Solving Economic Dispatch Problem Intelligent Metaheuristic Technique
DOI:
https://doi.org/10.71202/paper47Abstract
This paper proposes solving the Economic Dispatch (ED) problem under practical power system constraints using seven well-known metaheuristic algorithms including Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), Moth-Flame Optimization (MFO), Multi-Verse Optimizer (MVO), Whale Optimization Algorithm (WOA), Sine Cosine Algorithm (SCA), and Differential Evolution (DE). Each algorithm is tested on a MATLAB-based ED framework that includes ramp-rate limits, prohibited operating zones, and transmission losses. A normalized representation of generator outputs in [0,1] ensures a fair comparison, and a penalty mechanism enforces the power balance constraint. Results show that all algorithms can feasibly handle the ED constraints, though their performance varies widely. Differential Evolution (DE) demonstrates consistently high solution quality, achieving a best final cost of 15702.12 and the lowest standard deviation (3.39) across multiple runs. Particle Swarm Optimization (PSO) and Grey Wolf Optimizer (GWO) also converge rapidly and attain near-optimal costs, albeit with slightly higher variability. By contrast, Multi-Verse Optimizer (MVO) exhibits more pronounced fluctuations in some runs. While MFO, WOA, and SCA find strong solutions in some instances, they suffer moderate-to-high cost dispersion, reflecting sensitivity to initialization and parameter choices.
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Abdi, H., Fattahi, H., & Lumbreras, S. (2018). What metaheuristic solves the economic dispatch faster? A comparative case study. Electrical Engineering, 100(4), 2825-2837.
Marzbani, F., & Abdelfatah, A. (2024). Economic dispatch optimization strategies and problem formulation: A comprehensive review. Energies, 17(3), 550.
Urbanucci, L., & Testi, D. (2018). Optimal integrated sizing and operation of a CHP system with Monte Carlo risk analysis for long-term uncertainty in energy demands. Energy conversion and management, 157, 307-316.
Chauhan, G., Jain, A., & Verma, N. (2017, October). Solving economic dispatch problem using MiPower by lambda iteration method. In 2017 1st international conference on intelligent systems and information management (ICISIM) (pp. 95-99). IEEE.
Aurasopon, A., & Takeang, C. (2021). Multiple hybrid of lambda iteration and bee colony optimization method for solving economic dispatch problem. International Journal on Electrical Engineering and Informatics, 13(1), 57-72.
Turgut, O. E., Turgut, M. S., & Kırtepe, E. (2023). A systematic review of the emerging metaheuristic algorithms on solving complex optimization problems. Neural Computing and Applications, 35(19), 14275-14378.
Mirjalili, S., & Mirjalili, S. (2019). Genetic algorithm. Evolutionary algorithms and neural networks: Theory and applications, 43-55.
Wang, D., Tan, D., & Liu, L. (2018). Particle swarm optimization algorithm: an overview. Soft computing, 22(2), 387-408.
Eltaeib, T., & Mahmood, A. (2018). Differential evolution: A survey and analysis. Applied Sciences, 8(10), 1945.
Faris, H., Aljarah, I., Al-Betar, M. A., & Mirjalili, S. (2018). Grey wolf optimizer: a review of recent variants and applications. Neural computing and applications, 30, 413-435.
Shehab, M., Abualigah, L., Al Hamad, H., Alabool, H., Alshinwan, M., & Khasawneh, A. M. (2020). Moth–flame optimization algorithm: variants and applications. Neural Computing and Applications, 32(14), 9859-9884.
Nasiri, J., & Khiyabani, F. M. (2018). A whale optimization algorithm (WOA) approach for clustering. Cogent Mathematics & Statistics, 5(1), 1483565.
Aljarah, I., Mafarja, M., Heidari, A. A., Faris, H., & Mirjalili, S. (2020). Multi-verse optimizer: theory, literature review, and application in data clustering. Nature-inspired optimizers: theories, literature reviews and applications, 123-141.
Gabis, A. B., Meraihi, Y., Mirjalili, S., & Ramdane-Cherif, A. (2021). A comprehensive survey of sine cosine algorithm: variants and applications. Artificial Intelligence Review, 54(7), 5469-5540.
Makhadmeh, S. N., Al-Betar, M. A., Doush, I. A., Awadallah, M. A., Kassaymeh, S., Mirjalili, S., & Zitar, R. A. (2023). Recent advances in Grey Wolf Optimizer, its versions and applications. Ieee Access, 12, 22991-23028.
Verma, P., Alam, A., Sarwar, A., Tariq, M., Vahedi, H., Gupta, D., ... & Shah Noor Mohamed, A. (2021). Meta-heuristic optimization techniques used for maximum power point tracking in solar pv system. Electronics, 10(19), 2419.
Abualigah, L., Elaziz, M. A., Khasawneh, A. M., Alshinwan, M., Ibrahim, R. A., Al-Qaness, M. A., ... & Gandomi, A. H. (2022). Meta-heuristic optimization algorithms for solving real-world mechanical engineering design problems: a comprehensive survey, applications, comparative analysis, and results. Neural Computing and Applications, 1-30.
Abdel-Basset, M., Abdel-Fatah, L., & Sangaiah, A. K. (2018). Metaheuristic algorithms: A comprehensive review. Computational intelligence for multimedia big data on the cloud with engineering applications, 185-231.
He, L., Ishibuchi, H., Trivedi, A., Wang, H., Nan, Y., & Srinivasan, D. (2021). A survey of normalization methods in multiobjective evolutionary algorithms. IEEE Transactions on Evolutionary Computation, 25(6), 1028-1048.
Meidani, K., Mirjalili, S., & Farimani, A. B. (2022). Online metaheuristic algorithm selection. Expert Systems with Applications, 201, 117058.
Kumar, D. P., Sowmya, B. J., Kanavalli, A., Cornelio, V., Dsouza, J. P., Memon, W., & Prashanth, P. (2023). Building a hybridised meta-heuristic optimisation algorithm for efficient cluster analysis. International Journal of Business Intelligence and Data Mining, 22(1-2), 170-222.
Webb, R., Glimcher, P. W., & Louie, K. (2021). The normalization of consumer valuations: Context-dependent preferences from neurobiological constraints. Management Science, 67(1), 93-125.
Gerling, A., Ziekow, H., Hess, A., Schreier, U., Seiffer, C., & Abdeslam, D. O. (2022). Comparison of algorithms for error prediction in manufacturing with automl and a cost-based metric. Journal of Intelligent Manufacturing, 33(2), 555-573.
Mozaffari, A., Emami, M., & Fathi, A. (2019). A comprehensive investigation into the performance, robustness, scalability and convergence of chaos-enhanced evolutionary algorithms with boundary constraints. Artificial Intelligence Review, 52, 2319-2380.
A. J. Wood, B. F. Wollenberg, and G. B. Sheblé, Power Generation, Operation, and Control, 3rd ed., Hoboken, NJ, USA: Wiley, 2013.
Walters and G. B. Sheble, “Genetic Algorithm Solution of Economic Dispatch with Valve Point Loading,” IEEE Transactions on Power Systems, vol. 8, no. 3, pp. 1325–1332, 1993.
S. O. Orero and M. R. Irving, “Economic Dispatch of Generators with Prohibited Operating Zones: A Genetic Algorithm Approach,” IEE Proceedings - Generation, Transmission and Distribution, vol. 143, no. 6, pp. 529–534, 1997.
Z. L. Gaing, “Particle Swarm Optimization to Solving the Economic Dispatch Considering the Generator Constraints,” IEEE Transactions on Power Systems, vol. 18, no. 3, pp. 1187–1195, 2003.
Y. Shi and R. Eberhart, “A Modified Particle Swarm Optimizer,” in IEEE International Conference on Evolutionary Computation, pp. 69–73, 1998.
S. Mirjalili, S. M. Mirjalili, and A. Lewis, “Grey Wolf Optimizer,” Advances in Engineering Software, vol. 69, pp. 46–61, 2014.
S. Mirjalili, “Moth-Flame Optimization Algorithm: A Novel Nature-Inspired Heuristic Paradigm,” Knowledge-Based Systems, vol. 89, pp. 228–249, 2015.
S. Mirjalili, M. Mirjalili, and X. S. Yang, “Binary Multi-Verse Optimizer: A New Algorithm for Binary Problems,” Neural Computing and Applications, vol. 27, no. 6, pp. 1669–1694, 2016.
S. Mirjalili and A. Lewis, “The Whale Optimization Algorithm,” Advances in Engineering Software, vol. 95, pp. 51–67, 2016.
S. Mirjalili, “SCA: A Sine Cosine Algorithm for Solving Optimization Problems,” Knowledge-Based Systems, vol. 96, pp. 120–133, 2016.
R. Storn and K. Price, “Differential Evolution–A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces,” Journal of Global Optimization, vol. 11, no. 4, pp. 341–359, 1997.
L. S. Coelho and C. K. Chiang, “Solving Economic Load Dispatch Problems in Power Systems Using Chaotic and Gaussian Particle Swarm Optimization Approaches,” International Journal of Electrical Power & Energy Systems, vol. 29, no. 8, pp. 573–581, 2007.
L. S. Coelho and V. C. Mariani, “A Comprehensive Overview of High-Dimensional Optimization Problems Guided by the Differential Evolution Strategy,” Applied Computational Intelligence and Soft Computing, vol. 2007, Article ID 24357, 2007.
Boussaid, J. Lepagnot, and P. Siarry, “A Survey on Optimization Metaheuristics,” Information Sciences, vol. 237, pp. 82–117, 2013
