Skip to main content
SpringerLink
Log in

Self-adaptive DE algorithm without niching parameters for multi-modal optimization problems

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

To solve multi-modal optimization problems, the niching technique is widely used because it could find and preserve multiple stable sub-populations. However, the performances of most existing evolutionary algorithms with niching techniques heavily depend on niching parameters, such as niche radius, sub-population size and crowding factor. To our best knowledge, a self-adaptive differential evolution (DE) variant without niching parameters using ring topology has not been developed. In this paper, we proposed a Self-adaptive Niching Differential Evolution (SaNDE) algorithm. The ring topology plays a crucial role in slowing the information flow, resulting in scattered niches with restricted and overlapped communications. We introduced local memory (personal best) into the DE algorithm to present a new mutation operator “current-to-pnbest” when a ring population topology was used. Moreover, the two control parameters in DE were self-adapted by using a simple but effective strategy that is based on successful parametric values in history. To improve the capability of jumping out of local optima, an adaptive re-start mechanism by using opposition-based learning was proposed to address the issue of stagnation. The performances of the proposed method were investigated through standard benchmark functions and the problem of optimizing parameters for a feedforward neural network. Comparisons with other state-of-the-art multi-modal optimization algorithms demonstrated the competitiveness of the proposed methodology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Aljarah I, Faris H, Mirjalili S (2018) Optimizing connection weights in neural networks using the whale optimization algorithm. Soft Comput 22:1–15

    Article  Google Scholar 

  2. Ghosh I, Chaudhuri TD (2021) FEB-stacking and FEB-DNN models for stock trend prediction: a performance analysis for pre and post Covid-19 periods. Decis Making Appl Manag Eng 4:51–86

    Article  Google Scholar 

  3. Tsoulos IG, Tzallas A, Tsalikakis D (2018) Evolutionary based weight decaying method for neural network training. Neural Process Lett 47:463–473

    Google Scholar 

  4. Woo D, Choi J, Ali M, Jung H (2011) A novel multimodal optimization algorithm applied to electromagnetic optimization. IEEE Trans Magn 47:1667–1673

    Article  Google Scholar 

  5. Song S, Ji J, Chen X, Gao S, Tang Z, Todo Y (2018) Adoption of an improved PSO to explore a compound multi-objective energy function in protein structure prediction. Appl Soft Comput J 72:539–551

    Article  Google Scholar 

  6. Precup RE, Preitl S, Petriu E, Bojan-Dragos CA, Szedlak-Stinean AI, Roman RC, Hedrea EL (2020) Model-based fuzzy control results for networked control systems. Rep Mech Eng 1:10–25

    Article  Google Scholar 

  7. Negi G, Kumar A, Pnt S, Ram M (2021) Optimization of complex system reliability using hybrid grey wolf optimizer. Decis Making Appl Manag Eng 4:241–256

    Article  Google Scholar 

  8. Mohammadi M, Gheibi M, Fathollahi-Fard AM, Eftekhari M, Kian Z, Tian G (2021) A hybrid computational intelligence approach for bioremediation of amoxicillin based on fungus activities from soil resources and aflatoxin B1 controls. J Environ Manag 299:113594

    Article  Google Scholar 

  9. Islam MR, Ali SM, Fathollahi-Fard AM, Kabir G (2021) A novel particle swarm optimization-based grey model for the prediction of warehouse performance. J Comput Des Eng 8:705–727

    Google Scholar 

  10. Pasha J, Dulebenets MA, Fathollahi-Fard AM, Tian G, Lau Y, Singh P, Liang B (2021) An integrated optimization method for tactical-level planning in liner shipping with heterogeneous ship fleet and environmental considerations. Adv Eng Inform 48:101299

    Article  Google Scholar 

  11. Fathollahi-Fard AM, Woodward L, Akhrif O (2021a) Sustainable distributed permutation flow-shop scheduling model based on a triple bottom line concept. J Ind Inf Integr:100233

  12. Fathollahi-Fard AM, Hajiaghaei-Keshtelib M, Tavakkoli-Moghaddamc R, Smithd NR (2021b) Bi-level programming for home health care supply chain considering outsourcing. J Ind Inf Integr 25:100246

    Google Scholar 

  13. Gholizadeh H, Fazlollahtabar H, Fathollahi-Fard AM, Dulebenets MA (2021) Preventive maintenance for the flexible flowshop scheduling under uncertainty: a waste-to-energy system. Environ Sci Pollut Res Int. https://doi.org/10.1007/s11356-021-16234-x

  14. Yazdani M, Kabirifar K, Fathollahi-Fard AM, Mojtahedi M (2021) Production scheduling of off-site prefabricated construction components considering sequence dependent due dates. Environ Sci Pollut Res Int. https://doi.org/10.1007/s11356-021-16285-0

  15. Eftekhari M, Gheibi M, Azizi-Toupkanloo H, Hossein-Abadi Z, Khraisheh M, Fathollahi-Fard AM, Tian G (2021) Statistical optimization, soft computing prediction, mechanistic and empirical evaluation for fundamental appraisal of copper, lead and malachite green adsorption. J Ind Inf Integr 23:100219

    Google Scholar 

  16. Mojtahedi M, Fathollahi-Fard AM, Tavakkoli-Moghaddam R, Newton S (2021) Sustainable vehicle routing problem for coordinated solid waste management. J Ind Inf Integr 23:100220

    Google Scholar 

  17. Moosavi J, Naeni LM, Fathollahi-Fard AM, Fiore U (2021) Blockchain in supply chain management: a review, bibliometric, and network analysis. Environ Sci Pollut Res Int. https://doi.org/10.1007/s11356-021-13094-3

  18. Nejatian A, Makian M, Gheibi M, Fathollahi-Fard AM (2021) A novel viewpoint to the green city concept based on vegetation area changes and contributions to healthy days: a case study of Mashhad, Iran. Environ Sci Pollut Res Int 29:702–710

    Article  Google Scholar 

  19. Li Y, Zeng X (2010) Multi-population co-genetic algorithm with double chain-like agents structure for parallel global numerical optimization. Appl Intell 32:292–310

    Article  Google Scholar 

  20. Zeng X, Li Y, Qin J (2009) A dynamic chain-like agent genetic algorithm for global numerical optimization and feature selection. Neurocomputing 72:1214–1228

    Article  Google Scholar 

  21. Rim C, Piao S, Li G, Pak U (2018) A niching chaos optimization algorithm for multimodal optimization. Soft Comput 22:621–633

    Article  MATH  Google Scholar 

  22. Sareni B, Krahenbuhl L (1998) Fitness sharing and niching methods revisited. IEEE Trans Evol Comput 2:97–106

    Article  Google Scholar 

  23. Vitela JE, Castanos O (2012) A sequential niching memetic algorithm for continuous multimodal function optimization. Appl Math Comput 218:8242–8259

    MathSciNet  MATH  Google Scholar 

  24. Gao W, Yen GG, Liu S (2014) A cluster-based differential evolution with self-adaptive strategy for multimodal optimization. IEEE Trans Cybern 44:1314–1327

    Article  Google Scholar 

  25. Dick G, Whigham PA (2011) Weighted local sharing and local clearing for multimodal optimisation. Soft Comput 15:1707–1721

    Article  Google Scholar 

  26. Zou J, Deng Q, Zheng J, Yang S (2020) A close neighbor mobility method using particle swarm optimizer for solving multimodal optimization problems. Inf Sci 519:332–347

    Article  MathSciNet  Google Scholar 

  27. Chen Z, Zhan Z, Wang H, Zhang J (2020) Distributed individuals for multiple peaks: a novel differential evolution for multimodal optimization problems. IEEE Trans Evol Comput 24:708–719

    Article  Google Scholar 

  28. Biswas S, Kundu S, Das S (2015) Inducing niching behavior in differential evolution through local information sharing. IEEE Trans Evol Comput 19:246–263

    Article  Google Scholar 

  29. Zhao H, Zhan Z, Lin Y, Chen X, Luo X, Zhang J, Kwong S, Zhang J (2020) Local binary pattern-based adaptive differential evolution for multimodal optimization problems. IEEE Trans Cybern 50:3343–3357

    Article  Google Scholar 

  30. Biswas S, Kundu S, Das S (2014) An improved parent-centric mutation with normalized neighborhoods for inducing niching behavior in differential evolution. IEEE Trans Cybern 44:1726–1737

    Article  Google Scholar 

  31. Wang Z, Zhan Z, Lin Y, Yu W, Wang H, Kwong S, Zhang J (2020) Automatic niching differential evolution with contour prediction approach for multimodal optimization problems. IEEE Trans Evol Comput 24:114–128

    Article  Google Scholar 

  32. Yu W, Ji J, Gong Y, Yang Q, Zhang J (2018) A tri-objective differential evolution approach for multimodal optimization. Inf Sci 423:1–23

    Article  MathSciNet  MATH  Google Scholar 

  33. Das S, Mullick SS, Suganthan PN (2016) Recent advances in differential evolution-an updated survey. Swarm Evol Comput 27:1–30

    Article  Google Scholar 

  34. Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15:4–31

    Article  Google Scholar 

  35. Basak A, Das S, Tan KC (2013) Multimodal optimization using a biobjective differential evolution algorithm enhanced with mean distance-based selection. IEEE Trans Evol Comput 17:666–685

    Article  Google Scholar 

  36. Yue C, Suganthan PN, Liang J, Qu B, Yu K, Zhu Y, Yan L (2021) Differential evolution using improved crowding distance for multimodal multiobjective optimization. Swarm Evol Comput 62:100849

    Article  Google Scholar 

  37. Qu BY, Suganthan PN (2010) Novel multimodal problems and differential evolution with Ensemble of Restricted Tournament Selection. In: IEEE Congress on Evolutionary Computation. IEEE: New York

  38. Li X (2010) Niching without niching parameters: particle swarm optimization using a ring topology. IEEE Trans Evol Comput 14:150–169

    Article  Google Scholar 

  39. Yang GY, Dong ZY, Wong KP (2008) A modified differential evolution algorithm with fitness sharing for power system planning. IEEE Trans Power Syst 23:514–522

    Article  Google Scholar 

  40. Streichert F, Stein G, Ulmer H, Zell A (2004) A clustering based niching EA for multimodal search spaces. Springer Verlag, Marseille

    Book  MATH  Google Scholar 

  41. Halder U, Das S, Maity D (2013) A cluster-based differential evolution algorithm with external archive for optimization in dynamic environments. IEEE Trans Cybern 43:881–897

    Article  Google Scholar 

  42. Lynn N, Ali MZ, Suganthan PN (2018) Population topologies for particle swarm optimization and differential evolution. Swarm Evol Comput 39:24–35

    Article  Google Scholar 

  43. Wang C, Liu Y, Zhao Y, Chen Y (2014) A hybrid topology scale-free Gaussian-dynamic particle swarm optimization algorithm applied to real power loss minimization. Eng Appl Artif Intell 32:63–75

    Article  Google Scholar 

  44. Wang C, Liu Y, Chen Y, Wei Y (2016) Self-adapting hybrid strategy particle swarm optimization algorithm. Soft Comput 20:4933–4963

    Article  Google Scholar 

  45. Kennedy J (1999) Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. 1999 congress on evolutionary computation, Washington, DC, United States, pp. 1931-1938

  46. Janson S, Middendorf M (2005) A hierarchical particle swarm optimizer and its adaptive variant. IEEE Trans Syst Man Cybern Part B-Cybern 35:1272–1282

    Article  Google Scholar 

  47. Ni Q, Deng J (2013) A new logistic dynamic particle swarm optimization algorithm based on random topology. Sci World J 2013:Article ID 409167

    Article  Google Scholar 

  48. Huang F, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186:340–356

    MathSciNet  MATH  Google Scholar 

  49. Li Y, Zhan Z, Lin S, Zhang J, Luo X (2015) Competitive and cooperative particle swarm optimization with information sharing mechanism for global optimization problems. Inf Sci 293:370–382

    Article  Google Scholar 

  50. van den Bergh F, Engelbrecht AP (2004) A cooperative approach to participle swam optimization. IEEE Trans Evol Comput 8:225–239

    Article  Google Scholar 

  51. Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13:398–417

    Article  Google Scholar 

  52. Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13:945–958

    Article  Google Scholar 

  53. Brest J, Greiner S, Bokovi B, Mernik M, Zumer V (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10:646–657

    Article  Google Scholar 

  54. Gong W, Cai Z (2013) Differential evolution with ranking-based mutation operators. IEEE Trans Cybern 43:2066–2081

    Article  Google Scholar 

  55. Wang Y, Cai Z, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15:55–66

    Article  Google Scholar 

  56. Qu BY, Liang JJ, Suganthan PN (2012) Niching particle swarm optimization with local search for multi-modal optimization. Inf Sci 197:131–143

    Article  Google Scholar 

  57. Kennedy J, Mendes R (2002) Population structure and particle swarm performance. 2002 congress on evolutionary computation, Honolulu, HI, United States, pp. 1671-1676

  58. Cui L, Xu C, Li G, Ming Z, Feng Y, Lu N (2018a) A high accurate localization algorithm with DV-hop and differential evolution for wireless sensor network. Appl Soft Comput J 68:39–52

    Article  Google Scholar 

  59. Wang C, Liu Y, Zhang Q, Guo H, Liang X, Chen Y, Xu M, Wei Y (2019) Association rule mining based parameter adaptive strategy for differential evolution algorithms. Expert Syst Appl 123:54–69

    Article  Google Scholar 

  60. Yang M, Li C, Cai Z, Guan J (2015) Differential evolution with auto-enhanced population diversity. IEEE Trans Cybern 45:302–315

    Article  Google Scholar 

  61. Cui L, Li G, Zhu Z, Lin Q, Wong K, Chen J, Lu N, Lu J (2018b) Adaptive multiple-elites-guided composite differential evolution algorithm with a shift mechanism. Inf Sci 422:122–143

    Article  MathSciNet  Google Scholar 

  62. Ewees AA, Abd Elaziz M, Houssein EH (2018) Improved grasshopper optimization algorithm using opposition-based learning. Expert Syst Appl 112:156–172

    Article  Google Scholar 

  63. Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Tavakkoli-Moghaddam R (2018) The social engineering optimizer (SEO). Eng Appl Artif Intell 72:267–293

    Article  Google Scholar 

  64. Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Tavakkoli-Moghaddam R (2020a) Red deer algorithm (RDA): a new nature-inspired meta-heuristic. Soft Comput 24:14637–14665

    Article  Google Scholar 

  65. Fathollahi-Fard AM, Ahmadi A, Al-e-Hashem SM (2020d) Sustainable closed-loop supply chain network for an integrated water supply and wastewater collection system under uncertainty. J Environ Manag 275:111277

    Article  Google Scholar 

  66. Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Mirjalili S (2020b) A set of efficient heuristics for a home healthcare problem. Neural Comput & Applic 32:6185–6205

    Article  Google Scholar 

  67. Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Tian G, Li Z (2020c) An adaptive Lagrangian relaxation-based algorithm for a coordinated water supply and wastewater collection network design problem. Inf Sci 512:1335–1359

    Article  Google Scholar 

  68. Theophilus O, Dulebenets MA, Pasha J, Lau Y, Fathollahi-Fard AM, Mazaheri A (2021) Truck scheduling optimization at a cold-chain cross-docking terminal with product perishability considerations. Comput Ind Eng 156:107240

    Article  Google Scholar 

  69. Derrac J, Garcia S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1:3–18

    Article  Google Scholar 

  70. Garcia S, Fernandez A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power. Inf Sci 180:2044–2064

    Article  Google Scholar 

  71. Zhang C, Yi Z (2011) Scale-free fully informed particle swarm optimization algorithm. Inf Sci 181:4550–4568

    Article  MathSciNet  MATH  Google Scholar 

  72. 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 Part B-Cybern 42:482–500

    Article  Google Scholar 

  73. Mallipeddi R, Suganthan PN, Pan QK, Tasgetiren MF (2011) Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl Soft Comput 11:1679–1696

    Article  Google Scholar 

  74. Jiang R, Zhang J, Tang Y, Wang C, Feng J (2020) A collective intelligence based differential evolution algorithm for optimizing the structure and parameters of a neural network. IEEE Access 8:69601–69614

    Article  Google Scholar 

  75. Zhang L, Li H, Kong X (2019) Evolving feedforward artificial neural networks using a two-stage approach. Neurocomputing 360:25–36

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the fund of Research on Intelligent Ship Testing and Verification ([2018]473); Natural Science Foundation of China under Contract No. 51709027.

Author information

Authors and Affiliations

  1. Marine Engineering College, Dalian Maritime University, Dalian, Liaoning, 116026, People’s Republic of China

    Ruizheng Jiang, Jundong Zhang, Yuanyuan Tang, Jinhong Feng & Chuan Wang

Authors
  1. Ruizheng Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jundong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuanyuan Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jinhong Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Chuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ruizheng Jiang.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

Table 13 Transmission line data for IEEE 57-bus power system. (100MVA base)
Full size table
Table 14 Initialization of active power, reactive power and voltage for each bus in IEEE 57-bus power system. (p.u.) (100MVA)
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, R., Zhang, J., Tang, Y. et al. Self-adaptive DE algorithm without niching parameters for multi-modal optimization problems. Appl Intell 52, 12888–12923 (2022). https://doi.org/10.1007/s10489-021-03003-z

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-021-03003-z

Keywords

Search

Navigation