Profit Maximization for Generating Companies Using Chaotic Whale Optimization with Inertia Weight

Authors

DOI:

https://doi.org/10.64470/elene.2026.22

Keywords:

Chaotic Whale Optimization Algorithm, Electricity Market Optimization, Inertia Weight, Metaheuristic Algorithms, Profit Maximization

Abstract

Optimization of power generation scheduling is critical for generating companies (GENCOs) operating in deregulated electricity markets, where maximizing profit under operational constraints is challenging. Traditional metaheuristic algorithms often suffer from premature convergence and poor exploration-exploitation balance. Here we propose an improved Whale Optimization Algorithm incorporating chaotic mapping and inertia weight (CWOA-IW) to enhance population diversity and convergence behaviour. The algorithm is applied to the profit maximization problem of GENCOs, considering market prices and system constraints. Validation on 23 benchmark functions and three power system test cases (3-unit 10-bus, IEEE 39-bus, IEEE 118-bus) demonstrates superior accuracy, stability, and faster convergence compared to standard WOA, Grey Wolf Optimizer, and Particle Swarm Optimization. The results indicate that CWOA-IW provides a robust and scalable optimization framework, offering practical benefits for GENCOs in competitive electricity markets.

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Author Biographies

  • Kofi Afum Danso, Department of Electrical and Electronic Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

    Research and Teaching Assistant, Department of Electrical and Electronic Engineering

  • Peter Asigri, Department of Electrical and Electronic Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

    Lecturer, Department of Electrical and Electronic Engineering

  • Nicholas Kwesi Prah II, Department of Electrical and Electronic Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

    Lecturer, Department of Electrical and Electronic Engineering

  • Daniel Kwegyir, Department of Electrical and Electronic Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

    Lecturer, Department of Electrical and Electronic Engineering

  • Richeson Akwanfo, Department of Electrical and Electronic Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

    Student, Department of Electrical and Electronic Engineering

  • Mawuli Kweku Afenu, Department of Electrical and Electronic Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

    Student, Department of Electrical and Electronic Engineering

  • Nana Ama Abaka Mensah, Department of Electrical and Electronic Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

    Student, Department of Electrical and Electronic Engineering

  • Adwoa Darkoa Addi-Oppey, Department of Electrical and Electronic Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

    Student, Department of Electrical and Electronic Engineering

  • Daniel Opoku, Department of Electrical and Electronic Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

    Senior Lecturer, Department of Electrical and Electronic Engineering

References

Abdel-Basset, M., Abdel-Fatah, L., & Sangaiah, A. K. (2018). Metaheuristic algorithms: A comprehensive review. In Computational Intelligence for Multimedia Big Data on the Cloud with Engineering Applications (pp. 185–231). Elsevier. https://doi.org/10.1016/B978-0-12-813314-9.00010-4

Abdi, H. (2021). Profit-based unit commitment problem: A review of models, methods, challenges, and future directions. In Renewable and Sustainable Energy Reviews (Vol. 138). Elsevier Ltd. https://doi.org/10.1016/j.rser.2020.110504

Abdollahzadeh, B., Gharehchopogh, F. S., & Mirjalili, S. (2021). African vultures optimization algorithm: A new nature-inspired metaheuristic algorithm for global optimization problems. Computers and Industrial Engineering, 158(May), 107408. https://doi.org/10.1016/j.cie.2021.107408

Ayyarao, T. S. L. V., Ramakrishna, N. S. S., Elavarasan, R. M., Polumahanthi, N., Rambabu, M., Saini, G., Khan, B., & Alatas, B. (2022). War Strategy Optimization Algorithm: A New Effective Metaheuristic Algorithm for Global Optimization. IEEE Access, 10, 25073–25105.

Benaissa, B., Kobayashi, M., Al Ali, M., Khatir, T., & El Amine Elaissaoui Elmeliani, M. (2024). Metaheuristic optimization algorithms: An overview. HCMCOUJS-Advances in Computational Structures, 14(1), 34–62. https://doi.org/10.46223/HCMCOUJS

Cao, D., Xu, Y., Yang, Z., Dong, H., & Li, X. (2023). An enhanced whale optimization algorithm with improved dynamic opposite learning and adaptive inertia weight strategy. Complex and Intelligent Systems, 9(1), 767–795. https://doi.org/10.1007/s40747-022-00827-1

Deepa, R., & Venkataraman, R. (2021). Enhancing Whale Optimization Algorithm with Levy Flight for coverage optimization in wireless sensor networks. Computers and Electrical Engineering, 94. https://doi.org/10.1016/j.compeleceng.2021.107359

Dhaliwal, J. S., & Dhillon, J. S. (2019). Profit based unit commitment using memetic binary differential evolution algorithm. Applied Soft Computing Journal, 81. https://doi.org/10.1016/j.asoc.2019.105502

Dhaliwal, J. S., & Dhillon, J. S. (2021). A synergy of binary differential evolution and binary local search optimizer to solve multi-objective profit based unit commitment problem. Applied Soft Computing, 107. https://doi.org/10.1016/j.asoc.2021.107387

Durga, P., & Gayathri, K. (2024). Chaotic Sea-Horse Optimizer for Profit-Based Unit Commitment to Maximize the Profit of GENCOs in Restructured Power System Considering Reserve Allocation. Indian Journal Of Science And Technology, 17(39), 4048–4057. https://doi.org/10.17485/IJST/v17i39.2795

Gao, P., Ding, H., & Xu, R. (2021). Whale Optimization Algorithm Based on Skew Tent Chaotic Map and Nonlinear Strategy. Academic Journal of Computing & Information Science, 4(5). https://doi.org/10.25236/ajcis.2021.040513

Ghadi, M. J., Itami Karin, A., Baghramian, A., & Hosseini Imani, M. (2016). Optimal power scheduling of thermal units considering emission constraint for GENCOs’ profit maximization. International Journal of Electrical Power and Energy Systems, 82, 124–135. https://doi.org/10.1016/j.ijepes.2016.03.011

Gharehchopogh, F. S., & Gholizadeh, H. (2019). A comprehensive survey: Whale Optimization Algorithm and its applications. Swarm and Evolutionary Computation, 48, 1–24. https://doi.org/10.1016/j.swevo.2019.03.004

Gilvaei, M. N., Imani, M. H., Ghadi, M. J., Li, L., & Golrang, A. (2021). Profit-based unit commitment for a GENCO equipped with compressed air energy storage and concentrating solar power units. Energies, 14(3). https://doi.org/10.3390/en14030576

Illinois Institute of Technology. (2015). Index of /Data. http://motor.ece.iit.edu/data/

Kaveh, A., & Ghazaan, M. I. (2017). Enhanced whale optimization algorithm for sizing optimization of skeletal structures. Mechanics Based Design of Structures and Machines, 45(3). https://doi.org/10.1080/15397734.2016.1213639

Kennedy, J., Eberhart, R., & gov, bls. (1995). Particle Swarm Optimization.

Krishna, P. V. R., & Sao, S. (2016). An Improved TLBO Algorithm to Solve Profit Based Unit Commitment Problem under Deregulated Environment. Procedia Technology, 25, 652–659. https://doi.org/10.1016/j.protcy.2016.08.157

Kumar, V., Naresh, R., & Sharma, V. (2023). Profit based unit commitment problem solution using metaheuristic optimisation approach. International Journal of Systems Science: Operations and Logistics, 10(1). https://doi.org/10.1080/23302674.2022.2037026

Lin, L., & Gen, M. (2009). Auto-tuning strategy for evolutionary algorithms: Balancing between exploration and exploitation. Soft Computing, 13(2), 157–168. https://doi.org/10.1007/s00500-008-0303-2

Liu, J., Shi, J., Hao, F., & Dai, M. (2023). A novel enhanced global exploration whale optimization algorithm based on Lévy flights and judgment mechanism for global continuous optimization problems. Engineering with Computers, 39(4). https://doi.org/10.1007/s00366-022-01638-1

Mirjalili, S., & Lewis, A. (2016). The Whale Optimization Algorithm. Advances in Engineering Software, 95, 51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008

Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey Wolf Optimizer. Advances in Engineering Software, 69, 46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

Mohammed, H. M., Umar, S. U., & Rashid, T. A. (2019). A Systematic and Meta-Analysis Survey of Whale Optimization Algorithm. In Computational Intelligence and Neuroscience (Vol. 2019). https://doi.org/10.1155/2019/8718571

Nadimi-shahraki, M. H., Fatahi, A., Zamani, H., Mirjalili, S., & Oliva, D. (2022). Hybridizing of Whale and Moth-Flame Optimization Algorithms to Solve Diverse Scales of Optimal Power Flow Problem. Electronics (Switzerland), 11(5). https://doi.org/10.3390/electronics11050831

Nadimi-Shahraki, M. H., Zamani, H., & Mirjalili, S. (2022). Enhanced whale optimization algorithm for medical feature selection: A COVID-19 case study. Computers in Biology and Medicine, 148. https://doi.org/10.1016/j.compbiomed.2022.105858

Nasiri, J., & Khiyabani, F. M. (2018). A whale optimization algorithm (WOA) approach for clustering. Cogent Mathematics & Statistics, 5(1). https://doi.org/10.1080/25742558.2018.1483565

Pham, Q. V., Mirjalili, S., Kumar, N., Alazab, M., & Hwang, W. J. (2020). Whale Optimization Algorithm with Applications to Resource Allocation in Wireless Networks. IEEE Transactions on Vehicular Technology, 69(4). https://doi.org/10.1109/TVT.2020.2973294

Putz, D., Schwabeneder, D., Auer, H., & Fina, B. (2021). A comparison between mixed-integer linear programming and dynamic programming with state prediction as novelty for solving unit commitment. International Journal of Electrical Power and Energy Systems, 125(June 2020), 106426. https://doi.org/10.1016/j.ijepes.2020.106426

Qu, S. Z., Liu, H., Xu, Y., Wang, L., Liu, Y., Zhang, L., Song, J., & Li, Z. (2024). Application of spiral enhanced whale optimization algorithm in solving optimization problems. Scientific Reports, 14(1), 24534. https://doi.org/10.1038/s41598-024-74881-9

Ravichandran, S., & Subramanian, M. (2020). Profit maximization of GENCO’s using an elephant herding optimization algorithm. Studies in Informatics and Control, 29(1), 131–140. https://doi.org/10.24846/v29i1y202013

Sahoo, A., & Hota, P. K. (2019). Moth Flame Optimization Algorithm based Optimal Strategic Bidding in Deregulated Electricity Market. IEEE Region 10 Annual International Conference, Proceedings/TENCON, 2019-October, 2105–2110. https://doi.org/10.1109/TENCON.2019.8929290

Senthilvadivu, A., Gayathri, K., & Asokan, K. (2018). Exchange Market algorithm based Profit Based Unit Commitment for GENCOs Considering Environmental Emissions. In International Journal of Applied Engineering Research (Vol. 13).

Shehab, M., Sihwail, R., Daoud, M., Al-Mimi, H., & Abualigah, L. (2024). Nature-Inspired Metaheuristic Algorithms: A Comprehensive Review. International Arab Journal of Information Technology, 21(5), 815–831. https://doi.org/10.34028/iajit/21/5/4

Shukla, A., Lal, V. N., & Singh, S. N. (2015). Profit-based unit commitment problem using PSO with modified dynamic programming. 2015 18th International Conference on Intelligent System Application to Power Systems, ISAP 2015. https://doi.org/10.1109/ISAP.2015.7325550

Sudhakar, A. V. V., Karri, C., & Jaya Laxmi, A. (2017). Profit based unit commitment for GENCOs using Lagrange Relaxation–Differential Evolution. Engineering Science and Technology, an International Journal, 20(2), 738–747. https://doi.org/10.1016/j.jestch.2016.11.012

Sun, Y., Yang, T., & Liu, Z. (2019). A whale optimization algorithm based on quadratic interpolation for high-dimensional global optimization problems. Applied Soft Computing Journal, 85. https://doi.org/10.1016/j.asoc.2019.105744

Tomar, V., Bansal, M., & Singh, P. (2023). Metaheuristic Algorithms for Optimization: A Brief Review. Engineering Proceedings, 59(1). https://doi.org/10.3390/engproc2023059238

Wang, J., Bei, J., Song, H., Zhang, H., & Zhang, P. (2023). A whale optimization algorithm with combined mutation and removing similarity for global optimization and multilevel thresholding image segmentation [Formula presented]. Applied Soft Computing, 137. https://doi.org/10.1016/j.asoc.2023.110130

Wei, J., Gu, Y., Yan, Y., Li, Z., Lu, B., Pan, S., & Cheong, N. (2025). LSEWOA: An Enhanced Whale Optimization Algorithm with Multi-Strategy for Numerical and Engineering Design Optimization Problems. Sensors, 25(7). https://doi.org/10.3390/s25072054

Xue, J., & Shen, B. (2023). Dung beetle optimizer: a new meta-heuristic algorithm for global optimization. In Journal of Supercomputing (Vol. 79, Issue 7). https://doi.org/10.1007/s11227-022-04959-6

Zhou, Y., & Hao, Z. (2025). Multi-Strategy Improved Whale Optimization Algorithm and Its Engineering Applications. Biomimetics, 10(1). https://doi.org/10.3390/biomimetics10010047

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Published

2026-01-23

Data Availability Statement

The data used are publicly available datasets obtained from published literature

Issue

Vol. 5 No. 1 (2026): April 30

Section

Research Articles

License

Copyright (c) 2025 Kofi Afum Danso, Peter Asigri, Nicholas Kwesi Prah II, Daniel Kwegyir, Richeson Akwanfo, Mawuli Kweku Afenu, Nana Ama Abaka Mensah, Adwoa Darkoa Addi-Oppey, Daniel Opoku

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How to Cite

Danso, K. A. ., Asigri, P., Prah II, N. K. ., Kwegyir, D., Akwanfo, R., Afenu, M. K., Mensah, N. A. A., Addi-Oppey, A. D., & Opoku, D. (2026). Profit Maximization for Generating Companies Using Chaotic Whale Optimization with Inertia Weight. Electrical Engineering and Energy, 5(1), 72-99. https://doi.org/10.64470/elene.2026.22