A new metaheuristic called the Walrus Optimizer (WO) is inspired by the ways in which walruses move, roost, feed, spawn, gather, and flee in response to important cues (safety and danger signals). In this work, the WO was used to address the economic load dispatch (ELD) issue, which is one of the essential parts of a power system. One type of ELD was designed to reduce fuel consumption expenses. A variety of methodologies were used to compare the WO's performance in order to determine its reliability. These methods included rime-ice algorithm (RIME), moth search algorithm (MSA), the snow ablation algorithm (SAO), and chimp optimization algorithm (ChOA) for the identical case study. We employed six scenarios: Six generators operating at two loads of 700 and 1000 MW each were employed in the first two cases for the ELD problem. For the ELD problem, the second two scenarios involved ten generators operating at two loads of 2000 MW and 1000 MW. Twenty generators operating at a 3000 MW load were the five cases for the ELD issue. Thirty generators operating at a 5000 MW load were the six cases for the ELD issue. The power mismatch factor was the main cause of ELD problems. The ideal value of this component should be close to zero. Using the WO approach, the ideal power mismatch values of 4.1922E−13 and 4.5119E−13 were found for six generator units at demand loads of 700 MW and 1000 MW, respectively. Using metrics for the minimum, mean, maximum, and standard deviation of fitness function, the procedures were evaluated over thirty separate runs. The WO outperformed all other algorithms, as seen by the results generated for the six ELD case studies.
Citation: Mokhtar Said, Essam H. Houssein, Eman Abdullah Aldakheel, Doaa Sami Khafaga, Alaa A. K. Ismaeel. Performance of the Walrus Optimizer for solving an economic load dispatch problem[J]. AIMS Mathematics, 2024, 9(4): 10095-10120. doi: 10.3934/math.2024494
A new metaheuristic called the Walrus Optimizer (WO) is inspired by the ways in which walruses move, roost, feed, spawn, gather, and flee in response to important cues (safety and danger signals). In this work, the WO was used to address the economic load dispatch (ELD) issue, which is one of the essential parts of a power system. One type of ELD was designed to reduce fuel consumption expenses. A variety of methodologies were used to compare the WO's performance in order to determine its reliability. These methods included rime-ice algorithm (RIME), moth search algorithm (MSA), the snow ablation algorithm (SAO), and chimp optimization algorithm (ChOA) for the identical case study. We employed six scenarios: Six generators operating at two loads of 700 and 1000 MW each were employed in the first two cases for the ELD problem. For the ELD problem, the second two scenarios involved ten generators operating at two loads of 2000 MW and 1000 MW. Twenty generators operating at a 3000 MW load were the five cases for the ELD issue. Thirty generators operating at a 5000 MW load were the six cases for the ELD issue. The power mismatch factor was the main cause of ELD problems. The ideal value of this component should be close to zero. Using the WO approach, the ideal power mismatch values of 4.1922E−13 and 4.5119E−13 were found for six generator units at demand loads of 700 MW and 1000 MW, respectively. Using metrics for the minimum, mean, maximum, and standard deviation of fitness function, the procedures were evaluated over thirty separate runs. The WO outperformed all other algorithms, as seen by the results generated for the six ELD case studies.
| [1] | W. K. Hao, Y. P. Li, J. S. Wang, Q. Zhu, Solving economic load dispatch problem of power system based on differential evolution algorithm with different mutation strategies, IAENG Int. J. Comput. Sci., 49 (2022), 156–165. |
| [2] |
N. Singh, T. Chakrabarti, P. Chakrabarti, M. Margala, A. Gupta, S. P. Praveen, et al., Novel heuristic optimization technique to solve economic load dispatch and economic emission load dispatch problems, Electronics, 12 (2023), 2921. https://doi.org/10.3390/electronics12132921 doi: 10.3390/electronics12132921
|
| [3] |
G. Abbas, I. A. Khan, N. Ashraf, M. T. Raza, M. Rashad, R. Muzzammel, On employing a constrained nonlinear optimizer to constrained economic dispatch problems, Sustainability, 15 (2023), 9924. https://doi.org/10.3390/su15139924 doi: 10.3390/su15139924
|
| [4] |
D. S. AbdElminaam, E. H. Houssein, M. Said, D. Oliva, A. Nabil, An efficient heap-based optimizer for parameters identification of modified photovoltaic models, Ain Shams Eng. J., 13 (2022), 101728. https://doi.org/10.1016/j.asej.2022.101728 doi: 10.1016/j.asej.2022.101728
|
| [5] |
A. A. K. Ismaeel, E. H. Houssein, D. Oliva, M. Said, Gradient-based optimizer for parameter extraction in photovoltaic models, IEEE Access, 9 (2021), 13403–13416. https://doi.org/10.1109/ACCESS.2021.3052153 doi: 10.1109/ACCESS.2021.3052153
|
| [6] |
E. H. Houssein, S. Deb, D. Oliva, H. Rezk, H. Alhumade, M. Said, Performance of gradient-based optimizer on charging station placement problem, Mathematics, 9 (2021), 2821. https://doi.org/10.3390/math9212821 doi: 10.3390/math9212821
|
| [7] |
D. S. Abdelminaam, M. Said, E. H. Houssein, Turbulent flow of water-based optimization using new objective function for parameter extraction of six photovoltaic models, IEEE Access, 9 (2021), 35382–35398. https://doi.org/10.1109/ACCESS.2021.3061529 doi: 10.1109/ACCESS.2021.3061529
|
| [8] |
M. Said, E. H. Houssein, S. Deb, A. A. Alhussan, R. M. Ghoniem, A novel gradient-based optimizer for solving unit commitment problem, IEEE Access, 10 (2022), 18081–18092. https://doi.org/10.1109/ACCESS.2022.3150857 doi: 10.1109/ACCESS.2022.3150857
|
| [9] |
A. A. K. Ismaeel, E. H. Houssein, D. S. Khafaga, E. A. Aldakheel, A. S. AbdElrazek, M. Said, Performance of osprey optimization algorithm for solving economic load dispatch problem, Mathematics, 11 (2023), 4107. https://doi.org/10.3390/math11194107 doi: 10.3390/math11194107
|
| [10] |
A. Bhattacharya, P. K. Chattopadhyay, Biogeography-based optimization for different economic load dispatch problems, IEEE T. Power Syst., 25 (2010), 1064–1077. https://doi.org/10.1109/TPWRS.2009.2034525 doi: 10.1109/TPWRS.2009.2034525
|
| [11] | G. L. Andrade, C. Schepke, N. Lucca, J. P. J. Neto, Modified differential evolution algorithm applied to economic load dispatch problems, In: Computational science and its applications—ICCSA 2023, 2023. https://doi.org/10.1007/978-3-031-36805-9_2 |
| [12] |
M. Said, E. H. Houssein, S. Deb, R. M. Ghoniem, A. G. Elsayed, Economic load dispatch problem based on search and rescue optimization algorithm, IEEE Access, 10 (2022), 47109–47123. https://doi.org/10.1109/ACCESS.2022.3168653 doi: 10.1109/ACCESS.2022.3168653
|
| [13] |
M. A. Al-Betar, M. A. Awadallah, S. N. Makhadmeh, I. A. Doush, R. A. Zitar, S. Alshathri, et al., A hybrid Harris Hawks optimizer for economic load dispatch problems, Alex. Eng. J., 64 (2023), 365–389. https://doi.org/10.1016/j.aej.2022.09.010 doi: 10.1016/j.aej.2022.09.010
|
| [14] | A. Hazra, S. Das, A. Laddha, M. Basu, Economic power generation strategy for wind integrated large power network using heat transfer search algorithm, J. Inst. Eng. Ser. B, 101 (2020), 15–21. https://link.springer.com/article/10.1007/s40031-020-00427-y |
| [15] |
G. Xiong, D. Shi, X. Duan, Multi-strategy ensemble biogeography based optimization for economic dispatch problems. Appl. Energy, 111 (2013), 801–811. https://doi.org/10.1016/j.apenergy.2013.04.095 doi: 10.1016/j.apenergy.2013.04.095
|
| [16] | M. A. Al-Betar, M. A. Awadallah, R. A. Zitar, K. Assaleh, Economic load dispatch using memetic sine cosine algorithm, J. Ambient. Intell. Humaniz. Comput., 14 (2022), 11685–11713. https://link.springer.com/article/10.1007/s12652-022-03731-1 |
| [17] |
A. S. Alghamdi, Greedy sine-cosine non-hierarchical grey wolf optimizer for solving non-convex economic load dispatch problems, Energies, 15 (2022), 3904. https://doi.org/10.3390/en15113904 doi: 10.3390/en15113904
|
| [18] |
T. P. Van, V. Snasel, T. T. Nguyen, Antlion optimization algorithm for optimal non-smooth economic load dispatch, Int. J. Elec. Comput. Eng., 10 (2020), 1187–1199. http://doi.org/10.11591/ijece.v10i2.pp1187-1199 doi: 10.11591/ijece.v10i2.pp1187-1199
|
| [19] |
W. T. Elsayed, E. F. El-Saadany, A fully decentralized approach for solving the economic dispatch problem, IEEE T. Power Syst., 30 (2015), 2179–2189. https://doi.org/10.1109/TPWRS.2014.2360369 doi: 10.1109/TPWRS.2014.2360369
|
| [20] |
N. Ghorbani, E. Babaei, Exchange market algorithm for economic load dispatch, Int. J. Elec. Power Energy Syst., 75 (2016), 19–27. https://doi.org/10.1016/j.ijepes.2015.08.013 doi: 10.1016/j.ijepes.2015.08.013
|
| [21] |
F. Mohammadi, H. Abdi, A modified crow search algorithm (MCSA) for solving economic load dispatch problem, Appl. Soft Comput., 71 (2018), 51–65. https://doi.org/10.1016/j.asoc.2018.06.040 doi: 10.1016/j.asoc.2018.06.040
|
| [22] |
T. Jayabarathi, T. Raghunathan, B. R. Adarsh, P. N. Suganthan, Economic dispatch using hybrid grey wolf optimizer, Energy, 111 (2016), 630–641. https://doi.org/10.1016/j.energy.2016.05.105 doi: 10.1016/j.energy.2016.05.105
|
| [23] |
D. C. Secui, A modified symbiotic organisms search algorithm for large scale economic dispatch problem with valve-point effects, Energy, 113 (2016), 366–384. https://doi.org/10.1016/j.energy.2016.07.056 doi: 10.1016/j.energy.2016.07.056
|
| [24] |
A. A. Elsakaan, R. A. El-Sehiemy, S. S. Kaddah, M. I. Elsaid, An enhanced moth-flame optimizer for solving non-smooth economic dispatch problems with emissions, Energy, 157 (2018), 1063–1078. https://doi.org/10.1016/j.energy.2018.06.088 doi: 10.1016/j.energy.2018.06.088
|
| [25] |
T. T. Nguyen, D. N. Vo, The application of one rank cuckoo search algorithm for solving economic load dispatch problems, Appl. Soft Comput., 37 (2015), 763–773. https://doi.org/10.1016/j.asoc.2015.09.010 doi: 10.1016/j.asoc.2015.09.010
|
| [26] |
P. Zakian, A. Kaveh, Economic dispatch of power systems using an adaptive charged system search algorithm, Appl. Soft Comput., 73 (2018), 607–622. https://doi.org/10.1016/j.asoc.2018.09.008 doi: 10.1016/j.asoc.2018.09.008
|
| [27] |
S. H. A. Kaboli, A. K. Alqallaf, Solving non-convex economic load dispatch problem via artificial cooperative search algorithm, Expert Syst. Appl., 128 (2019), 14–27. https://doi.org/10.1016/j.eswa.2019.02.002 doi: 10.1016/j.eswa.2019.02.002
|
| [28] |
S. Cui, Y. W, Wang, X. Lin, X. K. Liu, Distributed auction optimization algorithm for the nonconvex economic dispatch problem based on the gossip communication mechanism, Int. J. Elec. Power Energy Syst., 95 (2018), 417–426. https://doi.org/10.1016/j.ijepes.2017.09.012 doi: 10.1016/j.ijepes.2017.09.012
|
| [29] |
K. Kapelinski, J. P. J. Neto, E. M. dos Santos, Firefly Algorithm with non-homogeneous population: A case study in economic load dispatch problem., J. Oper. Res. Soc., 72 (2021), 519–534. https://doi.org/10.1080/01605682.2019.1700184 doi: 10.1080/01605682.2019.1700184
|
| [30] |
A. Kaur, L. Singh, J. S. Dhillon, Modified krill herd algorithm for constrained economic load dispatch problem, Int. J. Ambient Energy, 43 (2022), 4332–4342. https://doi.org/10.1080/01430750.2021.1888798 doi: 10.1080/01430750.2021.1888798
|
| [31] |
R. Ramalingam, D. Karunanidy, S. S. Alshamrani, M. Rashid, S. Mathumohan, A. Dumka, Oppositional pigeon-inspired optimizer for solving the non-convex economic load dispatch problem in power systems, Mathematics, 10 (2022), 3315. https://doi.org/10.3390/math10183315 doi: 10.3390/math10183315
|
| [32] |
M. F. Tabassum, M. Saeed, N. A. Chaudhry, J. Ali, M. Farman, S. Akram, Evolutionary simplex adaptive HookeJeeves algorithm for economic load dispatch problem considering valve point loading effects., Ain Shams Eng. J., 12 (2021), 1001–1015. https://doi.org/10.1016/j.asej.2020.04.006 doi: 10.1016/j.asej.2020.04.006
|
| [33] |
S. Banerjee, D. Maity, C. K. Chanda, Teaching learning based optimization for economic load dispatch problem considering valve point loading effect. Int. J. Elec. Power Energy Syst., 73 (2015), 456–464. https://doi.org/10.1016/j.ijepes.2015.05.036 doi: 10.1016/j.ijepes.2015.05.036
|
| [34] |
H. Shayeghi, A. Ghasemi, A modified artificial bee colony based on chaos theory for solving non-convex emission/economic dispatch., Energy. Convers. Manag., 79 (2014), 344–354. https://doi.org/10.1016/j.enconman.2013.12.028 doi: 10.1016/j.enconman.2013.12.028
|
| [35] |
B. K. Panigrahi, V. R. Pandi, Bacterial foraging optimisation: Nelder–Mead hybrid algorithm for economic load dispatch., IET Gener. Transm. Dis., 2 (2008), 556–565. https://doi.org/10.1049/iet-gtd:20070422 doi: 10.1049/iet-gtd:20070422
|
| [36] |
G. B inetti, A. Davoudi, D. Naso, B. Turchiano, F. L. Lewis, A distributed auction-based algorithm for the nonconvex economic dispatch problem, IEEE T. Ind. Inform., 10 (2014), 1124–1132. https://doi.org/10.1109/TⅡ.2013.2287807 doi: 10.1109/TⅡ.2013.2287807
|
| [37] |
S. Deb, E. H. Houssein, M. Said, D. S. Abdelminaam, Performance of turbulent flow of water optimization on economic load dispatch problem, IEEE Access, 9 (2021), 77882–77893. https://doi.org/10.1109/ACCESS.2021.3083531 doi: 10.1109/ACCESS.2021.3083531
|
| [38] |
M. Han, Z. Du, Y. K. Yuan, H. Zhu, Y. Li, Q. Yuan, Walrus optimizer: A novel nature-inspired metaheuristic algorithm., Expert Syst. Appl., 239 (2024), 122413. https://doi.org/10.1016/j.eswa.2023.122413 doi: 10.1016/j.eswa.2023.122413
|
| [39] |
G. G. Wang, Moth search algorithm: A bio-inspired metaheuristic algorithm for global optimization problems, Memetic Comp., 10 (2018), 151–164. https://doi.org/10.1007/s12293-016-0212-3 doi: 10.1007/s12293-016-0212-3
|
| [40] |
L. Deng, S. Liu, Snow ablation optimization: A novel metaheuristic technique for numerical optimization and engineering design, Expert Syst. Appl., 225 (2023), 120069. https://doi.org/10.1016/j.eswa.2023.120069 doi: 10.1016/j.eswa.2023.120069
|
| [41] |
M. Khishe, M. R. Mosavi, Chimp optimization algorithm, Expert Syst. Appl., 149 (2020), 113338. https://doi.org/10.1016/j.eswa.2020.113338 doi: 10.1016/j.eswa.2020.113338
|
| [42] |
H. Su, D. Zhao, A. A. Heidari, L. Liu, X. Zhang, M. Mafarja, et al., RIME: A physics-based optimization, Neurocomputing, 532 (2023), 183–214. https://doi.org/10.1016/j.neucom.2023.02.010 doi: 10.1016/j.neucom.2023.02.010
|
| [43] |
M. Said, A. M. El-Rifaie, M. A. Tolba, E. H. Houssein, S. Deb, An efficient chameleon swarm algorithm for economic load dispatch problem, Mathematics, 9 (2021), 2770. https://doi.org/10.3390/math9212770 doi: 10.3390/math9212770
|
| [44] |
A. A. K. Ismaeel, E. H. Houssein, D. S. Khafaga, E. A. Aldakheel, A. S. AbdElrazek, M. Said, Performance of snow ablation optimization for solving optimum allocation of generator units., IEEE Access, 12 (2024), 17690–17707. https://doi.org/10.1109/ACCESS.2024.3357489 doi: 10.1109/ACCESS.2024.3357489
|
Figures(13) / Tables(19)
Mokhtar Said, Essam H. Houssein, Eman Abdullah Aldakheel, Doaa Sami Khafaga, Alaa A. K. Ismaeel. Performance of the Walrus Optimizer for solving an economic load dispatch problem[J]. AIMS Mathematics, 2024, 9(4): 10095-10120. doi: 10.3934/math.2024494
DownLoad: