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A Non-convex Economic Load Dispatch Using Hybrid Salp Swarm Algorithm

  • Research Article-Computer Engineering and Computer Science
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Abstract

In this paper, the economic load dispatch (ELD) problem with valve point effect is tackled using a hybridization between salp swarm algorithm (SSA) as a population-based algorithm and \(\beta \)-hill climbing optimizer as a single point-based algorithm. The proposed hybrid SSA is abbreviated as HSSA. This is to achieve the right balance between the intensification and diversification of the ELD search space. ELD is an important problem in the power systems which is concerned with scheduling the generation units in active generators in optimal way to minimize the fuel cost in accordance with equality and inequality constraints. The proposed HSSA is evaluated using six real-world ELD systems: 3-unit generator, two cases of 13-unit generator, 40-unit generator, 80-unit generator, and 140-unit generator system. These ELD systems are well circulated in the previous literature. The comparative results against 66 well-regarded algorithms are conducted. The results show that the proposed HSSA is able to produce viable and competitive solutions for ELD problems.

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References

  1. Mandal, B.; Roy, P.K.; Mandal, S.: Economic load dispatch using Krill Herd algorithm. Int. J. Electr. Power Energy Syst. 57, 1–10 (2014)

    Article  Google Scholar 

  2. Chatterjee, A.; Ghoshal, S.P.; Mukherjee, V.: Solution of combined economic and emission dispatch problems of power systems by an opposition-based harmony search algorithm. Int. J. Electr. Power Energy Syst. 39(1), 9–20 (2012)

    Article  Google Scholar 

  3. Panigrahi, B.K.; Ravikumar Pandi, V.; Das, S.; Cui, Z.; Sharma, R.: Economic load dispatch using population-variance harmony search algorithm. Trans. Inst. Meas. Control 34(6), 746–754 (2012)

    Article  Google Scholar 

  4. Alsumait, J.S.; Sykulski, J.K.; Al-Othman, A.K.: A hybrid GA-PS-SQP method to solve power system valve-point economic dispatch problems. Appl. Energy 87(5), 1773–1781 (2010)

    Article  Google Scholar 

  5. Cai, J.; Li, Q.; Li, L.; Peng, H.; Yang, Y.: A hybrid FCASO-SQP method for solving the economic dispatch problems with valve-point effects. Energy 38(1), 346–353 (2012)

    Article  Google Scholar 

  6. Cai, J.; Li, Q.; Li, L.; Peng, H.; Yang, Y.: A hybrid CPSO-SQP method for economic dispatch considering the valve-point effects. Energy Convers. Manag. 53(1), 175–181 (2012)

    Article  Google Scholar 

  7. Lin, W.-M.; Gow, H.-J.; Tsai, M.-T.: Combining of direct search and signal-to-noise ratio for economic dispatch optimization. Energy Convers. Manag. 52(1), 487–493 (2011)

    Article  Google Scholar 

  8. Tsai, M.-T.; Gow, H.-J.; Lin, W.-M.: A novel stochastic search method for the solution of economic dispatch problems with non-convex fuel cost functions. Int. J. Electr. Power Energy Syst. 33(4), 1070–1076 (2011)

    Article  Google Scholar 

  9. Sa-Ngiamvibool, W.; Pothiya, S.; Ngamroo, I.: Multiple Tabu search algorithm for economic dispatch problem considering valve-point effects. Int. J. Electr. Power Energy Syst. 33(4), 846–854 (2011)

    Article  Google Scholar 

  10. Al-Betar, M.A.; Awadallah, M.A.; Doush, I.A.; Alsukhni, E.; ALkhraisat, H.A.: A non-convex economic dispatch problem with valve loading effect using a new modified \(\beta \)-hill climbing local search algorithm. Arab. J. Sci. Eng. 43, 7439–7456 (2018)

    Article  Google Scholar 

  11. Neto, J.X.V.; Reynoso-Meza, G.; Ruppel, T.H.; Mariani, V.C.: 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 (2017)

    Article  Google Scholar 

  12. Tiwari, S.; Dave, M.P.; Dwivedi, B.: Economic Load Dispatch Using Particle Swarm Optimization. LAP LAMBERT Academic Publishing (2017)

  13. Kamboj, V.K.; Bath, S.K.; Dhillon, J.S.: Solution of non-convex economic load dispatch problem using grey wolf optimizer. Neural Comput. Appl. 27(5), 1301–1316 (2016)

    Article  Google Scholar 

  14. Bhattacharya, A.; Chattopadhyay, B.: Biogeography-based optimization for different economic load dispatch problems. IEEE Trans. Power Syst. 25(2), 1064–1077 (2009)

    Article  Google Scholar 

  15. James, J.Q.; Li, V.O.: A social spider algorithm for solving the non-convex economic load dispatch problem. Neurocomputing 171, 955–965 (2016)

    Article  Google Scholar 

  16. Aydin, D.; Yavuz, G.; Özyön, S.; Yaşar, C.; Stützle, T.: Artificial bee colony framework to non-convex economic dispatch problem with valve point effects: a case study. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, pp. 1311–1318. ACM (2017)

  17. Mirjalili, S.; Gandomi, A.H.; Mirjalili, S.Z.; Saremi, S.; Faris, H.; Mirjalili, S.M.: Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv. Eng. Softw. 114, 163–191 (2017)

    Article  Google Scholar 

  18. Faris, H.; Mafarja, M.M.; Heidari, A.A.; Aljarah, I.; AlaM, A.; Mirjalili, S.; Fujita, H.: An efficient binary salp swarm algorithm with crossover scheme for feature selection problems. Knowl.-Based Syst. 154, 43–67 (2018)

    Article  Google Scholar 

  19. Ibrahim, R.A.; Ewees, A.A.; Oliva, D.; Abd Elaziz, M.; Lu, S.: Improved salp swarm algorithm based on particle swarm optimization for feature selection. J. Ambient Intell. Humaniz. Comput. 10(8), 3155–3169 (2019)

    Article  Google Scholar 

  20. Qais, M.H.; Hasanien, H.M.; Alghuwainem, S.: Enhanced salp swarm algorithm: application to variable speed wind generators. Eng. Appl. Artif. Intell. 80, 82–96 (2019)

    Article  Google Scholar 

  21. Meraihi, Y.; Ramdane-Cherif, A.; Mahseur, M.; Achelia, D.: A chaotic binary salp swarm algorithm for solving the graph coloring problem. In: International Symposium on Modelling and Implementation of Complex Systems, pp. 106–118. Springer (2018)

  22. Xing, Z.; Jia, H.: Multilevel color image segmentation based on GLCM and improved salp swarm algorithm. IEEE Access 7, 37672–37690 (2019)

    Article  Google Scholar 

  23. El-Fergany, A.A.: Extracting optimal parameters of PEM fuel cells using salp swarm optimizer. Renew. Energy 119, 641–648 (2018)

    Article  Google Scholar 

  24. Abualigah, L., Shehab, M., Alshinwan, M., Alabool, H.: Salp swarm algorithm: a comprehensive survey. Neural Comput. Appl. pp 1–21 (2019)

  25. Mohammed, M.: \(\beta \)-Hill climbing: an exploratory local search. Neural Comput. Appl. 28(1), 153–168 (2017)

    Google Scholar 

  26. Alomari, O.A.; Khader, A.T.; Al-Betar, M.A.; Awadallah, M.A.: A novel gene selection method using modified MRMR and hybrid bat-inspired algorithm with \(\beta \)-hill climbing. Appl. Intell. 48(11), 4429–4447 (2018)

    Article  Google Scholar 

  27. Al-Betar, M.A.; Hammouri, A.I.; Awadallah, M.A.; Doush, I.A.: Binary \(\beta \)-hill climbing optimizer with s-shape transfer function for feature selection. J. Ambient Intell. Humaniz. Comput. pp. 1–29 (2020)

  28. Alsukni, E.; Arabeyyat, O.S.; Awadallah, M.A.; Alsamarraie, L.; Abu-Doush, I.; Al-Betar, M.A.: Multiple-reservoir scheduling using \(\beta \)-hill climbing algorithm. J. Intell. Syst. 28(4), 559–570 (2019)

    Google Scholar 

  29. Alweshah, M.; Al-Daradkeh, A.; Al-Betar, M.A.; Almomani, A.; Oqeili, A.: \(\beta \)-hill climbing algorithm with probabilistic neural network for classification problems. J. Ambient Intell. Humaniz. Comput. pp. 1–12 (2019)

  30. Al-Betar, M.A.: A \(\beta \)-hill climbing optimizer for examination timetabling problem. J. Ambient Intell. Humaniz. Comput. pp. 1–14

  31. Leandro, L.; Viviana, V.: An improved harmony search algorithm for power economic load dispatch. Energy Convers. Manag. 50(10), 2522–2526 (2009)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  33. Wang, X.; Gibson, G.R.: Effects of the in vitro fermentation of oligofructose and inulin by bacteria growing in the human large intestine. J. Appl. Bacteriol. 75(4), 373–380 (1993)

    Article  Google Scholar 

  34. Orero, S.O.; Irving, M.R.: Economic dispatch of generators with prohibited operating zones: a genetic algorithm approach. IEE Proc. Gen. Transm. Distrib. 143(6), 529–534 (1996)

    Article  Google Scholar 

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

    Article  Google Scholar 

  36. Al-Betar, M.A.; Khader, A.T.; Doush, I.A.: Memetic techniques for examination timetabling. Ann. Oper. Res. 218(1), 23–50 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  37. Blum, C.; Roli, A.: Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput. Surv. (CSUR) 35(3), 268–308 (2003)

    Article  Google Scholar 

  38. Rahmat, N.A.; Aziz, N.F.A.; Mansor, M.H.; Musirin, I.: Optimizing economic load dispatch with renewable energy sources via differential evolution immunized ant colony optimization technique. Int. J. Adv. Sci. Eng. Inf. Technol. 7(6), 2012–2017 (2017)

    Article  Google Scholar 

  39. Singh, H.; Mehta, S.; Prashar, S.: Economic load dispatch using multi verse optimization. Int. J. Eng. Res. Sci. (IJOER) 6(2), 2395–6992 (2016)

    Google Scholar 

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

    Article  Google Scholar 

  41. Prathiba, R.; Balasingh Moses, M.; Sakthivel, S.: Flower pollination algorithm applied for different economic load dispatch problems. Int. J. Eng. Technol. 6(2), 1009–1016 (2014)

    Google Scholar 

  42. Kamboj, V.K.; Bhadoria, A.; Bath, S.K.: Solution of non-convex economic load dispatch problem for small-scale power systems using ant lion optimizer. Neural Comput. Appl. 28(8), 2181–2192 (2017)

    Article  Google Scholar 

  43. Shaw, B.; Mukherjee, V.; Ghoshal, S.P.: Seeker optimisation algorithm: application to the solution of economic load dispatch problems. IET Gen. Transm. Distrib. 5(1), 81–91 (2011)

    Article  Google Scholar 

  44. Al-Betar, M.A.; Awadallah, M.A.; Krishan, M.M.: A non-convex economic load dispatch problem with valve loading effect using a hybrid grey wolf optimizer. Neural Comput. Appl. pp 1–28 (2019)

  45. Huang, Z.; Zhao, J.; Qi, L.; Gao, Z.; Duan, H.: Comprehensive learning cuckoo search with chaos-lambda method for solving economic dispatch problems. Appl. Intell. pp. 1–21 (2020)

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  48. Li, X.; Zhang, H.; Zhigang, L.: A differential evolution algorithm based on multi-population for economic dispatch problems with valve-point effects. IEEE Access 7, 95585–95609 (2019)

    Article  Google Scholar 

  49. Subathra, M.S.P.; Selvan, S.E.; Victoire, T.A.A.; Christinal, A.H.; Amato, U.: A hybrid with cross-entropy method and sequential quadratic programming to solve economic load dispatch problem. IEEE Syst. J. 9(3), 1031–1044 (2015)

    Article  Google Scholar 

  50. Sayah, S.; Hamouda, A.: A hybrid differential evolution algorithm based on particle swarm optimization for nonconvex economic dispatch problems. Appl. Soft Comput. 13(4), 1608–1619 (2013)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  53. Pothiya, S.; Ngamroo, I.; Kongprawechnon, W.: Ant colony optimisation for economic dispatch problem with non-smooth cost functions. Int. J. Electr. Power Energy Syst. 32(5), 478–487 (2010)

    Article  Google Scholar 

  54. Hemamalini, S.; Simon, S.P.: Artificial bee colony algorithm for economic load dispatch problem with non-smooth cost functions. Electr. Power Compon. Syst. 38(7), 786–803 (2010)

    Article  Google Scholar 

  55. Bhattacharya, A.; Chattopadhyay, P.K.: Solving complex economic load dispatch problems using biogeography-based optimization. Expert Syst. Appl. 37(5), 3605–3615 (2010)

    Article  Google Scholar 

  56. dos Santos, Coelho L.; Mariani, V.C.: An efficient cultural self-organizing migrating strategy for economic dispatch optimization with valve-point effect. Energy Convers. Manag. 51(12), 2580–2587 (2010)

    Article  Google Scholar 

  57. Immanuel Selvakumar, A.; Thanushkodi, K.: Optimization using civilized swarm: solution to economic dispatch with multiple minima. Electr. Power Syst. Res. 79(1), 8–16 (2009)

    Article  Google Scholar 

  58. Park, J.-B.; Jeong, Y.-W.; Shin, J.-R.; Lee, K.Y.: An improved particle swarm optimization for nonconvex economic dispatch problems. IEEE Trans. Power Syst. 25(1), 156–166 (2009)

    Article  Google Scholar 

  59. Wang, L.; Li, L.: An effective differential harmony search algorithm for the solving non-convex economic load dispatch problems. Int. J. Electr. Power Energy Syst. 44(1), 832–843 (2013)

    Article  Google Scholar 

  60. Fraga, E.S.; Yang, L.; Papageorgiou, L.G.: On the modelling of valve point loadings for power electricity dispatch. Appl. Energy 91(1), 301–303 (2012)

    Article  Google Scholar 

  61. Niknam, T.; Mojarrad, H.D.; Meymand, H.Z.; Firouzi, B.B.: A new honey bee mating optimization algorithm for non-smooth economic dispatch. Energy 36(2), 896–908 (2011)

    Article  Google Scholar 

  62. Suleiman, M.H.; Mustafa, Z.; Mohmed, M.R.: Grey wolf optimizer for solving economic dispatch problem with valve-loading effects. APRN J. Eng. Appl. Sci. pp. 1619–1628 (2015)

  63. Pradhan, M.; Roy, P.K.; Pal, T.: Grey wolf optimization applied to economic load dispatch problems. Int. J. Electr. Power Energy Syst. 83, 325–334 (2016)

    Article  Google Scholar 

  64. dos Santos, Coelho L.; Mariani, V.C.: An improved harmony search algorithm for power economic load dispatch. Energy Convers. Manag. 50(10), 2522–2526 (2009)

    Article  Google Scholar 

  65. dos Santos, Coelho L.; Mariani, V.C.: An efficient cultural self-organizing migrating strategy for economic dispatch optimization with valve-point effect. Energy Convers. Manag. 51(12), 2580–2587 (2010)

    Article  Google Scholar 

  66. Jayabarathi, T.; Raghunathan, T.; Adarsh, B.R.; Suganthan, P.N.: Economic dispatch using hybrid grey wolf optimizer. Energy 111, 630–641 (2016)

    Article  Google Scholar 

  67. Pandi, V.R.; Panigrahi, B.K.; Mohapatra, A.; Mallick, M.K.: Economic load dispatch solution by improved harmony search with wavelet mutation. Int. J. Comput. Sci. Eng. 6(1), 122–131 (2011)

    Google Scholar 

  68. Kumar, R.; Sharma, D.; Sadu, A.: A hybrid multi-agent based particle swarm optimization algorithm for economic power dispatch. Int. J. Electr. Power Energy Syst. 33(1), 115–123 (2011)

    Article  Google Scholar 

  69. Chakraborty, S.; Senjyu, T.; Yona, A.; Saber, A.Y.; Funabashi, T.: Solving economic load dispatch problem with valve-point effects using a hybrid quantum mechanics inspired particle swarm optimisation. IET Gen. Transm. Distrib. 5(10), 1042–1052 (2011)

    Article  Google Scholar 

  70. Bulbul, S.M.; Pradhan, M.; Roy, P.K.; Pal, T.: Opposition-based krill herd algorithm applied to economic load dispatch problem. Ain Shams Eng. J. 9(3), 423–440 (2018)

    Article  Google Scholar 

  71. Basu, M.: Kinetic gas molecule optimization for nonconvex economic dispatch problem. Int. J. Electr. Power Energy Syst. 80, 325–332 (2016)

    Article  Google Scholar 

  72. Mohammadi-Ivatloo, B.; Rabiee, A.; Soroudi, A.; Ehsan, M.: Iteration PSO with time varying acceleration coefficients for solving non-convex economic dispatch problems. Int. J. Electr. Power Energy Syst. 42(1), 508–516 (2012)

    Article  Google Scholar 

  73. Amjady, N.; Sharifzadeh, H.: Solution of non-convex economic dispatch problem considering valve loading effect by a new modified differential evolution algorithm. Int. J. Electr. Power Energy Syst. 32(8), 893–903 (2010)

    Article  Google Scholar 

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

    Article  Google Scholar 

  75. Awadallah, M.A.; Al-Betar, M.A.; Bolaji, A.L.; Alsukhni, E.M.; Al-Zoubi, H.: Natural selection methods for artificial bee colony with new versions of onlooker bee. Soft Comput. pp. 1–40 (2018)

  76. Subbaraj, P.; Rengaraj, R.; Salivahanan, S.; Senthilkumar, T.R.: Parallel particle swarm optimization with modified stochastic acceleration factors for solving large scale economic dispatch problem. Int. J. Electr. Power Energy Syst. 32(9), 1014–1023 (2010)

    Article  Google Scholar 

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

    Article  Google Scholar 

  78. Meng, K.; Wang, H.G.; Dong, Z.Y.; Wong, K.P.: Quantum-inspired particle swarm optimization for valve-point economic load dispatch. IEEE Trans. Power Syst. 25(1), 215–222 (2010)

    Article  Google Scholar 

  79. Moradi-Dalvand, M.; Mohammadi-Ivatloo, B.; Najafi, A.; Rabiee, A.: Continuous quick group search optimizer for solving non-convex economic dispatch problems. Electr. Power Syst. Res. 93, 93–105 (2012)

    Article  Google Scholar 

  80. Alawode, K.O.; Jubril, A.M.; Kehinde, L.O.; Ogunbona, P.O.: Semidefinite programming solution of economic dispatch problem with non-smooth, non-convex cost functions. Electr. Power Syst. Res. 164, 178–187 (2018)

    Article  Google Scholar 

  81. Srinivasa Reddy, A.; Vaisakh, K.: Shuffled differential evolution for economic dispatch with valve point loading effects. Int. J. Electr. Power Energy Syst. 46, 342–352 (2013)

    Article  Google Scholar 

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

    Article  Google Scholar 

  83. Al-Betar, M.A.; Awadallah, M.A.; Khader, A.T.; Bolaji, A.L.: Tournament-based harmony search algorithm for non-convex economic load dispatch problem. Appl. Soft Comput. 47, 449–459 (2016)

    Article  Google Scholar 

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

    Article  Google Scholar 

  85. Subbaraj, P.; Rengaraj, R.; Salivahanan, S.: Enhancement of self-adaptive real-coded genetic algorithm using Taguchi method for economic dispatch problem. Appl. Soft Comput. 11(1), 83–92 (2011)

    Article  Google Scholar 

  86. Azizipanah-Abarghooee, R.; Niknam, T.; Roosta, A.; Malekpour, A.R.; Zare, M.: Probabilistic multiobjective wind-thermal economic emission dispatch based on point estimated method. Energy 37(1), 322–335 (2012)

    Article  Google Scholar 

  87. Walters, D.C.; Sheble, G.B.: Genetic algorithm solution of economic dispatch with valve point loading. IEEE Trans. Power Syst. 8(3), 1325–1332 (1993)

    Article  Google Scholar 

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Acknowledgements

This work has been carried out during sabbatical leave granted to the author Mahmud Salem Alkoffash from Al-Balqa Applied University during the academic year 2018/2019.

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Alkoffash, M.S., Awadallah, M.A., Alweshah, M. et al. A Non-convex Economic Load Dispatch Using Hybrid Salp Swarm Algorithm. Arab J Sci Eng 46, 8721–8740 (2021). https://doi.org/10.1007/s13369-021-05646-z

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