Clustering cuckoo search optimization for economic load dispatch problem

Abstract

In this paper, a clustering cuckoo search optimization (CCSO) is proposed. Different from the randomly generated step size in CSO, the step size in CCSO is generated by a clustering mechanism, and the value is updated according to the average fitness value difference between each cluster and the whole swarm, thereby improving the searching balance between exploration and exploitation of each solution. The effectiveness of CCSO has been validated by six typical benchmark functions and economic load dispatch problems with 6, 10, 13, 15 and 40 generators. The results of CSO and CCSO are displayed and compared in aspects of convergence rate, objective function value and robustness. Moreover, the influences of parameters as step size \(\delta \), solution number P, egg abandon fraction \(p_a\) and cluster number K are all analyzed comprehensively in this study. The conclusion is that, in all the tested cases, CCSO behaves much more competitive than CSO under the same parameter setting conditions.

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References

  1. 1.

    Raja MAZ, Ahmed U, Zameer A, Kiani AK, Chaudhary NI (2019) Bio-inspired heuristics hybrid with sequential quadratic programming and interior-point methods for reliable treatment of economic load dispatch problem. Neural Comput Appl 31(1):447–475

    Article  Google Scholar 

  2. 2.

    Ciornei I, Kyriakides E (2012) A GA-API solution for the economic dispatch of generation in power system operation. IEEE Trans Power Syst 27(1):233–242

    Article  Google Scholar 

  3. 3.

    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

    Article  Google Scholar 

  4. 4.

    Zou D, Li S, Wang GG, Li Z, Ouyang H (2016) An improved differential evolution algorithm for the economic load dispatch problems with or without valve-point effects. Appl Energy 181:375–390

    Article  Google Scholar 

  5. 5.

    Noman N, Iba H (2008) Differential evolution for economic load dispatch problems. Electr Power Syst Res 78(8):1322–1331

    Article  Google Scholar 

  6. 6.

    Selvakumar AI, Thanushkodi K (2007) A new particle swarm optimization solution to nonconvex economic dispatch problems. IEEE Trans Power Syst 22(1):42–51

    Article  Google Scholar 

  7. 7.

    Chaturvedi KT, Pandit M (2008) Self-organizing hierarchical particle swarm optimization for nonconvex economic dispatch. IEEE Trans Power Syst 23(3):1079–1087

    Article  Google Scholar 

  8. 8.

    Al-Betar MA, Awadallah MA, Khader AT, Bolaji ALA, Almomani A (2018) Economic load dispatch problems with valve-point loading using natural updated harmony search. Neural Comput Appl 29(10):767–781

    Article  Google Scholar 

  9. 9.

    Al-Betar MA, Awadallah MA, Khader AT, Bolaji ALA (2016) Tournament-based harmony search algorithm non-convex economic load dispatch problem. Appl Soft Comput 47:449–459

    Article  Google Scholar 

  10. 10.

    Kamboj VK, Bath SK, Dhillon JS (2016) Solution of non-convex economic load dispatch problem using Grey Wolf Optimizer. Neural Comput Appl 27(5):1301–1316

    Article  Google Scholar 

  11. 11.

    Singh D, Dhillon JS (2019) Ameliorated grey wolf optimization for economic load dispatch problem. Energy 169:398–419

    Article  Google Scholar 

  12. 12.

    He XZ, Rao YQ, Huang JD (2016) A novel algorithm for economic load dispatch of power systems. Neurocomputing 171(1):1454–1461

    Article  Google Scholar 

  13. 13.

    Ali ES, Elazim SA (2018) Mine blast algorithm for environmental economic load dispatch with valve loading effect. Neural Comput Appl 30(1):261–270

    Article  Google Scholar 

  14. 14.

    Bhattacharya A, Chattopadhyay PK (2010) Biogeography-based optimization for different economic load dispatch problems. IEEE Trans Power Syst 25(2):1064–1077

    Article  Google Scholar 

  15. 15.

    Lohokare MR, Panigrahi BK, Pattnaik SS, Devi S, Mohapatra A (2012) Neighborhood search-driven accelerated biogeography-based optimization for optimal load dispatch. IEEE Trans Syst Man Cybern Part C Appl Rev 42(5):641–652

    Article  Google Scholar 

  16. 16.

    Bhattacharya A, Chattopadhyay PK (2010) Solution of economic power dispatch problems using oppositional biogeography-based optimization. Electr Power Compon Syst 38(10):1139–1160

    Article  Google Scholar 

  17. 17.

    Ozyon S, Aydin D (2013) Incremental artificial bee colony with local search to economic dispatch problem with ramp rate limits and prohibited operating zones. Energy Convers Manage 65:397–407

    Article  Google Scholar 

  18. 18.

    Elattar EE (2019) Environmental economic dispatch with heat optimization in the presence of renewable energy based on modified shuffle frog leaping algorithm. Energy 171:256–269

    Article  Google Scholar 

  19. 19.

    Yu JT, Kim CH, Wadood A, Khurshiad T, Rhee SB (2018) A novel multi-population based chaotic JAYA algorithm with application in solving economic load dispatch problem. Energies 11(8):1946

    Article  Google Scholar 

  20. 20.

    Yu JT, Kim CH, Wadood A, Khurshaid T, Rhee SB (2019) Jaya algorithm with self-adaptive multi-population and Lévy flights for solving economic load dispatch problems. IEEE Access 7:21372–21384

    Article  Google Scholar 

  21. 21.

    Barisal AK, Prusty RC (2015) Large scale economic dispatch of power systems using oppositional invasive weed optimization. Appl Soft Comput 29:122–137

    Article  Google Scholar 

  22. 22.

    Liang H, Liu Y, Shen Y, Li F, Man Y (2018) A hybrid bat algorithm for economic dispatch with random wind power. IEEE Trans Power Syst 33(5):5052–5061

    Article  Google Scholar 

  23. 23.

    Gholamghasemi M, Akbari E, Asadpoor MB, Ghasemi M (2019) A new solution to the non-convex economic load dispatch problems using phasor particle swarm optimization. Appl Soft Comput 79:111–124

    Article  Google Scholar 

  24. 24.

    Li F, Qin J, Kang Y (2018) Multi-agent system based distributed pattern search algorithm for non-convex economic load dispatch in smart grid. IEEE Trans Power Syst 34(3):2093–2102

    Article  Google Scholar 

  25. 25.

    Mohammadi F, Abdi H (2018) A modified crow search algorithm (MCSA) for solving economic load dispatch problem. Appl Soft Comput 71:51–65

    Article  Google Scholar 

  26. 26.

    Kumar M, Dhillon JS (2018) Hybrid artificial algae algorithm for economic load dispatch. Appl Soft Comput 71:89–109

    Article  Google Scholar 

  27. 27.

    Xiong G, Shi D (2018) Orthogonal learning competitive swarm optimizer for economic dispatch problems. Appl Soft Comput 66:134–148

    Article  Google Scholar 

  28. 28.

    Yang XS, Deb S (2009) Cuckoo search via Levy flights, In: Proceedings of world congress on nature and biologically inspired computing (NaBIC 2009) India, pp. 210-214

  29. 29.

    Basu M, Chowdhury A (2013) Cuckoo search algorithm for economic dispatch. Energy 60:99–108

    Article  Google Scholar 

  30. 30.

    Kanagaraj G, Ponnambalam SG, Jawahar N (2013) A hybrid cuckoo search and genetic algorithm for reliability-redundancy allocation problems. Comput Ind Eng 66(4):1115–1124

    Article  Google Scholar 

  31. 31.

    Sekhar P, Mohanty S (2016) An enhanced cuckoo search algorithm based contingency constrained economic load dispatch for security enhancement. Int J Electr Power Energy Syst 75:303–310

    Article  Google Scholar 

  32. 32.

    Nguyen TT, Vo DN (2015) The application of one rank cuckoo search algorithm for solving economic load dispatch problems. Appl Soft Comput 37:763–773

    Article  Google Scholar 

  33. 33.

    Nguyen TT, Nguyen TT, Vo DN (2018) An effective cuckoo search algorithm for large-scale combined heat and power economic dispatch problem. Neural Comput Appl 30(11):3545–3564

    Article  Google Scholar 

  34. 34.

    Mareli M, Twala B (2018) An adaptive Cuckoo search algorithm for optimisation. Appl Comput Inf 14(2):107–115

    Google Scholar 

  35. 35.

    Yang XS (2014) Nature-inspired optimization algorithms. Elsevier, Amsterdam

    Google Scholar 

  36. 36.

    Shokri-Ghaleh H, Alfi A (2014) Optimal synchronization of teleoperation systems via cuckoo optimization algorithm. Nonlinear Dyn 78(4):2359–2376

    MathSciNet  Article  Google Scholar 

  37. 37.

    Hatamlou A, Abdullah S, Nezamabadi-Pour H (2012) A combined approach for clustering based on K-means and gravitational search algorithms. Swarm Evol Comput 6:47–52

    Article  Google Scholar 

  38. 38.

    Liang X, Li W, Zhang Y, Zhou M (2015) An adaptive particle swarm optimization method based on clustering. Soft Comput 19(2):431–448

    Article  Google Scholar 

  39. 39.

    Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowledge Based Syst 89:228–249

    Article  Google Scholar 

  40. 40.

    Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295

    Article  Google Scholar 

  41. 41.

    Rao RV (2016) Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int J Ind Eng Comput 7(1):19–34

    Google Scholar 

  42. 42.

    Sinha N, Chakrabarti R, Chattopadhyay P (2003) Evolutionary programming techniques for economic load dispatch. IEEE Trans Evol Comput 7(1):83–94

    Article  Google Scholar 

  43. 43.

    Das DB, Patvardhan C (1999) Solution of economic load dispatch using real coded hybrid stochastic search. Int J Electr Power Energy Syst 21(3):165–170

    Article  Google Scholar 

  44. 44.

    Victoire TAA, Jeyakumar AE (2004) Hybrid PSO-SQP for economic dispatch with valve-point effect. Electr Power Syst Res 71(1):51–59

    Article  Google Scholar 

  45. 45.

    Cai J, Li Q (2012) A hybrid CPSO-SQP method for economic dispatch considering the valve-point effects. Energy Convers Manage 53(1):175–181

    Article  Google Scholar 

  46. 46.

    Niknam T (2010) A new fuzzy adaptive hybrid particle swarm optimization algorithm for non-linear, non-smooth and non-convex economic dispatch problem. Appl Energy 87(1):327–339

    Article  Google Scholar 

  47. 47.

    Niknam T, Mojarrad HD, Nayeripour M (2010) A new fuzzy adaptive particle swarm optimization for non-smooth economic dispatch. Energy 35(4):1764–1778

    Article  Google Scholar 

  48. 48.

    He DK, Wang FL, Mao ZZ (2008) Hybrid genetic algorithm for economic dispatch with valve-point effect. Electr Power Syst Res 78(4):626–633

    Article  Google Scholar 

  49. 49.

    Khamsawang S, Jiriwibhakorn S (2010) DSPSO-TSA for economic dispatch problem with nonsmooth and noncontinuous cost functions. Energy Convers Manage 51(2):365–375

    Article  Google Scholar 

  50. 50.

    Selvakumar AI, Thanushkodi K (2008) Anti-predatory particle swarm optimization: solution to nonconvex economic dispatch problems. Electr Power Syst Res 78(1):2–10

    Article  Google Scholar 

  51. 51.

    Panigrahi BK, Pandi VR (2008) Bacterial foraging optimisation: Nelder-Mead hybrid algorithm for economic load dispatch. IET Gener Transm Distrib 2(4):556–565

    Article  Google Scholar 

  52. 52.

    Lu H, Sriyanyong P, Song YH, Dillon T (2010) Experimental study of a new hybrid PSO with mutation for economic dispatch with non-smooth cost function. Int J Elect Power Energy Syst 32(9):921–935

    Article  Google Scholar 

  53. 53.

    Wang SK, Chiou JP, Liu CW (2007) Non-smooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm. IET Gener Transm Distrib 1(5):793–803

    Article  Google Scholar 

  54. 54.

    Niknam T (2010) A new fuzzy adaptive hybrid particle swarm optimization for nonelinear, nonesmooth and noneconvex dispatch problem. Appl Energy 87(1):327–339

    Article  Google Scholar 

  55. 55.

    Dos Santos Coelho L, Mariani VC (2010) An efficient cultural self-organizing migrating strategy for economic dispatch optimization with valve-point effect. Int J Energy Convers Manag 51(12):2580–2587

    Article  Google Scholar 

  56. 56.

    He D, Wang F, Mao Z (2008) A hybrid genetic algorithm approach based on differential evolution for economic dispatch with valve-point effect. Electr Power Energy Syst 30(1):31–38

    Article  Google Scholar 

  57. 57.

    Bhattacharya A, Chattopadhyay PK (2010) Hybrid differential evolution with biogeography-based optimization for solution of economic load dispatch. IEEE Trans Power Syst 25(4):1955–1964

    Article  Google Scholar 

  58. 58.

    Neto JXV, Reynoso-Meza G, Ruppel TH, Mariani VC, Dos Santos Coelho L (2017) Solving non-smooth economic dispatch by a new combination of continuous GRASP algorithm and differential evolution. Int J Electr Power Energy Syst 84:13–24

    Article  Google Scholar 

  59. 59.

    Pothiya S, Ngamroo I, Kongprawechnon W (2008) Application of multiple tabu search algorithm to solve dynamic economic dispatch considering generator constraints. Energy Convers Manage 49(4):506–516

    Article  Google Scholar 

  60. 60.

    Kuo CC (2008) A novel string structure for economic dispatch problems with practical constraints. Energy Convers Manage 49(12):3571–3577

    Article  Google Scholar 

  61. 61.

    Panigrahi BK, Yadav SR, Agrawal S, Tiwari MK (2007) A clonal algorithm to solve economic load dispatch. Electr Power Syst Res 77(10):1381–1389

    Article  Google Scholar 

  62. 62.

    Cai J, Ma X, Li L, Haipeng P (2007) Chaotic particle swarm optimization for economic dispatch considering the generator constraints. Energy Convers Manage 48(2):645–653

    Article  Google Scholar 

  63. 63.

    Sun J, Fang W, Wang D, Xu W (2009) Solving the economic dispatch problem with a modified quantum-behaved particle swarm optimization method. Energy Convers Manage 50(12):2967–2975

    Article  Google Scholar 

  64. 64.

    Yang YD, Wei BR, Liu H, Zhang YY, Zhao JH, Manla E (2018) Chaos firefly algorithm with self-adaptation mutation mechanism for solving large-scale economic dispatch with valve-point effects and multiple fuel options. IEEE Access 6:45907–45922

    Article  Google Scholar 

  65. 65.

    Jayabarathi T, Raghunathan T, Adarsh BR, Suganthan PN (2016) Economic dispatch using hybrid grey wolf optimizer. Energy 111:630–641

    Article  Google Scholar 

  66. 66.

    Chiang CL (2005) Improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels. IEEE Trans Power Syst 20(4):1690–1699

    Article  Google Scholar 

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Acknowledgements

This research was supported by Korea Electric Power Corporation (grant number R17XA05-38).

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Correspondence to Sang-Bong Rhee.

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Appendix A

Appendix A

See Tables 11, 12, 13, 14, 15.

Table 11 Outputs of \(F\_min\) by CSO and CCSO in Case 1
Table 12 Outputs of \(F\_min\) by CSO and CCSO in Case 2
Table 13 Outputs of \(F\_min\) by CSO and CCSO in Case 3
Table 14 Outputs of \(F\_min\) by CSO and CCSO in Case 4
Table 15 Outputs of \(F\_min\) by CSO and CCSO in Case 5

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Yu, J., Kim, C. & Rhee, S. Clustering cuckoo search optimization for economic load dispatch problem. Neural Comput & Applic (2020). https://doi.org/10.1007/s00521-020-05036-w

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Keywords

  • Cuckoo search algorithm
  • Cluster
  • Real-world optimization
  • Power system