Kısıtlı Mühendislik Tasarım Problemleri için Balina Güdümlü Fırtına Optimizasyon Algoritması

Öz

Bu çalışmada, kısıtlı mühendislik tasarım problemlerinin çözümü için Elektrik Fırtınası Optimizasyonu (ESO) üzerine kurulu Balina Güdümlü Fırtına (BGF) adlı hibrit bir meta-sezgisel yöntem önerilmektedir. BGF, ESO’nun keşif–sömürü dengesini, Balina Optimizasyon Algoritmasının (WOA) spiral güncelleme mekanizmasıyla zenginleştirilmiş yerel arama adımıyla birleştirir. Kısıtlı aramada fizibiliteyi öncelemek için aday çözümler Deb’in fizibilite kurallarıyla değerlendirilmekte; yerel optimumlara takılmayı azaltmak ve çeşitliliği korumak amacıyla durgunluk eşiği aşıldığında popülasyonun en kötü %20’sine OBL tabanlı yeniden konumlandırma uygulanmaktadır. Yöntem, Kumar vd. benchmark setindeki dört problem üzerinde sınanmıştır: RC23 (düzeltilmiş kademeli konik kasnak), RC24 (sıfır tuzağını engelleyen ek kısıtlı robot tutucu), RC29 (gaz iletim kompresörü) ve RC32 (Himmelblau). Tüm algoritmalar popülasyon=50 ve iterasyon=1000 ile 30 bağımsız koşuda çalıştırılmış; Min./Ort./Maks./Std. istatistikleri ve yakınsama eğrileri üzerinden WOA, JADE, TLO, EO ve ESO ile karşılaştırılmıştır. Sonuçlar, BGF’nin RC23, RC29 ve RC32’de en iyi ortalama performans ve en düşük saçılımı sağlayarak yüksek kararlılık sunduğunu, RC24’te ise rekabetçi olmakla birlikte JADE/TLO’nun gerisinde kaldığını göstermektedir. RC23 ve RC24’te literatürde gözlenen formülasyon hataları mühendislik tutarlılığı korunarak düzeltilmiş ve RC24’e minimum kuvvet eşiği eklenmiştir. Uygulama Python ortamında gerçekleştirilmiş, her koşu aynı başlangıç ayarlarıyla yürütülmüştür. Elde edilen bulgular BGF’nin kısıtlı optimizasyon için güçlü bir aday olduğunu, ancak keşif ağırlıklı problemlerde ek geliştirmelere açık kaldığını ortaya koymaktadır.

Anahtar Kelimeler

• Kısıtlı optimizasyon
• Meta-sezgisel algoritmalar
• Elektrik Fırtınası Optimizasyonu
• Balina Optimizasyon Algoritması
• Karşıtlık tabanlı öğrenme
• Mühendislik tasarım optimizasyonu

Etik Beyan

Bu çalışma insan veya hayvan denek içermediğinden etik kurul izni ve aydınlatılmış onam gerekmemektedir. Yazar çıkar çatışması olmadığını ve çalışma için dış fon desteği alınmadığını beyan eder.

Whale-Guided Storm Optimization Algorithm for Constrained Engineering Design Problems

Öz

This study proposes the Whale-Guided Storm (BGF) algorithm, a hybrid metaheuristic based on Electric Storm Optimization (ESO) for constrained engineering design. BGF enhances ESO by adding a local-search step using the Whale Optimization Algorithm (WOA) spiral update. Solutions are assessed with Deb’s feasibility rules; when stagnation is detected, opposition-based learning (OBL) repositions the worst 20% of the population to preserve diversity and reduce local-optimum trapping. BGF is tested on four constrained benchmarks from Kumar et al.: RC23 (corrected stepped conical pulley), RC24 (robot gripper with an added constraint to avoid the zero-trap), RC29 (gas transmission compressor), and RC32 (Himmelblau). All algorithms run with population=50 and iterations=1000 for 30 independent trials; min/mean/max/std statistics and convergence curves compare BGF against WOA, JADE, TLO, EO, and ESO. Results show BGF achieves the best mean performance and the lowest dispersion on RC23, RC29, and RC32, while on RC24 it is competitive but behind JADE/TLO. Formulation issues reported in the literature for RC23 and RC24 are corrected, and a minimum-force threshold is added to RC24. The Python implementation uses identical initial settings across runs. Overall, BGF is a strong candidate for constrained optimization, but remains open to further improvements on exploration-dominant problems.

Anahtar Kelimeler

• Constrained optimization
• Metaheuristic algorithms
• Electric Storm Optimization
• Whale Optimization Algorithm
• Opposition-Based Learning
• Engineering design optimization

Etik Beyan

This study does not involve human participants or animals. Therefore, ethics committee approval and informed consent are not required. The author declares no conflict of interest. This research received no external funding.

Kaynakça

1. [1] Rajwar, K., Deep, K., & Das, S. (2023). An exhaustive review of the metaheuristic algorithms for search and optimization: taxonomy, applications, and open challenges. Artificial Intelligence Review, 56(11), 13187–13257. https://doi.org/10.1007/S10462-023-10470-Y.
2. [2] Selvam, R., Hiremath, P., Cs, S. K., Ramakrishna Bhat, R., Tomar, V., Bansal, M., & Singh, P. (2024). Metaheuristic Algorithms for Optimization: A Brief Review. Engineering Proceedings, 59(1), 238. https://doi.org/10.3390/ENGPROC2023059238.
3. [3] Katoch, S., Chauhan, S. S., & Kumar, V. (2020). A review on genetic algorithm: past, present, and future. Multimedia Tools and Applications, 80(5), 8091–8126. https://doi.org/10.1007/S11042-020-10139-6.
4. [4] Zhu, D., Li, R., Zheng, Y., Zhou, C., Li, T., & Cheng, S. (2025). Cumulative Major Advances in Particle Swarm Optimization from 2018 to the Present: Variants, Analysis and Applications. Archives of Computational Methods in Engineering, 32(3), 1571–1595. https://doi.org/10.1007/S11831-024-10185-5.
5. [5] Fan, M., Chen, J., Xie, Z., Ouyang, H., Li, S., & Gao, L. (2022). Improved multi-objective differential evolution algorithm based on a decomposition strategy for multi-objective optimization problems. Scientific Reports, 12(1), 1–14. https://doi.org/10.1038/s41598-022-25440-7.
6. [6] Ahmad, M. F., Isa, N. A. M., Lim, W. H., & Ang, K. M. (2022). Differential evolution: A recent review based on state-of-the-art works. Alexandria Engineering Journal, 61(5), 3831–3872. https://doi.org/10.1016/J.AEJ.2021.09.013.
7. [7] Chakraborty, S., Saha, A. K., Sharma, S., Sahoo, S. K., & Pal, G. (2022). Comparative Performance Analysis of Differential Evolution Variants on Engineering Design Problems. Journal of Bionic Engineering, 19(4), 1140–1160. https://doi.org/10.1007/S42235-022-00190-4.
8. [8] Houssein, E. H., Hossam Abdel Gafar, M., Fawzy, N., & Sayed, A. Y. (2025). Recent metaheuristic algorithms for solving some civil engineering optimization problems. Scientific Reports, 15(1), 1–25. https://doi.org/10.1038/s41598-025-90000-8.

9. [9] Sharma, P., & Raju, S. (2023). Metaheuristic optimization algorithms: a comprehensive overview and classification of benchmark test functions. Soft Computing, 28(4), 3123–3186. https://doi.org/10.1007/S00500-023-09276-5.
10. [10] Qiao, K., Liang, J., Yu, K., Ban, X., Yue, C., Qu, B., & Suganthan, P. N. (2024). Constraints Separation Based Evolutionary Multitasking for Constrained Multi-Objective Optimization Problems. IEEE/CAA Journal of Automatica Sinica, 11(8), 1819–1835. https://doi.org/10.1109/JAS.2024.124545.
11. [11] Rahimi, I., Gandomi, A. H., Nikoo, M. R., Mousavi, M., & Chen, F. (2024). Efficient implicit constraint handling approaches for constrained optimization problems. Scientific Reports, 14(1), 1–39. https://doi.org/10.1038/s41598-024-54841-z.
12. [12] Wolpert, D. H., & Macready, W. G. (1997). No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1(1), 67–82. https://doi.org/10.1109/4235.585893.
13. [13] Seyyedabbasi, A., Tareq Tareq, W. Z., & Bacanin, N. (2024). An Effective Hybrid Metaheuristic Algorithm for Solving Global Optimization Algorithms. Multimedia Tools and Applications, 83(37), 85103–85138. https://doi.org/10.1007/S11042-024-19437-9.
14. [14] Bouaouda, A., & Sayouti, Y. (2022). Hybrid Meta-Heuristic Algorithms for Optimal Sizing of Hybrid Renewable Energy System: A Review of the State-of-the-Art. Archives of Computational Methods in Engineering, 29(6), 4049–4083. https://doi.org/10.1007/S11831-022-09730-X.
15. [15] Xu, H., Deng, Q., Zhang, Z., & Lin, S. (2025). A hybrid differential evolution particle swarm optimization algorithm based on dynamic strategies. Scientific Reports, 15(1), 1–49. https://doi.org/10.1038/s41598-024-82648-5.
16. [16] Lakbichi, R., Zitouni, F., Harous, S., Ferhat, A., Limane, A., Almazyad, A. S., Xiong, G., & Mohamed, A. W. (2025). Opposition-based learning techniques in metaheuristics: classification, comparison, and convergence analysis. PeerJ Computer Science, 11, e2935. https://doi.org/10.7717/PEERJ-CS.2935.
17. [17] 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.
18. [18] Rana, N., Latiff, M. S. A., Abdulhamid, S. M., & Chiroma, H. (2020). Whale optimization algorithm: a systematic review of contemporary applications, modifications and developments. Neural Computing and Applications, 32(20), 16245–16277. https://doi.org/10.1007/S00521-020-04849-Z.
19. [19] Tang, J., & Wang, L. (2024). A whale optimization algorithm based on atom-like structure differential evolution for solving engineering design problems. Scientific Reports, 14(1), 1–27. https://doi.org/10.1038/s41598-023-51135-8.
20. [20] Hsieh, C. H., Zhang, Q., Xu, Y., & Wang, Z. (2023). CMAIS-WOA: An Improved WOA with Chaotic Mapping and Adaptive Iterative Strategy. Discrete Dynamics in Nature and Society, 2023(1), 8160121. https://doi.org/10.1155/2023/8160121.
21. [21] Hosseinzadeh, M., Tanveer, J., Rahmani, A. M., Baptista, M. L., Abbaszadi, R., Gharehchopogh, F. S., Porntaveetus, T., & Lee, S. W. (2026). A Comprehensive Survey of Hybrid Whale Optimization Algorithm with Long-Short Term Memory: Applications, Improvements, and Future Perspective. Archives of Computational Methods in Engineering, 33(3), 3665–3706. https://doi.org/10.1007/S11831-025-10413-6.
22. [22] Sosnowski, M., Grabowska, K., Skrobek, D., Moeen Uddin, G., Soto Calvo, M., & Soo Lee, H. (2025). Electrical Storm Optimization (ESO) Algorithm: Theoretical Foundations, Analysis, and Application to Engineering Problems. Machine Learning and Knowledge Extraction, 7(1), 24. https://doi.org/10.3390/MAKE7010024.
23. [23] Kumar, A., Wu, G., Ali, M. Z., Mallipeddi, R., Suganthan, P. N., & Das, S. (2020). A test-suite of non-convex constrained optimization problems from the real-world and some baseline results. Swarm and Evolutionary Computation, 56, 100693. https://doi.org/10.1016/J.SWEVO.2020.100693.
24. [24] Deb, K. (2000). An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering, 186(2–4), 311–338. https://doi.org/10.1016/S0045-7825(99)00389-8.
25. [25] Zhang, J., & Sanderson, A. C. (2009). JADE: Adaptive differential evolution with optional external archive. IEEE Transactions on Evolutionary Computation, 13(5), 945–958. https://doi.org/10.1109/TEVC.2009.2014613.
26. [26] 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. https://doi.org/10.1016/J.CAD.2010.12.015.
27. [27] Faramarzi, A., Heidarinejad, M., Stephens, B., & Mirjalili, S. (2020). Equilibrium optimizer: A novel optimization algorithm. Knowledge-Based Systems, 191, 105190. https://doi.org/10.1016/j.knosys.2019.105190.