Comprehensive learning cuckoo search with chaos-lambda method for solving economic dispatch problems


Economic dispatch (ED) is an important part in the economic operation of power systems. It is an NP-hard problem with multiple practical constraints. This paper proposes a novel approach that combines a swarm intelligence algorithm with a constraint-handling mechanism to solve the ED problem. First, we design a comprehensive learning cuckoo search algorithm with two strengthen strategies. A comprehensive learning strategy is designed to give the algorithm advanced learning ability in high-dimensional and multi-modal environment and thus enhance the search ability. A duplicate elimination strategy is utilized as an elite strategy to improve the evolving efficiency of the algorithm. Then, we propose a constraint-based population generation method named chaos-lambda method to reduce the searching complexity, and a solution repair method to repair unfeasible solutions that violate the constraints. The proposed approach is tested on 5 systems with different benchmarks and compared with the state-of-the-art algorithms. Our approach achieves the best performance on every test.

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  1. 1.

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

    Article  Google Scholar 

  2. 2.

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

    Article  Google Scholar 

  3. 3.

    Bai T, Yb Kan, Jx Chang, Huang Q, Chang FJ (2017) Fusing feasible search space into pso for multi-objective cascade reservoir optimization. Appl Soft Comput 51:328–340

    Article  Google Scholar 

  4. 4.

    Barani F, Mirhosseini M, Nezamabadi-Pour H (2017) Application of binary quantum-inspired gravitational search algorithm in feature subset selection. Appl Intell 47(2):304–318

    Article  Google Scholar 

  5. 5.

    Basu M (2015) Modified particle swarm optimization for nonconvex economic dispatch problems. International Journal of Electrical Power & Energy Systems 69:304–312

    Article  Google Scholar 

  6. 6.

    Basu M (2016) Kinetic gas molecule optimization for nonconvex economic dispatch problem. International Journal of Electrical Power & Energy Systems 80:325–332

    Article  Google Scholar 

  7. 7.

    Chen G, Ding X (2015) Optimal economic dispatch with valve loading effect using self-adaptive firefly algorithm. Appl Intell 42(2):276–288

    MathSciNet  Article  Google Scholar 

  8. 8.

    Cheng J, Wang L, Jiang Q, Xiong Y (2018) A novel cuckoo search algorithm with multiple update rules. Appl Intell 48(11):4192–4211

    Article  Google Scholar 

  9. 9.

    Del Ser J, Osaba E, Molina D, Yang XS, Salcedo-Sanz S, Camacho D, Das S, Suganthan PN, Coello CAC, Herrera F (2019) Bio-inspired computation: Where we stand and what’s next. Swarm and Evolutionary Computation 48:220–250

    Article  Google Scholar 

  10. 10.

    Dieu VN, Schegner P, Ongsakul W (2011) A newly improved particle swarm optimization for economic dispatch with valve point loading effects. In: 2011 IEEE Power and Energy Society General Meeting, IEEE, pp 1–8

  11. 11.

    Duman S, Yorukeren N, Altas IH (2015) A novel modified hybrid psogsa based on fuzzy logic for non-convex economic dispatch problem with valve-point effect. International Journal of Electrical Power & Energy Systems 64:121–135

    Article  Google Scholar 

  12. 12.

    Elsayed W, Hegazy Y, El-Bages M, Bendary F (2017) Improved random drift particle swarm optimization with self-adaptive mechanism for solving the power economic dispatch problem. IEEE Trans Ind Inform PP(99):1–1

    Google Scholar 

  13. 13.

    Gaing ZL (2003) Particle swarm optimization to solving the economic dispatch considering the generator constraints. IEEE Trans Power Syst 18(3):1187–1195

    Article  Google Scholar 

  14. 14.

    Gaing ZL (2004) Closure to” discussion of’particle swarm optimization to solving the economic dispatch considering the generator constraints’”. IEEE Trans Power Syst 19(4):2122–2123

    Article  Google Scholar 

  15. 15.

    He X, Rao Y, Huang J (2016) A novel algorithm for economic load dispatch of power systems. Neurocomputing 171:1454–1461

    Article  Google Scholar 

  16. 16.

    Hosseinnezhad V, Rafiee M, Ahmadian M, Ameli MT (2014) Species-based quantum particle swarm optimization for economic load dispatch. International Journal of Electrical Power & Energy Systems 63:311–322

    Article  Google Scholar 

  17. 17.

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

    Article  Google Scholar 

  18. 18.

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

    Article  Google Scholar 

  19. 19.

    Mandal B, Roy PK, Mandal S (2014) Economic load dispatch using krill herd algorithm. International Journal of Electrical Power & Energy Systems 57:1–10

    Article  Google Scholar 

  20. 20.

    Meng X, Chang J, Wang X, Wang Y (2019) Multi-objective hydropower station operation using an improved cuckoo search algorithm. Energy 168:425–439

    Article  Google Scholar 

  21. 21.

    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. International Journal of Electrical Power & Energy Systems 84:13–24

    Article  Google Scholar 

  22. 22.

    Niknam T, Mojarrad HD, Meymand HZ (2011) Non-smooth economic dispatch computation by fuzzy and self adaptive particle swarm optimization. Appl Soft Comput 11(2):2805–2817

    Article  Google Scholar 

  23. 23.

    Niu Q, Zhang H, Wang X, Li K, Irwin GW (2014) A hybrid harmony search with arithmetic crossover operation for economic dispatch. International Journal of Electrical Power & Energy Systems 62:237–257

    Article  Google Scholar 

  24. 24.

    Park JB, Jeong YW, Shin JR, Lee KY (2010) An improved particle swarm optimization for nonconvex economic dispatch problems. IEEE Trans Power Syst 25(1):156–166

    Article  Google Scholar 

  25. 25.

    Pradhan M, Roy PK, Pal T (2016) Grey wolf optimization applied to economic load dispatch problems. International Journal of Electrical Power & Energy Systems 83:325–334

    Article  Google Scholar 

  26. 26.

    Qin Q, Cheng S, Chu X, Lei X, Shi Y (2017) Solving non-convex/non-smooth economic load dispatch problems via an enhanced particle swarm optimization. Appl Soft Comput 59:229–242

    Article  Google Scholar 

  27. 27.

    Reddy AS, Vaisakh K (2013) Shuffled differential evolution for large scale economic dispatch. Electr Power Syst Res 96:237–245

    Article  Google Scholar 

  28. 28.

    Sayed GI, Khoriba G, Haggag MH (2018) A novel chaotic salp swarm algorithm for global optimization and feature selection. Appl Intell 48(10):3462–3481

    Article  Google Scholar 

  29. 29.

    Secui DC (2016) A modified symbiotic organisms search algorithm for large scale economic dispatch problem with valve-point effects. Energy 113:366–384

    Article  Google Scholar 

  30. 30.

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

    Article  Google Scholar 

  31. 31.

    Tharwat A, Hassanien AE (2018) Chaotic antlion algorithm for parameter optimization of support vector machine. Appl Intell 48(3):670–686

    Article  Google Scholar 

  32. 32.

    Thirugnanasambandam K, Prakash S, Subramanian V, Pothula S, Thirumal V (2019) Reinforced cuckoo search algorithm-based multimodal optimization. Appl Intell 49(6):2059–2083

    Article  Google Scholar 

  33. 33.

    Wang X, Chang J, Meng X, Wang Y (2017) Research on multi-objective operation based on improved nsga-ii for lower yellow river. J Hydraul Eng 48:135–145

    Google Scholar 

  34. 34.

    Wood AJ, Wollenberg BF et al (2013) Power generation, operation, and control. John Wiley & Sons

  35. 35.

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

    Article  Google Scholar 

  36. 36.

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

  37. 37.

    Yang XS, Deb S (2009) Cuckoo search via lévy flights. In: 2009 World Congress on Nature & Biologically Inspired Computing, NaBIC, IEEE, pp 210–214

  38. 38.

    Yang XS, Hosseini SSS, Gandomi AH (2012) Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect. Appl soft Comput 12(3):1180– 1186

    Article  Google Scholar 

  39. 39.

    Yang Y, Wei B, Liu H, Zhang Y, Zhao J, 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 

  40. 40.

    Yu JT, Kim CH, Wadood A, Khurshiad T, Rhee SB (2019) Self-adaptive multi-population jaya algorithm with lévy flights for solving economic load dispatch problems. IEEE Access

  41. 41.

    Zhao J, Liu S, Zhou M, Guo X, Qi L (2018) Modified cuckoo search algorithm to solve economic power dispatch optimization problems. IEEE/CAA Journal of Automatica Sinica 5(4):794– 806

    MathSciNet  Article  Google Scholar 

  42. 42.

    Zhong H, Xia Q, Wang Y, Kang C (2013) Dynamic economic dispatch considering transmission losses using quadratically constrained quadratic program method. IEEE Trans Power Syst 28(3):2232–2241

    Article  Google Scholar 

  43. 43.

    Zhu H, Qi X, Chen F, He X, Chen L, Zhang Z (2019) Quantum-inspired cuckoo co-search algorithm for no-wait flow shop scheduling. Appl Intell 49(2):791–803

    Article  Google Scholar 

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This work is supported in part by NSFC (61472229, 616-02279, and 71704096), Sci. & Tech. Development Fund of Shandong Province of China (ZR2017BF015 and ZR2017M-F027), the Humanities and Social Science Research Project of the Ministry of Education (18YJAZH017), the Taishan Scholar Climbing Program of Shandong Province, and SDUST Research Fund (2015TDJH102).

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Correspondence to Liang Qi or Zhengzhong Gao or Hua Duan.

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Huang, Z., Zhao, J., Qi, L. et al. Comprehensive learning cuckoo search with chaos-lambda method for solving economic dispatch problems. Appl Intell 50, 2779–2799 (2020).

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  • Economic dispatch
  • Swarm intelligence
  • Cuckoo search
  • Power systems