Enhanced Whale Optimizer: An Enhanced Approach Using Opposition Learning Solving PV maximum power point tracking problem

عباسی نیا, مینا; ملازاده, فرامرز

doi:10.48306/estm.2026.556791.1013

Enhanced Whale Optimizer: An Enhanced Approach Using Opposition Learning Solving PV maximum power point tracking problem

نوع مقاله : مقاله پژوهشی

نویسندگان

مینا عباسی نیا

فرامرز ملازاده

Engineering Department, Islamic Azad University branch Sirjan, Sirjan, Iran

10.48306/estm.2026.556791.1013

چکیده

This paper proposes an Enhanced Whale Optimizer (EWO), a variant of the recently introduced Whale Optimizer (WO), motivated by the cooperative and foraging behaviors of groups of Whales. Although the original WO achieves a good exploration–exploitation balance, it often gets trapped in premature convergence and reduces population diversity at later search stages. To overcome these limitations, two adaptive strategies are combined: Opposition-Based Learning (OBL) and the Golden-Sine Strategy (GSS). The OBL mechanism ensures diversity of the initial population and global exploration, and assures a more comprehensive exploration of the search domain. The GSS, conversely, adaptively balances exploration and exploitation, resulting in improved convergence and enhanced local optimization capabilities. Performance of the proposed EWO is also confirmed with the CEC-2019 benchmark suite and several difficult real-world engineering problems, such as economic load dispatch, microgrid energy management, and Traveling Salesman Problem (TSP). Comparative analyses with well-known algorithms such as Particle Swarm Optimization (PSO), Dwarf Mongoose Optimization Algorithm (DMO), and White Shark Optimizer (WO) confirm EWO's better accuracy, convergence rate, and stability. Statistical tests and boxplot visualization also confirm its stability and consistency. It is evidenced that EWO has smaller mean errors, lower standard deviations, and higher reliability across multiple problem areas, citing its strength as a strong and general-purpose optimization algorithm suitable for both benchmark and engineering problems.

کلیدواژه‌ها

Metaheuristics

Complex Optimization

Problems

Opposition-Based Learning

Golden-Sine Strategy

Enhanced Whale Optimize

موضوعات

Energy Systems

[1] Lartey, D., & Law, K. M. (2025). Artificial intelligence adoption in urban planning governance: A systematic review of advancements in decision-making, and policy making. Landscape and Urban Planning, 258, 105337.

[2] Wang, G., Lin, Z., Chen, Y., Ji, H., Chen, D., Zhang, H., ... & Yan, J. (2025). Ai-optimized decision-making in energy systems: Toward a decision-aware machine learning framework. Engineering.

[3] Jawad, Z. N., & János, V. B. (2025). A Comprehensive Review of AI-Enhanced Decision Making: An Empirical Analysis for Optimizing Medication Market Business. Machine Learning with Applications, 100676.

[4] Younis, A., & Dong, Z. (2024). Adaptive surrogate assisted multi-objective optimization approach for highly nonlinear and complex engineering design problems. Applied Soft Computing, 150, 111065.

[5] Daoud, M. S., Shehab, M., Al-Mimi, H. M., Abualigah, L., Zitar, R. A., & Shambour, M. K. Y. (2023). Gradient-based optimizer (GBO): a review, theory, variants, and applications. Archives of Computational Methods in Engineering, 30(4), 2431-2449.

[6] Shethiya, A. S. (2024). Smarter Systems: Applying Machine Learning to Complex, Real-Time Problem Solving. Integrated Journal of Science and Technology, 1(1).

[7] Sharifi, T., Mirsalim, M., Soleimanian Gharehchopogh, F., & Mirjalili, S. (2025). Cultural history optimization algorithm: a new human-inspired metaheuristic algorithm for engineering optimization problems. Neural Computing and Applications, 1-60.

[8] Kumari, M. (2025). A review on metaheuristic algorithms: Recent and future trends. Metaheuristics-Based Materials Optimization, 103-128.

[9] Naderipour, A., Nowdeh, S. A., Saftjani, P. B., Abdul-Malek, Z., Mustafa, M. W. B., Kamyab, H., & Davoudkhani, I. F. (2021). Deterministic and probabilistic multi-objective placement and sizing of wind renewable energy sources using improved spotted hyena optimizer. Journal of Cleaner Production, 286, 124941.

[10] Otshwe, J. N., Li, B., Chen, S., Gong, F., Qi, B., & Chabrol, N. J. (2025). Adaptive Control and Market Integration: Optimizing Distributed Power Resources for a Sustainable Grid. Energies, 18(7), 1658.

[11] Mendonça, M., & Santos, V. (2025). Advancing sustainable energy solutions: AI hybrid renewable energy systems with hybrid optimization algorithms and multi-objective optimization in Portugal. Journal of Cleaner Production, 145564.

[12] Al-Shalabi, M., Shehab, M., Alshammari, M. T., Alazmi, M., Alrawashdeh, R. O., & Mahdi, M. A. (2025). Enhanced Lotus Effect Optimization Algorithm for Efficient Problem-Solving in High-Dimensional Complex Landscapes. Case Studies in Thermal Engineering, 106437.

[13] Han, M., Du, Z., Yuen, K. F., Zhu, H., Li, Y., & Yuan, Q. (2024). Whale optimizer: A novel nature-inspired metaheuristic algorithm. Expert Systems with Applications, 239, 122413.

[14] Zhao, Y., & Liu, H. (2025). Opposition-based learning Harris hawks optimization with steepest convergence for engineering design problems. The Journal of Supercomputing, 81(1), 148.

[15] Li, M., Liu, Z., & Song, H. (2024). An improved algorithm optimization algorithm based on RungeKutta and golden sine strategy. Expert Systems with Applications, 247, 123262.

[16] Kennedy, J., & Eberhart, R. (1995, November). Particle swarm optimization. In Proceedings of ICNN'95-international conference on neural networks (Vol. 4, pp. 1942-1948). ieee.

[17] Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in engineering software, 69, 46-61.

[18] Agushaka, J. O., Ezugwu, A. E., & Abualigah, L. (2022). Dwarf mongoose optimization algorithm. Computer methods in applied mechanics and engineering, 391, 114570.

[19] Wang, L., Cao, Q., Zhang, Z., Mirjalili, S., & Zhao, W. (2022). Artificial rabbits optimization: A new bio-inspired meta-heuristic algorithm for solving engineering optimization problems. Engineering Applications of Artificial Intelligence, 114, 105082.

[20] Braik, M., Hammouri, A., Atwan, J., Al-Betar, M. A., & Awadallah, M. A. (2022). White Shark Optimizer: A novel bio-inspired meta-heuristic algorithm for global optimization problems. Knowledge-Based Systems, 243, 108457.

[21] MiarNaeimi, F., Azizyan, G., & Rashki, M. (2021). Horse herd optimization algorithm: A nature-inspired algorithm for high-dimensional optimization problems. Knowledge-Based Systems, 213, 106711.

[22] Abdel-Basset, M., Mohamed, R., & Abouhawwash, M. (2024). Crested Porcupine Optimizer: A new nature-inspired metaheuristic. Knowledge-Based Systems, 284, 111257.

[23] Hashim, F. A., & Hussien, A. G. (2022). Snake Optimizer: A novel meta-heuristic optimization algorithm. Knowledge-Based Systems, 242, 108320.

[24] Zhong, C., Li, G., & Meng, Z. (2022). Beluga whale optimization: A novel nature-inspired metaheuristic algorithm. Knowledge-based systems, 251, 109215.

[25] Zhao, S., Zhang, T., Ma, S., & Chen, M. (2022). Dandelion Optimizer: A nature-inspired metaheuristic algorithm for engineering applications. Engineering Applications of Artificial Intelligence, 114, 105075.

[26] Chopra, N., & Ansari, M. M. (2022). Golden jackal optimization: A novel nature-inspired optimizer for engineering applications. Expert Systems with Applications, 198, 116924.

[27] Abualigah, L., Yousri, D., Abd Elaziz, M., Ewees, A. A., Al-Qaness, M. A., & Gandomi, A. H. (2021). Aquila optimizer: a novel meta-heuristic optimization algorithm. Computers & Industrial Engineering, 157, 107250.

[28] Fathollahi-Fard, A. M., Hajiaghaei-Keshteli, M., & Tavakkoli-Moghaddam, R. (2020). Red deer algorithm (RDA): a new nature-inspired meta-heuristic. Soft computing, 24(19), 14637-14665.

[29] Mitchell, M. (1998). An introduction to genetic algorithms. MIT press.

[30] Das, S., & Suganthan, P. N. (2010). Differential evolution: A survey of the state-of-the-art. IEEE transactions on evolutionary computation, 15(1), 4-31.

[31] Hansen, N., Arnold, D. V., & Auger, A. (2015). Evolution strategies. In Springer handbook of computational intelligence (pp. 871-898). Berlin, Heidelberg: Springer Berlin Heidelberg.

[32] Golalipour, K., Davoudkhani, I. F., Nasri, S., Naderipour, A., Mirjalili, S., Abdelaziz, A. Y., & El-Shahat, A. (2023). The corona virus search optimizer for solving global and engineering optimization problems. Alexandria Engineering Journal, 78, 614-642.

[33] Oyelade, O. N., Ezugwu, A. E. S., Mohamed, T. I., & Abualigah, L. (2022). Ebola optimization search algorithm: A new nature-inspired metaheuristic optimization algorithm. IEEE Access, 10, 16150-16177.

[34] Al-Betar, M. A., Alyasseri, Z. A. A., Awadallah, M. A., & Abu Doush, I. (2021). Coronavirus herd immunity optimizer (CHIO). Neural Computing and Applications, 33(10), 5011-5042.

[35] Bertsimas, D., & Tsitsiklis, J. (1993). Simulated annealing. Statistical science, 8(1), 10-15.

[36] Rashedi, E., Nezamabadi-Pour, H., & Saryazdi, S. (2009). GSA: a gravitational search algorithm. Information sciences, 179(13), 2232-2248.

[37] Abedinpourshotorban, H., Shamsuddin, S. M., Beheshti, Z., & Jawawi, D. N. (2016). Electromagnetic field optimization: a physics-inspired metaheuristic optimization algorithm. Swarm and Evolutionary Computation, 26, 8-22.

[38] Abualigah, L., Diabat, A., Mirjalili, S., Abd Elaziz, M., & Gandomi, A. H. (2021). The arithmetic optimization algorithm. Computer methods in applied mechanics and engineering, 376, 113609.

[39] Shehadeh, H. A. (2023). Chernobyl disaster optimizer (CDO): a novel meta-heuristic method for global optimization. Neural Computing and Applications, 35(15), 10733-10749.

[40] Azizi, M. (2021). Atomic orbital search: A novel metaheuristic algorithm. Applied Mathematical Modelling, 93, 657-683.

[41] Qais, M. H., Hasanien, H. M., Alghuwainem, S., & Loo, K. H. (2023). Propagation search algorithm: a physics-based optimizer for engineering applications. Mathematics, 11(20), 4224.

[42] Rao, R. V., Savsani, V. J., & Vakharia, D. P. (2011). Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Computer-aided design, 43(3), 303-315.

[43] Shi, Y. (2011, June). Brain storm optimization algorithm. In International conference in swarm intelligence (pp. 303-309). Berlin, Heidelberg: Springer Berlin Heidelberg.

[44] Lian, J., & Hui, G. (2024). Human evolutionary optimization algorithm. Expert Systems with Applications, 241, 122638.

[45] Faridmehr, I., Nehdi, M. L., Davoudkhani, I. F., & Poolad, A. (2023). Mountaineering team-based optimization: A novel human-based metaheuristic algorithm. Mathematics, 11(5), 1273.

[46] Emami, H. (2022). Stock exchange trading optimization algorithm: a human-inspired method for global optimization. The Journal of Supercomputing, 78(2), 2125-2174.

[47] Moosavi, S. H. S., & Bardsiri, V. K. (2019). Poor and rich optimization algorithm: A new human-based and multi populations algorithm. Engineering applications of artificial intelligence, 86, 165-181.

[48] Veysari, E. F. (2022). A new optimization algorithm inspired by the quest for the evolution of human society: human felicity algorithm. Expert Systems with Applications, 193, 116468.

[49] Eltamaly, A. M., & Rabie, A. H. (2023). A novel musical chairs optimization algorithm. Arabian Journal for Science and Engineering, 48(8), 10371-10403.

[50] Rashki, M., & Faes, M. G. (2023). No-free-lunch theorems for reliability analysis. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 9(3), 04023019.

[51] Abualigah, L., Abd Elaziz, M., Sumari, P., Geem, Z. W., & Gandomi, A. H. (2022). Reptile Search Algorithm (RSA): A nature-inspired meta-heuristic optimizer. Expert Systems with Applications, 191, 116158.

[52] Ahmed, M., Sulaiman, M. H., Mohamad, A. J., & Rahman, M. (2024). Gooseneck barnacle optimization algorithm: A novel nature inspired optimization theory and application. Mathematics and Computers in Simulation, 218, 248-265.

[53] Zhu, Y., Huang, H., Wei, J., Yi, J., Liu, J., & Li, M. (2025). ISO: An improved snake optimizer with multi-strategy enhancement for engineering optimization. Expert Systems with Applications, 281, 127660.

[54] soufyane Benyoucef, A., Chouder, A., Kara, K., & Silvestre, S. (2015). Artificial bee colony based algorithm for maximum power point tracking (MPPT) for PV systems operating under partial shaded conditions. Applied Soft Computing, 32, 38-48.

[55] Barua, S., & Merabet, A. (2024). Lévy arithmetic algorithm: an enhanced metaheuristic algorithm and its application to engineering optimization. Expert Systems with Applications, 241, 122335.

[56] Fathy, A. (2023). Bald eagle search optimizer-based energy management strategy for microgrid with renewable sources and electric vehicles. Applied Energy, 334, 120688.