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Combined economic and emission power dispatch problems through multi-objective Honey Badger optimizer

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Abstract

Honey Badger algorithm (HBA) is an intelligent adaptive meta-heuristic optimization algorithm with few parameters, fast convergence and good convergence accuracy for single-objective problems. However, many real-world optimization problems involve multiple conflicting objectives that need to be optimized simultaneously. A new multi-objective Honey Badger algorithm is proposed to solve the combined economic and environmental power scheduling problem. The proposed MOHBA combines the HBA with the Pareto dominance principle to produce a non-dominated solution. It uses an external elite storage mechanism with congested distance ordering to maintain the diversity of the distribution during the evolution of the Pareto optimal solutions. Furthermore, a fuzzy decision strategy is used to select the best compromise solution from the obtained Pareto bound. Then, to validate the performance of the proposed MOHBA, 20 different benchmark test functions are used to test it against other multi-objective optimization techniques. Moreover, the method is implemented on the multi-objective CEEPD problem for the IEEE 30-bus 6 generator and IEEE 118-bus 14 generator systems. Various objective function s in a multi-objective optimization space is confirmed by comparative studies with minimization schemes and fuzzy decision strategies are utilized to achieve the best scheduling solution for energy and emissions savings. The predominance of the algorithm and its potentiality to handle CEEPD problem several other algorithms.

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The data used to support the findings of this study are available from the corresponding author upon request.

References

  1. Khodaei, A., Shahidehpour, M., Kamalinia, S.: Transmission switching in expansion planning. IEEE Trans. Power Syst. 25(3), 1722–1733 (2010)

    Article  Google Scholar 

  2. Le, K., Golden, J., Stansberry, C., Vice, R., Wood, J., Ballance, J., Brown, G., Kamya, J., Nielsen, E., Nakajima, H., et al.: Potential impacts of clean air regulations on system operations. IEEE Trans. Power Syst. 10(2), 647–656 (1995)

    Article  Google Scholar 

  3. Londono-Pulgarin, D., Cardona-Montoya, G., Restrepo, J.C., Munoz-Leiva, F.: Fossil or bioenergy? Global fuel market trends. Renew. Sustain. Energy Rev. 143, 110905 (2021)

    Article  Google Scholar 

  4. Abou El Ela, A., Abido, M., Spea, S.R.: Differential evolution algorithm for emission constrained economic power dispatch problem. Electr. Power Syst. Res. 80(10), 1286–1292 (2010)

    Article  Google Scholar 

  5. Talbi, E.H., Abaali, L., Skouri, R., El Moudden, M.: Solution of economic and environmental power dispatch problem of an electrical power system using BFGS-AL algorithm. Procedia Comput. Sci. 170, 857–862 (2020)

    Article  Google Scholar 

  6. Braik, M.S., Awadallah, M.A., Al-Betar, M.A., Hammouri, A.I., Zitar, R.A.: A non-convex economic load dispatch problem using chameleon swarm algorithm with roulette wheel and Levy flight methods. Appl. Intell. 53, 17508–17547 (2023)

    Article  Google Scholar 

  7. Mandal, K., Mandal, S., Bhattacharya, B., Chakraborty, N.: Non-convex emission constrained economic dispatch using a new self-adaptive particle swarm optimization technique. Appl. Soft Comput. 28, 188–195 (2015)

    Article  Google Scholar 

  8. Zhan, J., Wu, Q., Guo, C., Zhou, X.: Fast \( \lambda - \)iteration method for economic dispatch with prohibited operating zones. IEEE Trans. Power Syst. 29(2), 990–991 (2013)

    Article  Google Scholar 

  9. Mohammadian Bishe, H., Rahimi Kian, A., Sayyed Esfahani, M.: Solving environmental/economic power dispatch problem by a trust region based augmented lagrangian method. Iran. J. Electr. Electron. Eng. 8(2), 177–187 (2012)

    Google Scholar 

  10. Chen, S.-D., Chen, J.-F.: A direct newton-raphson economic emission dispatch. Int. J. Electr. Power Energy Syst. 25(5), 411–417 (2003)

    Article  Google Scholar 

  11. Fan, J.-Y., Zhang, L.: Real-time economic dispatch with line flow and emission constraints using quadratic programming. IEEE Trans. Power Syst. 13(2), 320–325 (1998)

    Article  Google Scholar 

  12. Dodu, J., Martin, P., Merlin, A., Pouget, J.: An optimal formulation and solution of short-range operating problems for a power system with flow constraints. Proc. IEEE 60(1), 54–63 (1972)

    Article  Google Scholar 

  13. El-Keib, A., Ma, H., Hart, J.: Environmentally constrained economic dispatch using the lagrangian relaxation method. IEEE Trans. Power Syst. 9(4), 1723–1729 (1994)

    Article  Google Scholar 

  14. Franco, P., Carvalho, M., Soares, S.: A network flow model for short-term hydro-dominated hydrothermal scheduling problems. IEEE Trans. Power Syst. 9(2), 1016–1022 (1994)

    Article  Google Scholar 

  15. Chen, C.-L., Wang, S.-C.: Branch-and-bound scheduling for thermal generating units. IEEE Trans. Energy Convers. 8(2), 184–189 (1993)

    Article  Google Scholar 

  16. Liang, Z.-X., Glover, J.D.: A zoom feature for a dynamic programming solution to economic dispatch including transmission losses. IEEE Trans. Power Syst. 7(2), 544–550 (1992)

    Article  Google Scholar 

  17. Chang, S.-C., Chen, C.-H., Fong, I.-K., Luh, P.B.: Hydroelectric generation scheduling with an effective differential dynamic programming algorithm. IEEE Trans. Power Syst. 5(3), 737–743 (1990)

    Article  Google Scholar 

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

    Article  Google Scholar 

  19. Lee, F.N., Breipohl, A.M.: Reserve constrained economic dispatch with prohibited operating zones. IEEE Trans. Power Syst. 8(1), 246–254 (1993)

    Article  Google Scholar 

  20. Mamdouh, K., Shehata, A., Korovkin, N.: Multi-objective voltage control and reactive power optimization based on multi-objective particle swarm algorithm. In: IOP Conference Series: Materials Science and Engineering, vol. 643, p. 012089 (2019). IOP, Paris

  21. Mahdavi, S., Shiri, M.E., Rahnamayan, S.: Metaheuristics in large-scale global continues optimization: a survey. Inf. Sci. 295, 407–428 (2015)

    Article  MathSciNet  Google Scholar 

  22. Djenouri, Y., Comuzzi, M.: Combining apriori heuristic and bio-inspired algorithms for solving the frequent itemsets mining problem. Inf. Sci. 420, 1–15 (2017)

    Article  Google Scholar 

  23. Ray, T., Liew, K.: A swarm metaphor for multiobjective design optimization. Eng. Optim. 34(2), 141–153 (2002)

    Article  Google Scholar 

  24. Mahapatra, S., Raj, S.: Management of var sources for the reactive power planning problem by oppositional harris hawk optimizer. J. Electr. Syst. Inf. Technol. 10(1), 45 (2023)

    Article  Google Scholar 

  25. Mahapatra, S., Raj, S., et al.: A novel meta-heuristic approach for optimal rpp using series compensated facts controller. Intell. Syst. Appl. 18, 200220 (2023)

    Google Scholar 

  26. Raj, S., Mahapatra, S., Babu, R., Verma, S.: Hybrid intelligence strategy for techno-economic reactive power dispatch approach to ensure system security. Chaos Solitons Fractals 170, 113363 (2023)

    Article  Google Scholar 

  27. Mahapatra, S., Raj, S., Sharma, R.: Enhancing power system security by chaotic hybrid intelligence strategy for reactive power dispatch. In: 2022 2nd Odisha International Conference on Electrical Power Engineering, Communication and Computing Technology (ODICON), pp. 1–6. IEEE (2022)

  28. Mahor, A., Prasad, V., Rangnekar, S.: Economic dispatch using particle swarm optimization: a review. Renew. Sustain. Energy Rev. 13(8), 2134–2141 (2009)

    Article  Google Scholar 

  29. Xue, M., **e, J., Chen, F., Ke, X., Xu, T., Hou, H.: Review on multi-objective joint economic dispatching of microgrid in power system. Procedia Comput. Sci. 130, 1152–1157 (2018)

    Article  Google Scholar 

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

    Article  Google Scholar 

  31. Ghasemi, M., Taghizadeh, M., Ghavidel, S., Abbasian, A.: Colonial competitive differential evolution: an experimental study for optimal economic load dispatch. Appl. Soft Comput. 40, 342–363 (2016)

    Article  Google Scholar 

  32. 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 

  33. Alomoush, M.I., Oweis, Z.B.: Environmental-economic dispatch using stochastic fractal search algorithm. Int. J. Electr. Power Energy Syst. 28(5), 2530 (2018)

    Google Scholar 

  34. 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 

  35. He, D.-K., Wang, F.-L., Mao, Z.-Z.: Hybrid genetic algorithm for economic dispatch with valve-point effect. Electr. Power Syst. Res. 78(4), 626–633 (2008)

    Article  Google Scholar 

  36. Kheshti, M., Kang, X., Li, J., Regulski, P., Terzija, V.: Lightning flash algorithm for solving non-convex combined emission economic dispatch with generator constraints. IET Gen. Transm. Distrib. 12(1), 104–116 (2018)

    Article  Google Scholar 

  37. 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 

  38. Santos Coelho, L., Mariani, V.C.: Economic dispatch optimization using hybrid chaotic particle swarm optimizer. In: 2007 IEEE International Conference on Systems, Man and Cybernetics, pp. 1963–1968. IEEE (2007)

  39. 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 

  40. Wang, L., Singh, C.: Reserve-constrained multiarea environmental/economic dispatch based on particle swarm optimization with local search. Eng. Appl. Artif. Intell. 22(2), 298–307 (2009)

    Article  Google Scholar 

  41. Mekhilef, S., Saidur, R., Kamalisarvestani, M.: Effect of dust, humidity and air velocity on efficiency of photovoltaic cells. Renew. Sustain. Energy Rev. 16(5), 2920–2925 (2012)

    Article  Google Scholar 

  42. Ruyi, D., Shengsheng, W.: New optimization algorithm inspired by fluid mechanics for combined economic and emission dispatch problem. Turk. J. Electr. Eng. Comput. Sci. 26(6), 3305–3318 (2018)

    Google Scholar 

  43. Song, Y.H., Chou, C.S.V., Min, Y.: Large-scale economic dispatch by artificial ant colony search algorithms. Electr. Mach. Power Syst. 27(7), 679–690 (1999)

    Article  Google Scholar 

  44. Sharifi, S., Sedaghat, M., Farhadi, P., Ghadimi, N., Taheri, B.: Environmental economic dispatch using improved artificial bee colony algorithm. Evol. Syst. 8, 233–242 (2017)

    Article  Google Scholar 

  45. Abdelaziz, A.Y., Ali, E.S., Abd Elazim, S.: Implementation of flower pollination algorithm for solving economic load dispatch and combined economic emission dispatch problems in power systems. Energy 101, 506–518 (2016)

    Article  Google Scholar 

  46. Modiri-Delshad, M., Kaboli, S.H.A., Taslimi-Renani, E., Abd Rahim, N.: Backtracking search algorithm for solving economic dispatch problems with valve-point effects and multiple fuel options. Energy 116, 637–649 (2016)

    Article  Google Scholar 

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

    Article  Google Scholar 

  48. Rajasomashekar, S., Aravindhababu, P.: Biogeography based optimization technique for best compromise solution of economic emission dispatch. Swarm Evol. Comput. 7, 47–57 (2012)

    Article  Google Scholar 

  49. Bulbul, S.M.A., 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 

  50. 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 

  51. Secui, D.C.: Large-scale multi-area economic/emission dispatch based on a new symbiotic organisms search algorithm. Energy Convers. Manage. 154, 203–223 (2017)

    Article  Google Scholar 

  52. Panigrahi, B., Pandi, V.R.: Bacterial foraging optimisation: Nelder-mead hybrid algorithm for economic load dispatch. IET Gen. Transm. Distrib. 2(4), 556–565 (2008)

    Article  Google Scholar 

  53. Benasla, L., Belmadani, A., Rahli, M.: Spiral optimization algorithm for solving combined economic and emission dispatch. Int. J. Electr. Power Energy Syst. 62, 163–174 (2014)

    Article  Google Scholar 

  54. Bhattacharjee, K., Bhattacharya, A., Dey, S.H.: Oppositional real coded chemical reaction optimization for different economic dispatch problems. Int. J. Electr. Power Energy Syst. 55, 378–391 (2014)

    Article  Google Scholar 

  55. Güvenc, U., Sönmez, Y., Duman, S., Yörükeren, N.: Combined economic and emission dispatch solution using gravitational search algorithm. Sci. Iran. 19(6), 1754–1762 (2012)

    Article  Google Scholar 

  56. Hassan, M.H., Kamel, S., Eid, A., Nasrat, L., Jurado, F., Elnaggar, M.F.: A developed eagle-strategy supply-demand optimizer for solving economic load dispatch problems. Ain Shams Eng. J. 14(5), 102083 (2023)

    Article  Google Scholar 

  57. Swetha Shekarappa, G., Mahapatra, S., Raj, S.: Var strategic planning for reactive power using hybrid soft computing techniques. Int. J. Bio-Inspir. Comput. 20(1), 38–48 (2022)

    Article  Google Scholar 

  58. Selvakumar, A.I., 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 

  59. Tiwari, S., Kumar, A., Basetti, V.: Multi-objective micro phasor measurement unit placement and performance analysis in distribution system using NSGA-II and PROMETHEE-II. Measurement 198, 111443 (2022)

    Article  Google Scholar 

  60. Arunachalam, S., Saranya, R., Sangeetha, N.: Hybrid artificial bee colony algorithm and simulated annealing algorithm for combined economic and emission dispatch including valve point effect. In: Swarm, Evolutionary, and Memetic Computing: 4th International Conference, SEMCCO 2013, Chennai, India, 19–21 December 2013, Proceedings, Part I 4, pp. 354–365. Springer (2013).

  61. Arunachalam, S., AgnesBhomila, T., Ramesh Babu, M.: Hybrid particle swarm optimization algorithm and firefly algorithm based combined economic and emission dispatch including valve point effect. In: Swarm, Evolutionary, and Memetic Computing: 5th International Conference, SEMCCO 2014, Bhubaneswar, India, December 18-20, 2014, Revised Selected Papers 5, pp. 647–660. Springer, New York (2015)

  62. Gherbi, Y.A., Bouzeboudja, H., Gherbi, F.Z.: The combined economic environmental dispatch using new hybrid metaheuristic. Energy 115, 468–477 (2016)

    Article  Google Scholar 

  63. Radosavljević, J.: A solution to the combined economic and emission dispatch using hybrid PSOGSA algorithm. Appl. Artif. Intell. 30(5), 445–474 (2016)

    Article  Google Scholar 

  64. Agrawal, S., Panigrahi, B.K., Tiwari, M.K.: Multiobjective particle swarm algorithm with fuzzy clustering for electrical power dispatch. IEEE Trans. Evol. Comput. 12(5), 529–541 (2008)

    Article  Google Scholar 

  65. Basu, M.: Economic environmental dispatch using multi-objective differential evolution. Appl. Soft Comput. 11(2), 2845–2853 (2011)

    Article  Google Scholar 

  66. Zhang, L., Xu, X., Wang, S., Zhou, C., Sun, C.: Environmental/economic dispatch using a improved differential evolution. In: 2010 2nd International Conference on Computer Engineering and Technology. Citeseer.

  67. Abido, M.A.: Multiobjective evolutionary algorithms for electric power dispatch problem. IEEE Trans. Evol. Comput. 10(3), 315–329 (2006)

    Article  Google Scholar 

  68. Zhang, R., Zhou, J., Mo, L., Ouyang, S., Liao, X.: Economic environmental dispatch using an enhanced multi-objective cultural algorithm. Electr. Power Syst. Res. 99, 18–29 (2013)

    Article  Google Scholar 

  69. Abido, M.: Multiobjective particle swarm optimization for environmental/economic dispatch problem. Electr. Power Syst. Res. 79(7), 1105–1113 (2009)

    Article  Google Scholar 

  70. Tiwari, S., Kumar, A.: Advances and bibliographic analysis of particle swarm optimization applications in electrical power system: concepts and variants. Evol. Intell. 16(1), 23–47 (2023)

    Article  MathSciNet  Google Scholar 

  71. Muthuswamy, R., Krishnan, M., Subramanian, K., Subramanian, B.: Environmental and economic power dispatch of thermal generators using modified NSGA-II algorithm. International Transactions on Electrical Energy Systems 25(8), 1552–1569 (2015)

    Article  Google Scholar 

  72. Sundaram, A., Erdogmus, P.: Solution of combined economic emission dispatch problem with valve-point effect using hybrid NSGA II-MOPSO. In: Particle Swarm Optimization with Applications, vol. 78. InTech, London (2017)

  73. Mahdi, F.P., Vasant, P., Kallimani, V., Watada, J., Fai, P.Y.S., Abdullah-Al-Wadud, M.: A holistic review on optimization strategies for combined economic emission dispatch problem. Renew. Sustain. Energy Rev. 81, 3006–3020 (2018)

    Article  Google Scholar 

  74. Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1(1), 67–82 (1997)

    Article  Google Scholar 

  75. Hashim, F.A., Houssein, E.H., Hussain, K., Mabrouk, M.S., Al-Atabany, W.: Honey badger algorithm: new metaheuristic algorithm for solving optimization problems. Math. Comput. Simul. 192, 84–110 (2022)

    Article  MathSciNet  Google Scholar 

  76. Kaur, S., Awasthi, L.K., Sangal, A.: A brief review on multi-objective software refactoring and a new method for its recommendation. Arch. Comput. Methods Eng. 28, 3087–3111 (2021)

    Article  MathSciNet  Google Scholar 

  77. Edgeworth, F.: Mathematical Physics. Pat Keegan, London (1881)

    Google Scholar 

  78. Pareto, V.: Cours D’économie Politique, vol. 1. Librairie Droz, Geneva (1964)

    Book  Google Scholar 

  79. Coello Coello, C.A.: Evolutionary multi-objective optimization: some current research trends and topics that remain to be explored. Front. Comput. Sci. China 3(1), 18–30 (2009)

    Article  Google Scholar 

  80. Ngatchou, P., Zarei, A., El-Sharkawi, A.: Pareto multi objective optimization. In: Proceedings of the 13th International Conference On, Intelligent Systems Application to Power Systems, pp. 84–91 (2005). IEEE

  81. Shaheen, A.M., Ginidi, A.R., El-Sehiemy, R.A., Elattar, E.E.: Optimal economic power and heat dispatch in cogeneration systems including wind power. Energy 225, 120263 (2021)

    Article  Google Scholar 

  82. Gupta, S., Kumar, N., Srivastava, L.: Bat search algorithm for solving multi-objective optimal power flow problem. In: Applications of Computing, Automation and Wireless Systems in Electrical Engineering: Proceedings of MARC 2018, pp. 347–362. Springer (2019).

  83. Mohamed, A.-A.A., Mohamed, Y.S., El-Gaafary, A.A., Hemeida, A.M.: Optimal power flow using moth swarm algorithm. Electr. Power Syst. Res. 142, 190–206 (2017)

    Article  Google Scholar 

  84. Srinivasan, N., Deb, K.: Multi-objective function optimisation using non-dominated sorting genetic algorithm. Evol. Comput. 2(3), 221–248 (1994)

    Article  Google Scholar 

  85. Deb, K., Pratap, A., Agrawal, S. and Meyarivan, T. (2000). A fast and elitist multiobjective genetic algorithm: NSGA-II. Technical Report No. 200001. Kanpur Genetic Algorithms Laboratory, India (2000)

  86. Chen, J., Huang, H., Tian, S., Qu, Y.: Feature selection for text classification with naïve bayes. Expert Syst. Appl. 36(3), 5432–5435 (2009)

    Article  Google Scholar 

  87. Wang, M., Wang, J.-S., Song, H.-M., Zhang, M., Zhang, X.-Y., Zheng, Y., Zhu, J.-H.: Hybrid multi-objective harris hawk optimization algorithm based on elite non-dominated sorting and grid index mechanism. Adv. Eng. Softw. 172, 103218 (2022)

    Article  Google Scholar 

  88. Derrac, J., García, S., Hui, S., Suganthan, P.N., Herrera, F.: Analyzing convergence performance of evolutionary algorithms: a statistical approach. Inf. Sci. 289, 41–58 (2014)

    Article  Google Scholar 

  89. Carrasco, J., García, S., Rueda, M., Das, S., Herrera, F.: Recent trends in the use of statistical tests for comparing swarm and evolutionary computing algorithms: practical guidelines and a critical review. Swarm Evol. Comput. 54, 100665 (2020)

    Article  Google Scholar 

  90. 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. J. Heuristics 15, 617–644 (2009)

    Article  Google Scholar 

  91. Abido, M.A.: Environmental/economic power dispatch using multiobjective evolutionary algorithms. IEEE Trans. Power Syst. 18(4), 1529–1537 (2003)

    Article  Google Scholar 

  92. Wang, L., Singh, C.: Environmental/economic power dispatch using a fuzzified multi-objective particle swarm optimization algorithm. Electr. Power Syst. Res. 77(12), 1654–1664 (2007)

    Article  Google Scholar 

  93. Coello, C.C., Lechuga, M.S.: Mopso: a proposal for multiple objective particle swarm optimization. In: Proceedings of the 2002 Congress on Evolutionary Computation. CEC’02 (Cat. No. 02TH8600), vol. 2, pp. 1051–1056. IEEE (2002).

  94. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  95. Mirjalili, S., Jangir, P., Saremi, S.: Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems. Appl. Intell. 46, 79–95 (2017)

    Article  Google Scholar 

  96. Mirjalili, S.: Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput. Appl. 27, 1053–1073 (2016)

    Article  Google Scholar 

  97. 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 

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Funding

This work is partly supported by NSFC under Grant No. 62006213, No. 61873246, Henan Youth Talent Promotion Project No. 2022HYTP005.

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  1. School of Electrical and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou, 450000, People’s Republic of China

    Fengxian Wang, Senlin Bi, Shaozhi Feng, Huanlong Zhang & Chenglin Guo

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  1. Fengxian Wang
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Fengxian Wang: Conceptualization; methodology; analysis; resources; writing—review and editing; investigation; supervision. Senlin Bi: Data curation; investigation; software; validation; writing—original draft and editing. Shaozhi Feng: Conceptualizatio; methodology; validation analysis; review and editing; visualization. Huanlong Zhang: Conceptualization; methodology; analysis; resources; investigation; supervision. Chenglin Guo: Data curation; investigation; software; resources; data curation.

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Correspondence to Huanlong Zhang.

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Appendix 1

Appendix 1


IEEE-30 bus system B-factor

$$\begin{aligned} B_{i j}= & {} \left[ \begin{array}{cccccc} 0.1382 &{} -0.0299 &{} 0.0044 &{} -0.0022 &{} -0.0010 &{} -0.0008 \\ -0.0299 &{} 0.0487 &{} -0.0025 &{} 0.0004 &{} 0.0016 &{} 0.0041 \\ 0.0044 &{} -0.0025 &{} 0.0182 &{} -0.0070 &{} -0.0066 &{} -0.0066 \\ -0.0022 &{} 0.0004 &{} -0.0070 &{} 0.0137 &{} 0.0050 &{} 0.0033 \\ -0.0010 &{} 0.0016 &{} -0.0066 &{} 0.0050 &{} 0.0109 &{} 0.0005 \\ -0.0008 &{} 0.0041 &{} -0.0066 &{} 0.0033 &{} 0.0005 &{} 0.0244 \end{array}\right] \\ B_{0}= & {} [-0.01070.0060-0.00170.00090.00020.0030]\\ B_{00}= & {} 9.8573 \times 10^{-4} \end{aligned}$$

See Table 16.

Table 16 Unconstrained multi-objective testing functions of CEC2009 (UF1-UF7)
Full size table

IEEE-180 bus system B-factor

$$\begin{aligned} B_{11}= & {} \left[ \begin{array}{ccccccc} 0.042741 &{} 0.030108 &{} 0.019242 &{} 0.021506 &{} -0.00288 &{} -0.00400 &{} -0.00447 \\ 0.030108 &{} 0.037946 &{} 0.020710 &{} 0.020912 &{} -0.00363 &{} -0.00525 &{} -0.00448 \\ 0.019242 &{} 0.02071 &{} 0.026780 &{} 0.024696 &{} -0.00247 &{} -0.00378 &{} -0.00298 \\ 0.021506 &{} 0.020912 &{} 0.024696 &{} 0.024393 &{} -0.00232 &{} -0.00352 &{} -0.00309 \\ -0.00288 &{} -0.00363 &{} -0.00247 &{} -0.00232 &{} 0.009543 &{} 0.003659 &{} 0.002951 \\ -0.00400 &{} -0.00525 &{} -0.00378 &{} -0.00352 &{} 0.003659 &{} 0.010678 &{} 0.005763 \\ -0.00447 &{} -0.00448 &{} -0.00298 &{} -0.00309 &{} -0.002951 &{} 0.005763 &{} 0.008092 \end{array}\right] \\ B_{12}= & {} \left[ \begin{array}{lllllll} -0.00272 &{} -0.00323 &{} -0.00694 &{} -0.00745 &{} -0.01952 &{} -0.01217 &{} -0.01718 \\ -0.00366 &{} -0.00359 &{} -0.00695 &{} -0.01018 &{} -0.02004 &{} -0.01844 &{} -0.02057 \\ -0.00239 &{} -0.00231 &{} -0.00467 &{} -0.00786 &{} -0.01583 &{} -0.01529 &{} -0.01668 \\ -0.00223 &{} -0.00230 &{} -0.00475 &{} -0.00715 &{} -0.01600 &{} -0.01346 &{} -0.01588 \\ 0.003116 &{} 0.004207 &{} 0.002066 &{} 0.000366 &{} -0.00365 &{} -0.00381 &{} -0.00424 \\ 0.003740 &{} 0.003341 &{} 0.002486 &{} 0.001192 &{} -0.00279 &{} -0.00288 &{} -0.00331 \\ 0.003370 &{} 0.003566 &{} 0.003054 &{} 0.001293 &{} -0.00252 &{} -0.00192 &{} -0.00272 \end{array}\right] \\ B_{21}= & {} \left[ \begin{array}{lllllll} -0.00272 &{} -0.00366 &{} -0.00239 &{} -0.00223 &{} 0.003116 &{} 0.00374 &{} 0.00337 \\ -0.00323 &{} -0.00359 &{} -0.00231 &{} -0.00230 &{} 0.004207 &{} 0.003341 &{} 0.003566 \\ -0.00694 &{} -0.00695 &{} -0.00467 &{} -0.00475 &{} 0.002066 &{} 0.002486 &{} 0.003054 \\ -0.00745 &{} -0.01018 &{} -0.00786 &{} -0.00715 &{} 0.000366 &{} 0.001192 &{} 0.001293 \\ -0.01952 &{} -0.02004 &{} -0.01583 &{} -0.01600 &{} -0.00365 &{} -0.00279 &{} -0.00252 \\ -0.01217 &{} -0.01844 &{} -0.01529 &{} -0.01346 &{} -0.00381 &{} -0.00288 &{} -0.00192 \\ -0.01718 &{} -0.02057 &{} -0.01668 &{} -0.01588 &{} -0.00424 &{} -0.00331 &{} -0.00188 \end{array}\right] \\ B_{22}= & {} \left[ \begin{array}{lllllll} 0.003876&{}0.003746&{}0.002934&{}0.002063&{}-0.00152&{}-0.00142&{}-0.00188\\ 0.003746&{}0.005404&{}0.002869&{}0.001477&{}-0.00225&{}-0.00189&{}-0.00254\\ 0.002934&{}0.002869&{}0.006738&{}0.003054&{}0.001212&{}0.001331&{}0.000955\\ 0.002063&{}0.001477&{}0.003054&{}0.008576&{}0.006171&{}0.008179&{}0.007260\\ -0.00152&{}-0.00225&{}0.001212&{}0.006171&{}0.036152&{}0.018390&{}0.020017\\ -0.00142&{}-0.00189&{}0.001331&{}0.008179&{}0.018390&{}0.033117&{}0.029414\\ -0.00188&{}-0.00254&{}0.000955&{}0.007260&{}0.020017&{}0.029414&{}0.041297 \end{array}\right] \\ B_{ij}= & {} \begin{bmatrix} B_{11} &{}B_{12} \\ B_{21} &{}B_{22} \end{bmatrix}\times 10^{-2}\\ B_{10}= & {} \begin{bmatrix} -0.538520&-0.283225&-0.19294&-0.26424&0.017755&0.021917&0.040508 \end{bmatrix}\times 10^{-2}\\ B_{20}= & {} \begin{bmatrix} 0.012216&0.014007&0.0044072&0.032732&0.217820&0.032560&0.155630 \end{bmatrix}\times 10^{-2}\\ B_{00}= & {} 2.8378. \end{aligned}$$

See Tables 17, 18, 19 and 20.

Table 17 Unconstrained multi-objective testing functions of CEC2009 (UF8-UF10)
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Table 18 Details of the benchmark functions(ZDT1-ZDT4,ZDT6)
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Table 19 Fuel and emission factors for the IEEE-30 bus system
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Table 20 Fuel and emission factors for the IEEE-118 bus system
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Wang, F., Bi, S., Feng, S. et al. Combined economic and emission power dispatch problems through multi-objective Honey Badger optimizer. Cluster Comput (2024). https://doi.org/10.1007/s10586-024-04345-2

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