Search Advanced

AIMS Mathematics

2026, Volume 11, Issue 10: 33768-33810. doi: 10.3934/math.20261320
Previous Article Next Article
Research article

Economic and environmental optimization of hybrid wind-combined heat and power dispatch: A static and dynamic analysis

  • 1.
    Department of Electrical Engineering, Faculty of Applied Science, Kasdi Merbah University, Ghardaia Road, P.O. Box 511, Ouargla 30000, Algeria
  • 2.
    LDREI Laboratory, Higher School of Electrical Engineering and Energetic of Oran, Oran 31000, Algeria
  • 3.
    Laboratoire de Développement Durable de l'Energie Electrique, LDDEE, UST-MB, Oran, Algeria
  • 4.
    Department of Computer sciences, University of Sciences and the technology of Oran, (USTO-MB), 31000, Algeria
  • 5.
    Department of Electrical and Electronics Engineering, Yalova University, Yalova, Turkey
  • 6.
    Zero Emission Technologies Innovation Center, University of Tabuk, Tabuk, 47913, Saudi Arabia
  • 7.
    Department of Electrical Engineering, Dong-A University, Busan 49315, Republic of Korea
  • 8.
    Department of ICT Integrated Safe Ocean Smart Cities Engineering, Dong-A University, Busan 49315, Republic of Korea
  • Published: 19 October 2026

  • MSC : 68T20, 68W50, 90C59, 65K10

  • This study introduces the Mexican Axolotl Optimization (MAO) algorithm to address the combined heat and power economic-emission dispatch (CHPEED) problem. The objective is to optimize power and heat generation from online units in a power system, including wind power plants under deterministic conditions, over a specified timeframe, to reduce operating costs and emissions simultaneously while satisfying all generators' limits. The effectiveness of the MAO approach was evaluated through extensive testing on three CHPD issues: static economic environmental dispatch, dynamic economic environmental dispatch (DEED), and hybrid wind-CHPDEED. The inclusion of the practical constraints, such as valve point loading effects (VPLE), transmission losses, feasible operating regions (FOR), and ramp rate limits (RRL), renders MO-CHPDEED problems with non-convex characteristics. A weighting method was employed to convert the MO-CHPD issues into single-objective optimization problems. Standard test systems with 5 and 7 units were employed to demonstrate the algorithm's performance across varying levels of complexity. The numerical results were compared with those obtained using various other optimization methods from the literature. The MAO approach demonstrates competitive performance, achieving the best results in environmental dispatch and MO-CHPD scenarios, while showing good performance in economic dispatch, despite some methods achieving lower costs.

    Citation: Benyekhlef Larouci, Houari Boudjella, Khaled Guerraiche, Latifa Dekhici, Aykut Fatih Güven, Abdul Wadood, Herie Park, Byung O Kang. Economic and environmental optimization of hybrid wind-combined heat and power dispatch: A static and dynamic analysis[J]. AIMS Mathematics, 2026, 11(10): 33768-33810. doi: 10.3934/math.20261320

    Related Papers:

  • This study introduces the Mexican Axolotl Optimization (MAO) algorithm to address the combined heat and power economic-emission dispatch (CHPEED) problem. The objective is to optimize power and heat generation from online units in a power system, including wind power plants under deterministic conditions, over a specified timeframe, to reduce operating costs and emissions simultaneously while satisfying all generators' limits. The effectiveness of the MAO approach was evaluated through extensive testing on three CHPD issues: static economic environmental dispatch, dynamic economic environmental dispatch (DEED), and hybrid wind-CHPDEED. The inclusion of the practical constraints, such as valve point loading effects (VPLE), transmission losses, feasible operating regions (FOR), and ramp rate limits (RRL), renders MO-CHPDEED problems with non-convex characteristics. A weighting method was employed to convert the MO-CHPD issues into single-objective optimization problems. Standard test systems with 5 and 7 units were employed to demonstrate the algorithm's performance across varying levels of complexity. The numerical results were compared with those obtained using various other optimization methods from the literature. The MAO approach demonstrates competitive performance, achieving the best results in environmental dispatch and MO-CHPD scenarios, while showing good performance in economic dispatch, despite some methods achieving lower costs.



    加载中


    [1] R. Hite, Cogeneration/combined heat and power: An overview, Cogener. Compet. Power J. , 17 (2002), 64–79. https://doi.org/10.1080/10668680209508981 doi: 10.1080/10668680209508981
    [2] T. Guo, M. I. Henwood, M. Van Ooijen, An algorithm for combined heat and power economic dispatch, IEEE Trans. Power Syst. , 11 (1996), 1778–1784. https://doi.org/10.1109/59.544642 doi: 10.1109/59.544642
    [3] M. A. Brown, V. S. Herrera, Combined heat and power as a platform for clean energy systems, Appl. Energy, 304 (2021), 117686. https://doi.org/10.1016/j.apenergy.2021.117686 doi: 10.1016/j.apenergy.2021.117686
    [4] N. Ghorbani, Combined heat and power economic dispatch using exchange market algorithm, Int. J. Electr. Power Energy Syst. , 82 (2016), 58–66. https://doi.org/10.1016/j.ijepes.2016.03.004 doi: 10.1016/j.ijepes.2016.03.004
    [5] P. K. Adhvaryyu, S. Adhvaryyu, S. Prabhakar, S. Bid, Application of bio-inspired social spider algorithm in valve-point and prohibited operating zones constrained optimal load flow of combined heat and power system, In: International Conference on Innovation in Modern Science and Technology, Springer, 2019,853–862. https://doi.org/10.1007/978-3-030-42363-6_98
    [6] B. Shi, L. X. Yan, W. Wu, Multi-objective optimization for combined heat and power economic dispatch with power transmission loss and emission reduction, Energy, 56 (2013), 135–143. https://doi.org/10.1016/j.energy.2013.04.066 doi: 10.1016/j.energy.2013.04.066
    [7] A. Wadood, B. S. Khan, H. Albalawi, A. M. Alatwi, Design of the novel fractional order hybrid whale optimizer for thermal wind power generation systems with integration of chaos infused wind power, Fractal Fract. , 8 (2024), 379. https://doi.org/10.3390/fractalfract8070379 doi: 10.3390/fractalfract8070379
    [8] Q. Meng, X. Tong, S. Hussain, F. Luo, F. Zhou, Y. He, et al., Enhancing distribution system stability and efficiency through multi-power supply startup optimization for new energy integration, IET Gener. Transm. Distrib. , 18 (2024), 3487–3500. https://doi.org/10.1049/gtd2.13299 doi: 10.1049/gtd2.13299
    [9] V. Bhandari, S. Rose, E. J. Wilson, Non-financial barriers to combined heat and power in the United States—A qualitative study, Electr. J. , 32 (2019), 49–56. https://doi.org/10.1016/j.tej.2019.02.011 doi: 10.1016/j.tej.2019.02.011
    [10] L. Li, Y. Sun, Y. Han, W. Chen, Seasonal hydrogen energy storage sizing: Two-stage economic-safety optimization for integrated energy systems in northwest China, iScience, 27 (2024), 110691. https://doi.org/10.1016/j.isci.2024.110691 doi: 10.1016/j.isci.2024.110691
    [11] H. Albalawi, A. Wadood, H. Park, Economic load dispatch problem analysis based on modified moth flame optimizer (MMFO) considering emission and wind power, Mathematics, 12 (2024), 3326. https://doi.org/10.3390/math12213326 doi: 10.3390/math12213326
    [12] A. Wadood, B. S. Khan, B. M. Khan, H. Park, B. O. Kang, A fractional hybrid strategy for reliable and cost-optimal economic dispatch in wind-integrated power systems, Fractal Fract. , 10 (2026), 64. https://doi.org/10.3390/fractalfract10010064 doi: 10.3390/fractalfract10010064
    [13] S. Murugan, B. Horák, A review of micro combined heat and power systems for residential applications, Renew. Sust. Energ. Rev. , 64 (2016), 144–162. https://doi.org/10.1016/j.rser.2016.04.064 doi: 10.1016/j.rser.2016.04.064
    [14] D. C. Secui, Large-scale multi-area economic/emission dispatch based on a new symbiotic organisms search algorithm, Energy Convers. Manag. , 154 (2017), 203–223. https://doi.org/10.1016/j.enconman.2017.09.075 doi: 10.1016/j.enconman.2017.09.075
    [15] T. Niknam, R. Azizipanah-Abarghooee, A. Roosta, B. Amiri, A new multi-objective reserve constrained combined heat and power dynamic economic emission dispatch, Energy, 42 (2012), 530–545. https://doi.org/10.1016/j.energy.2012.02.041 doi: 10.1016/j.energy.2012.02.041
    [16] M. Nazari-Heris, B. Mohammadi-Ivatloo, G. B. Gharehpetian, A comprehensive review of heuristic optimization algorithms for optimal combined heat and power dispatch from economic and environmental perspectives, Renew. Sust. Energ. Rev. , 81 (2018), 2128–2143. https://doi.org/10.1016/j.rser.2017.06.024 doi: 10.1016/j.rser.2017.06.024
    [17] M. Singh, J. S. Dhillon, Multiobjective thermal power dispatch using opposition-based greedy heuristic search, Int. J. Electr. Power Energy Syst. , 82 (2016), 339–353. https://doi.org/10.1016/j.ijepes.2016.03.016 doi: 10.1016/j.ijepes.2016.03.016
    [18] A. M. Elaiw, X. Xia, A. M. Shehata, Hybrid DE-SQP method for solving combined heat and power dynamic economic dispatch problem, Math. Probl. Eng. , 2013 (2013), 982305. https://doi.org/10.1155/2013/982305 doi: 10.1155/2013/982305
    [19] N. Nwulu, Combined heat and power dynamic economic emissions dispatch with valve point effects and incentive-based demand response programs, Computation, 8 (2020), 101. https://doi.org/10.3390/computation8040101 doi: 10.3390/computation8040101
    [20] H. Albalawi, Y. Muhammad, A. Wadood, B. S. Khan, S. T. Zainab, A. M. Alatwi, Leveraging the performance of integrated power systems with wind uncertainty using fractional computing-based hybrid method, Fractal Fract. , 8 (2024), 532. https://doi.org/10.3390/fractalfract8090532 doi: 10.3390/fractalfract8090532
    [21] A. Sashirekha, J. Pasupuleti, N. H. Moin, C. S. Tan, Combined heat and power (CHP) economic dispatch solved using Lagrangian relaxation with surrogate subgradient multiplier updates, Int. J. Electr. Power Energy Syst. , 44 (2013), 421–430. https://doi.org/10.1016/j.ijepes.2012.07.038 doi: 10.1016/j.ijepes.2012.07.038
    [22] H. R. Abdolmohammadi, A. Kazemi, A Benders decomposition approach for a combined heat and power economic dispatch, Energy Convers. Manag. , 71 (2013), 21–31. https://doi.org/10.1016/j.enconman.2013.03.013 doi: 10.1016/j.enconman.2013.03.013
    [23] J. S. Kim, T. F. Edgar, Optimal scheduling of combined heat and power plants using mixed-integer nonlinear programming, Energy, 77 (2014), 675–690. https://doi.org/10.1016/j.energy.2014.09.062 doi: 10.1016/j.energy.2014.09.062
    [24] A. Rong, R. Lahdelma, An efficient envelope-based branch and bound algorithm for non-convex combined heat and power production planning, Eur. J. Oper. Res. , 183 (2007), 412–431. https://doi.org/10.1016/j.ejor.2006.09.072 doi: 10.1016/j.ejor.2006.09.072
    [25] F. J. Rooijers, R. A. M. van Amerongen, Static economic dispatch for co-generation systems, IEEE Trans. Power Syst. , 9 (1994), 1392–1398. https://doi.org/10.1109/59.336125 doi: 10.1109/59.336125
    [26] M. Moradi-Dalvand, M. Nazari-Heris, B. Mohammadi-Ivatloo, S. Galavani, A. Rabiee, A two-stage mathematical programming approach for the solution of combined heat and power economic dispatch, IEEE Syst. J. , 14 (2019), 2873–2881. https://doi.org/10.1109/JSYST.2019.2958179 doi: 10.1109/JSYST.2019.2958179
    [27] H. Abdi, Profit-based unit commitment problem: A review of models, methods, challenges, and future directions, Renew. Sust. Energ. Rev. , 138 (2021), 110504. https://doi.org/10.1016/j.rser.2020.110504 doi: 10.1016/j.rser.2020.110504
    [28] M. Basu, Combined heat and power economic dispatch by using differential evolution, Electr. Power Compon. Syst. , 38 (2010), 996–1004. https://doi.org/10.1080/15325000903571574 doi: 10.1080/15325000903571574
    [29] D. Liu, Z. Hu, Q. Su, Neighborhood-based differential evolution algorithm with direction-induced strategy for the large-scale combined heat and power economic dispatch problem, Inform. Sci. , 613 (2022), 469–493. https://doi.org/10.1016/j.ins.2022.09.025 doi: 10.1016/j.ins.2022.09.025
    [30] A. Haghrah, M. A. Nekoui, M. Nazari-Heris, B. Mohammadi-Ivatloo, An improved real-coded genetic algorithm with random walk-based mutation for solving combined heat and power economic dispatch, J. Ambient Intell. Humaniz. Comput. , 12 (2021), 8561–8584. https://doi.org/10.1007/s12652-020-02589-5 doi: 10.1007/s12652-020-02589-5
    [31] A. Meng, P. Mei, H. Yin, X. Peng, Z. Guo, Crisscross optimization algorithm for solving combined heat and power economic dispatch problem, Energy Convers. Manag. , 105 (2015), 1303–1317. https://doi.org/10.1016/j.enconman.2015.09.003 doi: 10.1016/j.enconman.2015.09.003
    [32] M. I. Alomoush, Optimal combined heat and power economic dispatch using stochastic fractal search algorithm, J. Mod. Power Syst. Clean Energy, 8 (2020), 276–286. https://doi.org/10.35833/MPCE.2018.000753 doi: 10.35833/MPCE.2018.000753
    [33] F. Özbilgin, O. Ö. Mengi, A. Wadood, A. F. Güven, H. Park, Comparative optimization of PIDN and fractional order controllers for a quarter car active suspension system using recent metaheuristic algorithms, Sci. Rep. , 15 (2025), 35222. https://doi.org/10.1038/s41598-025-19505-6 doi: 10.1038/s41598-025-19505-6
    [34] Q. Yang, P. Liu, J. Zhang, N. Dong, Combined heat and power economic dispatch using an adaptive cuckoo search with differential evolution mutation, Appl. Energy, 307 (2022), 118057. https://doi.org/10.1016/j.apenergy.2021.118057 doi: 10.1016/j.apenergy.2021.118057
    [35] M. Nazari-Heris, M. Mehdinejad, B. Mohammadi-Ivatloo, G. Babamalek-Gharehpetian, Combined heat and power economic dispatch problem solution by implementation of whale optimization method, Neural Comput. Appl. , 31 (2019), 421–436. https://doi.org/10.1007/s00521-017-3074-9 doi: 10.1007/s00521-017-3074-9
    [36] B. M. Khan, A. Wadood, H. Park, S. Khan, H. Ali, Optimal coordination of directional overcurrent relays using an innovative fractional-order derivative war algorithm, Fractal Fract. , 9 (2025), 169. https://doi.org/10.3390/fractalfract9030169 doi: 10.3390/fractalfract9030169
    [37] A. Wadood, H. Albalawi, A. M. Alatwi, H. Park, Modified swarm-based artificial intelligence optimization for optimal coordination of directional overcurrent relays in power system, IEEE Access, 13 (2025), 71007–71026. https://doi.org/10.1109/ACCESS.2025.3563338 doi: 10.1109/ACCESS.2025.3563338
    [38] A. Wadood, A. F. Yousaf, A. M. Alatwi, An enhanced multiple unmanned aerial vehicle swarm formation control using a novel fractional swarming strategy approach, Fractal Fract. , 8 (2024), 334. https://doi.org/10.3390/fractalfract8060334 doi: 10.3390/fractalfract8060334
    [39] A. Wadood, H. Park, A novel application of fractional order derivative moth flame optimization algorithm for solving the problem of optimal coordination of directional overcurrent relays, Fractal Fract. , 8 (2024), 251. https://doi.org/10.3390/fractalfract8050251 doi: 10.3390/fractalfract8050251
    [40] A. Wadood, E. Ahmed, S. B. Rhee, B. S. Khan, A fractional-order Archimedean spiral moth–flame optimization strategy to solve optimal power flows, Fractal Fract. , 8 (2024), 225. https://doi.org/10.3390/fractalfract8040225 doi: 10.3390/fractalfract8040225
    [41] A. M. Alatwi, H. Albalawi, A. Wadood, I. E. Atawi, K. S. S. Alatawi, Novel GBest–Lévy adaptive differential ant bee colony optimization for optimal allocation of electric vehicle charging stations and distributed generators in smart distribution systems, Energies, 18 (2025), 6018. https://doi.org/10.3390/en18226018 doi: 10.3390/en18226018
    [42] J. Sun, Y. Li, Social cognitive optimization with tent map for combined heat and power economic dispatch, Int. Trans. Electr. Energy Syst. , 29 (2019), e2660. https://doi.org/10.1002/etep.2660 doi: 10.1002/etep.2660
    [43] M. F. Shehzad, M. Dan, V. Mariani, S. Srinivasan, D. Liuzza, C. Mongiello, et al., A heuristic algorithm for combined heat and power system operation management, Energies, 14 (2021), 1588. https://doi.org/10.3390/en14061588 doi: 10.3390/en14061588
    [44] A. R. Ginidi, A. M. Elsayed, A. M. Shaheen, E. E. Elattar, R. A. El-Sehiemy, A novel heap-based optimizer for scheduling of large-scale combined heat and power economic dispatch, IEEE Access, 9 (2021), 83695–83708. https://doi.org/10.1109/ACCESS.2021.3087449 doi: 10.1109/ACCESS.2021.3087449
    [45] S. Duman, H. Ozbay, E. Celik, S. B. Efe, E. Isen, B. Duman, Improvement of the fitness-distance balance-based supply–demand optimization algorithm for solving the combined heat and power economic dispatch problem, Iran. J. Sci. Technol. Trans. Electr. Eng. , 47 (2023), 513–548. https://doi.org/10.1007/s40998-022-00560-y doi: 10.1007/s40998-022-00560-y
    [46] A. Vasebi, M. Fesanghary, S. M. T. Bathaee, Combined heat and power economic dispatch by harmony search algorithm, Int. J. Electr. Power Energy Syst. , 29 (2007), 713–719. https://doi.org/10.1016/j.ijepes.2007.06.006 doi: 10.1016/j.ijepes.2007.06.006
    [47] J. K. Pattanaik, M. Basu, D. P. Dash, Heat transfer search algorithm for combined heat and power economic dispatch, Iran. J. Sci. Technol. Trans. Electr. Eng. , 44 (2020), 963–978. https://doi.org/10.1007/s40998-019-00280-w doi: 10.1007/s40998-019-00280-w
    [48] P. Kaur, K. Chaturvedi, An economic dispatch model for combined heat and power plant using Rao-Ⅰ optimisation algorithm, In: Proceedings of the 2022 Second International Conference on Power, Control and Computing Technologies (ICPC2T), Raipur, India, 2022, 1–6. https://doi.org/10.1109/ICPC2T53885.2022.9777079
    [49] M. J. Kim, T. S. Kim, R. J. Flores, J. Brouwer, Neural-network-based optimization for economic dispatch of combined heat and power systems, Appl. Energy, 265 (2020), 114785. https://doi.org/10.1016/j.apenergy.2020.114785 doi: 10.1016/j.apenergy.2020.114785
    [50] S. D. Beigvand, H. Abdi, M. La Scala, Combined heat and power economic dispatch problem using gravitational search algorithm, Electr. Power Syst. Res. , 133 (2016), 160–172. https://doi.org/10.1016/j.epsr.2015.10.007 doi: 10.1016/j.epsr.2015.10.007
    [51] J. Chen, Y. Zhang, A Lagrange relaxation-based alternating iterative algorithm for non-convex combined heat and power dispatch problem, Electr. Power Syst. Res. , 177 (2019), 105982. https://doi.org/10.1016/j.epsr.2019.105982 doi: 10.1016/j.epsr.2019.105982
    [52] A. Ginidi, A. Elsayed, A. Shaheen, E. Elattar, R. El-Sehiemy, An innovative hybrid heap-based and jellyfish search algorithm for combined heat and power economic dispatch in electrical grids, Mathematics, 9 (2021), 2053. https://doi.org/10.3390/math9172053 doi: 10.3390/math9172053
    [53] M. Ramachandran, S. Mirjalili, M. Nazari-Heris, D. S. Parvathysankar, A. Sundaram, C. A. R. C. Gnanakkan, A hybrid grasshopper optimization algorithm and Harris hawks optimizer for combined heat and power economic dispatch problem, Eng. Appl. Artif. Intell. , 111 (2022), 104753. https://doi.org/10.1016/j.engappai.2022.104753 doi: 10.1016/j.engappai.2022.104753
    [54] R. M. Rizk-Allah, A. E. Hassanien, V. Snášel, A hybrid chameleon swarm algorithm with superiority of feasible solutions for optimal combined heat and power economic dispatch problem, Energy, 254 (2022), 124340. https://doi.org/10.1016/j.energy.2022.124340 doi: 10.1016/j.energy.2022.124340
    [55] M. Ramachandran, S. Mirjalili, M. M. Ramalingam, C. A. R. C. Gnanakkan, D. S. Parvathysankar, A. Sundaram, A ranking-based fuzzy adaptive hybrid crow search algorithm for combined heat and power economic dispatch, Expert Syst. Appl., 197 (2022), 116625. https://doi.org/10.1016/j.eswa.2022.116625https://doi.org/10.1016/j.energy.2022.124340
    [56] M. Nasir, A. Sadollah, I. B. Aydilek, A. L. Ara, S. A. Nabavi-Niaki, A combination of FA and SRPSO algorithm for combined heat and power economic dispatch, Appl. Soft Comput. , 102 (2021), 107088. https://doi.org/10.1016/j.asoc.2021.107088 doi: 10.1016/j.asoc.2021.107088
    [57] P. Kaur, K. T. Chaturvedi, M. L. Kolhe, Combined heat and power economic dispatching within energy network using hybrid metaheuristic technique, Energies, 16 (2023), 1221. https://doi.org/10.3390/en16031221 doi: 10.3390/en16031221
    [58] X. Chen, S. Fang, K. Li, Reinforcement-learning-based multi-objective differential evolution algorithm for large-scale combined heat and power economic emission dispatch, Energies, 16 (2023), 3753. https://doi.org/10.3390/en16093753 doi: 10.3390/en16093753
    [59] Y. A. Shaabani, A. R. Seifi, M. J. Kouhanjani, Stochastic multi-objective optimization of combined heat and power economic/emission dispatch, Energy, 141 (2017), 1892–1904. https://doi.org/10.1016/j.energy.2017.11.124 doi: 10.1016/j.energy.2017.11.124
    [60] M. Basu, Combined heat and power economic emission dispatch using nondominated sorting genetic algorithm-Ⅱ, Int. J. Electr. Power Energy Syst. , 53 (2013), 135–141. https://doi.org/10.1016/j.ijepes.2013.04.014 doi: 10.1016/j.ijepes.2013.04.014
    [61] J. Sun, J. Deng, Y. Li, Indicator and crowding distance-based evolutionary algorithm for combined heat and power economic emission dispatch, Appl. Soft Comput. , 90 (2020), 106158. https://doi.org/10.1016/j.asoc.2020.106158 doi: 10.1016/j.asoc.2020.106158
    [62] V. Tiwari, H. M. Dubey, M. Pandit, S. R. Salkuti, CHP-based economic emission dispatch of microgrid using Harris hawks optimization, Fluids, 7 (2022), 248. https://doi.org/10.3390/fluids7070248 doi: 10.3390/fluids7070248
    [63] A. Sundaram, Multiobjective multi-verse optimization algorithm to solve combined economic, heat and power emission dispatch problems, Appl. Soft Comput. , 91 (2020), 106195. https://doi.org/10.1016/j.asoc.2020.106195 doi: 10.1016/j.asoc.2020.106195
    [64] A. Sundaram, Combined heat and power economic emission dispatch using hybrid NSGA Ⅱ-MOPSO algorithm incorporating an effective constraint handling mechanism, IEEE Access, 8 (2020), 13748–13768. https://doi.org/10.1109/ACCESS.2020.2963887 doi: 10.1109/ACCESS.2020.2963887
    [65] Y. Li, J. Wang, D. Zhao, G. Li, C. Chen, A two-stage approach for combined heat and power economic emission dispatch: Combining multi-objective optimization with integrated decision making, Energy, 162 (2018), 237–254. https://doi.org/10.1016/j.energy.2018.07.200 doi: 10.1016/j.energy.2018.07.200
    [66] V. K. Jadoun, G. R. Prashanth, S. S. Joshi, K. Narayanan, H. Malik, F. P. G. Márquez, Optimal fuzzy-based economic emission dispatch of combined heat and power units using dynamically controlled whale optimization algorithm, Appl. Energy, 315 (2022), 119033. https://doi.org/10.1016/j.apenergy.2022.119033 doi: 10.1016/j.apenergy.2022.119033
    [67] G. Xiong, M. Shuai, X. Hu, Combined heat and power economic emission dispatch using improved bare-bone multi-objective particle swarm optimization, Energy, 244 (2022), 123108. https://doi.org/10.1016/j.energy.2022.123108 doi: 10.1016/j.energy.2022.123108
    [68] F. Sadikoglu, E. Babaei, Combined heat and power economic emission dispatch applying exchange market algorithm with fuzzy satisfying techniques, In: Proceedings of the 14th International Conference on Theory and Application of Fuzzy Systems and Soft Computing (ICAFS 2020), Springer, 2021,165–173. https://doi.org/10.1007/978-3-030-64058-3_20
    [69] Y. Sharifian, H. Abdi, Solving multi-zone combined heat and power economic emission dispatch problem considering wind uncertainty by applying grasshopper optimization algorithm, Sustain. Energy Technol. Assess. , 53 (2022), 102512. https://doi.org/10.1016/j.seta.2022.102512 doi: 10.1016/j.seta.2022.102512
    [70] W. Lai, X. Zheng, Q. Song, F. Hu, Q. Tao, H. Chen, Multi-objective membrane search algorithm: A new solution for economic emission dispatch, Appl. Energy, 326 (2022), 119969. https://doi.org/10.1016/j.apenergy.2022.119969 doi: 10.1016/j.apenergy.2022.119969
    [71] B. Ozkaya, H. T. Kahraman, S. Duman, U. Guvenc, M. Akbel, Combined heat and power economic emission dispatch using dynamic switched crowding-based multi-objective symbiotic organism search algorithm, Appl. Soft Comput. , 151 (2024), 111106. https://doi.org/10.1016/j.asoc.2023.111106 doi: 10.1016/j.asoc.2023.111106
    [72] A. M. Elaiw, X. Xia, A. M. Shehata, Combined heat and power dynamic economic dispatch with emission limitations using hybrid DE-SQP method, Abstr. Appl. Anal. , 2013 (2013), 120849. https://doi.org/10.1155/2013/120849 doi: 10.1155/2013/120849
    [73] H. R. Sadeghian, M. M. Ardehali, A novel approach for optimal economic dispatch scheduling of integrated combined heat and power systems for maximum economic profit and minimum environmental emissions based on Benders decomposition, Energy, 102 (2016), 10–23. https://doi.org/10.1016/j.energy.2016.02.044 doi: 10.1016/j.energy.2016.02.044
    [74] A. M. Shehata, Hybrid PSO-SQP for solving combined heat and power dynamic economic emission dispatch problem with non-smooth cost function, J. Adv. Stud. Topol. , 8 (2017), 85–96. http://doi.org/10.20454/jast.2017.1332 doi: 10.20454/jast.2017.1332
    [75] D. Zou, D. Gong, H. Ouyang, The dynamic economic emission dispatch of the combined heat and power system integrated with a wind farm and a photovoltaic plant, Appl. Energy, 351 (2023), 121890. https://doi.org/10.1016/j.apenergy.2023.121890 doi: 10.1016/j.apenergy.2023.121890
    [76] M. I. Alomoush, Microgrid dynamic combined power–heat economic-emission dispatch with deferrable loads and price-based energy storage elements and power exchange, Sustain. Energy Grids Netw. , 26 (2021), 100479. https://doi.org/10.1016/j.segan.2021.100479 doi: 10.1016/j.segan.2021.100479
    [77] M. Basu, Multi-county combined heat and power dynamic economic emission dispatch incorporating electric vehicle parking lot, Energy, 275 (2023), 127523. https://doi.org/10.1016/j.energy.2023.127523 doi: 10.1016/j.energy.2023.127523
    [78] Q. Meng, Y. Gao, S. Wang, X. Hu, L. Zhao, Q. She, et al., Two-stage scheduling of electric vehicle flexible load regulation and generation-grid-load-storage resources in new-type power systems, Energy Rep. , 15 (2026), 109090. https://doi.org/10.1016/j.egyr.2026.109090 doi: 10.1016/j.egyr.2026.109090
    [79] Y. Villuendas-Rey, J. L. Velázquez-Rodriguez, M. D. Alanis-Tamez, M. A. Moreno-Ibarra, C. Yáñez-Márquez, Mexican axolotl optimization: A novel bioinspired heuristic, Mathematics, 9 (2021), 781. https://doi.org/10.3390/math9070781 doi: 10.3390/math9070781
    [80] C. S. V. P. Rao, A. Pandian, C. R. Reddy, F. Aymen, M. Alqarni, M. M. Alharthi, Location determination of electric vehicles parking lot with distribution system by Mexican axolotl optimization and wild horse optimizer, IEEE Access, 10 (2022), 55408–55427. https://doi.org/10.1109/ACCESS.2022.3176370 doi: 10.1109/ACCESS.2022.3176370
    [81] A. R. Nair, S. Kirthiga, Nature-inspired approach toward elimination of nonlinearities in SWIPT-enabled energy harvesting networks, IEEE Access, 10 (2022), 100837–100856. https://doi.org/10.1109/ACCESS.2022.3208157 doi: 10.1109/ACCESS.2022.3208157
    [82] R. Ramachandran, S. Kannan, S. K. Ganesan, B. Annamalai, Optimal economic-emission load dispatch in microgrid incorporating renewable energy sources by golden jackal optimization (GJO) and Mexican axolotl optimization (MAO), Energy Environ. , 36 (2025), 2001–2026. https://doi.org/10.1177/0958305X231204605 doi: 10.1177/0958305X231204605
    [83] A. Kumar, J. Choudhary, Power quality improvement of hybrid renewable energy systems-based microgrid for STATCOM: Hybrid-deep-learning model and Mexican axolotl dingo optimizer (MADO), Eng. Res. Express, 5 (2023), 045031. https://doi.org/10.1088/2631-8695/ad0287 doi: 10.1088/2631-8695/ad0287
    [84] H. K. Vijayvergia, U. S. Modani, TEAMR-AMAA: trust and energy aware multicast routing based on adaptive Mexican axolotl algorithm in WSN, Int. J. Syst. Syst. Eng. , 13 (2023), 306–323. https://doi.org/10.1504/IJSSE.2023.133017 doi: 10.1504/IJSSE.2023.133017
    [85] C. Balasubramanian, G. Sathya, R. Praveen, Hybrid Mexican axolotl and bitterling fish optimization algorithm-based spectrum sensing multi-hop clustering routing protocol for cognitive sensor networks, Sci. Rep. , 14 (2024), 31102. https://doi.org/10.1038/s41598-024-82311-z doi: 10.1038/s41598-024-82311-z
    [86] B. Houari, L. Mohammed, B. Hamid, A. A. Nour El Islam, B. Farid, S. Abdallah, Solution of economic load dispatch problems using novel improved harmony search algorithm, Int. J. Electr. Eng. Inform. , 13 (2021), 224–240. https://doi.org/10.15676/ijeei.2021.13.1.13 doi: 10.15676/ijeei.2021.13.1.13
    [87] B. Larouci, A. N. E. I. Ayad, H. Alharbi, T. E. A. Alharbi, H. Boudjella, A. S. Tayeb, et al., Investigation on new metaheuristic algorithms for solving dynamic combined economic environmental dispatch problems, Sustainability, 14 (2022), 5554. https://doi.org/10.3390/su14095554 doi: 10.3390/su14095554
    [88] B. Larouci, A. Sitayeb, H. Boudjella, A. N. E. I. Ayad, Cuckoo search algorithm to solve the problem of economic emission dispatch with the incorporation of FACTS devices under the valve-point loading effect, Facta Univ. Ser. Electron. Energ. , 34 (2021), 569–588. https://doi.org/10.2298/FUEE2104569B doi: 10.2298/FUEE2104569B
    [89] M. Shirkhani, J. Tavoosi, S. Danyali, A. K. Sarvenoee, A. Abdali, A. Mohammadzadeh, et al., A review on microgrid decentralized energy/voltage control structures and methods, Energy Rep. , 10 (2023), 368–380. https://doi.org/10.1016/j.egyr.2023.06.022 doi: 10.1016/j.egyr.2023.06.022
    [90] B. Dey, S. K. Roy, B. Bhattacharyya, Solving multi-objective economic emission dispatch of a renewable-integrated microgrid using latest bio-inspired algorithms, Eng. Sci. Technol. Int. J. , 22 (2019), 55–66. https://doi.org/10.1016/j.jestch.2018.10.001 doi: 10.1016/j.jestch.2018.10.001
    [91] S. L. Gbadamosi, N. I. Nwulu, Optimal power dispatch and reliability analysis of hybrid CHP-PV-wind systems in farming applications, Sustainability, 12 (2020), 8199. https://doi.org/10.3390/su12198199 doi: 10.3390/su12198199
    [92] B. Larouci, H. Boudjella, A. Si Tayeb, A. N. E. I. Ayad, Dynamic economic load dispatch problems in microgrid containing renewable energy sources based on tunicate swarm algorithm, Eng. Rev. , 44 (2024), 37–50. https://doi.org/10.30765/er.2402 doi: 10.30765/er.2402
    [93] N. Augustine, S. Suresh, P. Moghe, K. Sheikh, Economic dispatch for a microgrid considering renewable energy cost functions, In: Proceedings of the 2012 IEEE PES Innovative Smart Grid Technologies (ISGT), 2012, 1–7. https://doi.org/10.1109/ISGT.2012.6175747
    [94] R. T. Marler, J. S. Arora, The weighted sum method for multi-objective optimization: New insights, Struct. Multidiscip. Optim. , 41 (2010), 853–862. https://doi.org/10.1007/s00158-009-0460-7 doi: 10.1007/s00158-009-0460-7
    [95] W. Zhao, L. Wang, Z. Zhang, Atom search optimization and its application to solve a hydrogeologic parameter estimation problem, Knowl. -Based Syst. , 163 (2019), 283–304. https://doi.org/10.1016/j.knosys.2018.08.030 doi: 10.1016/j.knosys.2018.08.030
    [96] S. Mirjalili, A. Lewis, A. S. Sadiq, Autonomous particles groups for particle swarm optimization, Arab. J. Sci. Eng. , 39 (2014), 4683–4697. https://doi.org/10.1007/s13369-014-1156-x doi: 10.1007/s13369-014-1156-x
    [97] H. Nourianfar, H. Abdi, Solving power systems optimization problems in the presence of renewable energy sources using modified exchange market algorithm, Sustain. Energy Grids Netw. , 26 (2021), 100449. https://doi.org/10.1016/j.segan.2021.100449 doi: 10.1016/j.segan.2021.100449
    [98] A. Faramarzi, M. Heidarinejad, B. Stephens, S. Mirjalili, Equilibrium optimizer: A novel optimization algorithm, Knowl. -Based Syst. , 191 (2020), 105190. https://doi.org/10.1016/j.knosys.2019.105190 doi: 10.1016/j.knosys.2019.105190
    [99] A. M. Eltamaly, M. A. Alotaibi, Novel hybrid Mexican axolotl optimization with fuzzy logic for maximum power point tracker of partially shaded photovoltaic systems, Energies, 17 (2024), 2445. https://doi.org/10.3390/en17112445 doi: 10.3390/en17112445
    [100] A. Haghrah, M. Nazari-Heris, B. Mohammadi-Ivatloo, Solving combined heat and power economic dispatch problem using real-coded genetic algorithm with improved Mühlenbein mutation, Appl. Therm. Eng. , 99 (2016), 465–475. https://doi.org/10.1016/j.applthermaleng.2015.12.136 doi: 10.1016/j.applthermaleng.2015.12.136
    [101] E. Khorram, M. Jaberipour, Harmony search algorithm for solving combined heat and power economic dispatch problems, Energy Convers. Manag. , 52 (2011), 1550–1554. https://doi.org/10.1016/j.enconman.2010.10.017 doi: 10.1016/j.enconman.2010.10.017
    [102] S. H. Huang, P. C. Lin, A harmony-genetic-based heuristic approach toward economic dispatching combined heat and power, Int. J. Electr. Power Energy Syst. , 53 (2013), 482–487. https://doi.org/10.1016/j.ijepes.2013.05.027 doi: 10.1016/j.ijepes.2013.05.027
    [103] B. Mohammadi-Ivatloo, M. Moradi-Dalvand, A. Rabiee, Combined heat and power economic dispatch problem solution using particle swarm optimization with time-varying acceleration coefficients, Electr. Power Syst. Res. , 95 (2013), 9–18. https://doi.org/10.1016/j.epsr.2012.08.005 doi: 10.1016/j.epsr.2012.08.005
    [104] A. M. Shaheen, A. R. Ginidi, R. A. El-Sehiemy, S. S. M. Ghoneim, Economic power and heat dispatch in cogeneration energy systems using manta ray foraging optimizer, IEEE Access, 8 (2020), 208281–208295. https://doi.org/10.1109/ACCESS.2020.3038740 doi: 10.1109/ACCESS.2020.3038740
    [105] N. Jayakumar, S. Subramanian, S. Ganesan, E. B. Elanchezhian, Grey wolf optimization for combined heat and power dispatch with cogeneration systems, Int. J. Electr. Power Energy Syst. , 74 (2016), 252–264. https://doi.org/10.1016/j.ijepes.2015.07.031 doi: 10.1016/j.ijepes.2015.07.031
    [106] J. Jurasz, M. Guezgouz, P. E. Campana, A. Kies, On the impact of load profile data on the optimization results of off-grid energy systems, Renew. Sust. Energ. Rev. , 159 (2022), 112199. https://doi.org/10.1016/j.rser.2022.112199 doi: 10.1016/j.rser.2022.112199
    [107] Q. Meng, Y. Gao, Y. He, S. Hussain, J. Lu, Y. Chen, et al., PowerMistral: A data-efficient wind power forecasting framework leveraging pre-trained large language models, Appl. Energy, 411 (2026), 127625. https://doi.org/10.1016/j.apenergy.2026.127625 doi: 10.1016/j.apenergy.2026.127625
  • Reader Comments
  • © 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
AIMS Mathematics
1.8 3.6

Metrics

Article views(2) PDF downloads(0) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Figures(18)  /  Tables(17)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog