.1007/s11831-021-09532-7

34. Parouha RP, Das KN. A memory based differential evolution algorithm for unconstrained optimization. Applied Soft Computing 2016; 38: 501–517. doi: 10.1016/j.asoc.2015.10.022

35. Brest J, Greiner S, Boskovic B, et al. Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems. IEEE Transactions on Evolutionary Computation 2006; 10(6): 646–657. doi: 10.1109/tevc.2006.872133

36. Qin AK, Huang VL, Suganthan PN. Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Transactions on Evolutionary Computation 2009; 13(2): 398–417. doi: 10.1109/tevc.2008.927706

37. Das KN, Parouha RP. An ideal tri-population approach for unconstrained optimization and applications. Applied Mathematics and Computation 2015; 256: 666–701. doi: 10.1016/j.amc.2015.01.076

38. Verma P, Parouha RP. An advanced hybrid algorithm for engineering design optimization. Neural Processing Letters 2021; 53(5): 3693–3733. doi: 10.1007/s11063-021-10541-7

39. Das S, Abraham A, Chakraborty UK, Konar A. Differential evolution using a neighborhood-based mutation operator. IEEE Transactions on Evolutionary Computation 2009; 13(3): 526–553. doi: 10.1109/tevc.2008.2009457

40. Cheshmehgaz HR, Desa MI, Wibowo A. Effective local evolutionary searches distributed on an island model solving bi-objective optimization problems. Applied Intelligence 2013; 38(3): 331–356. doi: 10.1007/s10489-012-0375-7

41. Han MF, Liao SH, Chang JY, Lin CT. Dynamic group-based differ-ential evolution using a self-adaptive strategy for global optimization problems. Applied Intelligence 2013; 39(1): 41–56. doi: 10.1007/s10489-012-0393-5

42. Liu H, Cai Z, Wang Y. Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization. Applied Soft Computing 2010; 10(2): 629–664. doi: 10.1016/j.asoc.2009.08.031

43. Derrac J, Garcia S, Molina D, Herrera F. A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm and Evolutionary Computation 2011; 1(1): 3–18. doi: 10.1016/j.swevo.2011.02.002

44. García S, Molina D, Lozano M, Herrera F. A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 Special Session on Real Parameter Optimization. Journal of Heuristics 2009; 15: 617–644. doi: 10.1007/s10732-008-9080-4

45. Parouha RP, Das KN. DPD: An intelligent parallel hybrid algorithm for economic load dispatch problems with various practical constraints. Expert Systems with Applications 2016; 63: 295–309. doi: 10.1016/j.eswa.2016.07.012




DOI: https://doi.org/10.32629/jai.v7i3.1103

Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 Pooja Tiwari, Vishnu Narayan Mishra, Raghav Prasad Parouha

License URL: https://creativecommons.org/licenses/by-nc/4.0/