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Sayısal İyileştirme Problemleri İçin İki-Aşamalı Temel İyileştirme Algoritması

Year 2021, Issue: 26 - Ejosat Special Issue 2021 (HORA), 466 - 471, 31.07.2021
https://doi.org/10.31590/ejosat.953349

Abstract

Sayısal iyileştirme, bilgisayar biliminde iyi bilinen sorunlardan biridir. Gün geçtikçe birçok araştırmacı tarafından yeni yöntemler geliştirilmektedir. Son zamanlarda iyileştirme yapmak, mühendislik, tıp, yönetim ve diğerleri gibi birçok disiplin için önemli bir zorunluluk haline geldi. Çoğu durumda, iyileştirme problemleri, gerçek zamanlı uygulamalar için hızlı ve verimli algoritmalar gerektirebilir. Bu yazıda, hem tek-modelli hem de çoklu-modelli kıyaslama fonksiyonlarının iyileştirilmesi için basit, hızlı ve uygulanabilir bir algoritma sunulmuştur. Popülasyon tabanlı Bi-Attempted Base Optimizasyon Algoritması (ABaOA), iki sabit adım kaydırma parametresi ve iki mutasyon operatörü ile bir çözüm alanını arayan stokastik bir arama yöntemidir. Önerilen algoritma, temel aritmetik işlemleri kullanan Base Optimizasyon Algoritmasından (BaOA) türetilmiştir. ABaOA'nın performansı, iyi bilinen yirmi kıyaslama fonksiyonu üzerinde test edilmiş ve sonuçlar, iyi bilinen yedi stokastik optimizasyon algoritması ile istatistiksel olarak karşılaştırılmıştır. ABaOA'dan elde edilen sonuçlar üzerinde üç farklı istatistiksel analiz yapılmıştır. Sign ve Wilcoxon testleri kullanılarak ortalama değerlerle iki parametrik olmayan istatistiksel karşılaştırma yapılmıştır. Önerilen algoritmanın parametrik olmayan istatistiksel çoklu karşılaştırması Friedman testi kullanılarak gerçekleştirilmiştir. Bu algoritmaların tekrarlanan ölçümleri arasındaki farklılıkların parametrik olmayan Friedman testi 67.337'lik bir Ki-kare değeri istatistiksel olarak anlamlı bulundu (p <0.05). ABaOA'nın diğer algoritmalar arasındaki farkını istatistiksel olarak analiz etmek için Wilcoxon parametrik olmayan ikili karşılaştırma testi uygulanmıştır. Test, sunulan algoritmanın diğer algoritmalardan istatistiksel olarak anlamlı olduğunu ve p <0,05 anlamlılık düzeyine sahip olduğunu göstermektedir. Deneysel sonuçlar ayrıca ABaOA'nın karşılaştırılan stokastik iyileştirme algoritmalarından açıkça üstün olduğunu göstermektedir.

References

  • Bednár, D., Lištjak, M., Slimák, A., & Nečas, V. (2019). Comparison of deterministic and stochastic methods for external gamma dose rate calculation in the decommissioning of nuclear power plants. Annals of Nuclear Energy, 134, 67-76.
  • Campbell, S. D., Sell, D., Jenkins, R. P., Whiting, E. B., Fan, J. A., & Werner, D. H. (2019). Review of numerical optimization techniques for meta-device design. Optical Materials Express, 9(4), 1842-1863.
  • Cao, Y., Lu, Y., Pan, X., & Sun, N. (2019). An improved global best guided artificial bee colony algorithm for continuous optimization problems. Cluster computing, 22(2), 3011-3019.
  • Chakri, A., Khelif, R., Benouaret, M., & Yang, X. S. (2017). New directional bat algorithm for continuous optimization problems. Expert Systems with Applications, 69, 159-175.
  • de Melo, V. V., & Banzhaf, W. (2018). Drone squadron optimization: a novel self-adaptive algorithm for global numerical optimization. Neural Computing and Applications, 30(10), 3117-3144.
  • Deb, K., & Padhye, N. (2014). Enhancing performance of particle swarm optimization through an algorithmic link with genetic algorithms. Computational Optimization and Applications, 57(3), 761-794.
  • Dorigo, M., & Blum, C. (2005). Ant colony optimization theory: A survey. Theoretical computer science, 344(2-3), 243-278. Holland, J. H. (1962). Outline for a logical theory of adaptive systems. Journal of the ACM (JACM), 9(3), 297-314.
  • Karaboga, D., & Akay, B. (2009). A comparative study of artificial bee colony algorithm. Applied mathematics and computation, 214(1), 108-132. Liberti, L., & Kucherenko, S. (2005). Comparison of deterministic and stochastic approaches to global optimization. International Transactions in Operational Research, 12(3), 263-285.
  • Song, Y., Wang, F., & Chen, X. (2019). An improved genetic algorithm for numerical function optimization. Applied Intelligence, 49(5), 1880-1902.
  • Xing, B., & Gao, W. J. (2014). Innovative computational intelligence: a rough guide to 134 clever algorithms (Vol. 62, pp. 22-28). Cham: Springer international publishing.
  • Yadav, A., Sadollah, A., Yadav, N., & Kim, J. H. (2020). Self-adaptive global mine blast algorithm for numerical optimization. Neural Computing and Applications, 32(7), 2423-2444.
  • Zang, W., Ren, L., Zhang, W., & Liu, X. (2018). A cloud model based DNA genetic algorithm for numerical optimization problems. Future Generation Computer Systems, 81, 465-477.

Bi-Attempted Based Optimization Algorithm For Numerical Optimization Problems

Year 2021, Issue: 26 - Ejosat Special Issue 2021 (HORA), 466 - 471, 31.07.2021
https://doi.org/10.31590/ejosat.953349

Abstract

Numerical optimization is one of the well-known problems in computer science. Day by day, new methods are developed by many researchers. Recently, optimization became an essential task for many disciplines, such as engineering, medicine, management and others. In many cases, optimization problems may require fast and efficient algorithms for real-time implementations. In this paper, a simple, fast and feasible algorithm is presented for the optimization of both uni-modal and multi-modal benchmark functions. A population based Bi-Attempted Based Optimization Algorithm (ABaOA) is a stochastic search method which searches a solution space with two fixed step-size displacement parameters and two mutation operators. The proposed algorithm is derived from Base Optimization Algorithm (BaOA) which uses basic arithmetic operations. The performance of ABaOA is tested on twenty well-known benchmark functions and the results are statistically compared with the seven well-known stochastic optimization algorithms. Three different statistical analyses were done on the results obtained from the ABaOA. Two non-parametric statistical comparisons with the mean values are performed by using Sign and Wilcoxon tests. The non-parametric statistical multiple comparisons of the proposed algorithm is performed by using the Friedman test. The non-parametric Friedman test of differences among repeated measures of these algorithms was conducted and referred a Chi-square value of 67.337, which was significant (p<0.05). Wilcoxon non-parametric pairwise comparison test was applied to analyze the difference of ABaOA statistically among the other algorithms. The test indicates that the introduced algorithm is statistically significant than other algorithms with a level of significance p < 0.05. The experimental results also show that the ABaOA is clearly superior to the compared stochastic optimization algorithms.

References

  • Bednár, D., Lištjak, M., Slimák, A., & Nečas, V. (2019). Comparison of deterministic and stochastic methods for external gamma dose rate calculation in the decommissioning of nuclear power plants. Annals of Nuclear Energy, 134, 67-76.
  • Campbell, S. D., Sell, D., Jenkins, R. P., Whiting, E. B., Fan, J. A., & Werner, D. H. (2019). Review of numerical optimization techniques for meta-device design. Optical Materials Express, 9(4), 1842-1863.
  • Cao, Y., Lu, Y., Pan, X., & Sun, N. (2019). An improved global best guided artificial bee colony algorithm for continuous optimization problems. Cluster computing, 22(2), 3011-3019.
  • Chakri, A., Khelif, R., Benouaret, M., & Yang, X. S. (2017). New directional bat algorithm for continuous optimization problems. Expert Systems with Applications, 69, 159-175.
  • de Melo, V. V., & Banzhaf, W. (2018). Drone squadron optimization: a novel self-adaptive algorithm for global numerical optimization. Neural Computing and Applications, 30(10), 3117-3144.
  • Deb, K., & Padhye, N. (2014). Enhancing performance of particle swarm optimization through an algorithmic link with genetic algorithms. Computational Optimization and Applications, 57(3), 761-794.
  • Dorigo, M., & Blum, C. (2005). Ant colony optimization theory: A survey. Theoretical computer science, 344(2-3), 243-278. Holland, J. H. (1962). Outline for a logical theory of adaptive systems. Journal of the ACM (JACM), 9(3), 297-314.
  • Karaboga, D., & Akay, B. (2009). A comparative study of artificial bee colony algorithm. Applied mathematics and computation, 214(1), 108-132. Liberti, L., & Kucherenko, S. (2005). Comparison of deterministic and stochastic approaches to global optimization. International Transactions in Operational Research, 12(3), 263-285.
  • Song, Y., Wang, F., & Chen, X. (2019). An improved genetic algorithm for numerical function optimization. Applied Intelligence, 49(5), 1880-1902.
  • Xing, B., & Gao, W. J. (2014). Innovative computational intelligence: a rough guide to 134 clever algorithms (Vol. 62, pp. 22-28). Cham: Springer international publishing.
  • Yadav, A., Sadollah, A., Yadav, N., & Kim, J. H. (2020). Self-adaptive global mine blast algorithm for numerical optimization. Neural Computing and Applications, 32(7), 2423-2444.
  • Zang, W., Ren, L., Zhang, W., & Liu, X. (2018). A cloud model based DNA genetic algorithm for numerical optimization problems. Future Generation Computer Systems, 81, 465-477.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mehtap Köse Ulukök 0000-0003-4335-483X

Publication Date July 31, 2021
Published in Issue Year 2021 Issue: 26 - Ejosat Special Issue 2021 (HORA)

Cite

APA Köse Ulukök, M. (2021). Bi-Attempted Based Optimization Algorithm For Numerical Optimization Problems. Avrupa Bilim Ve Teknoloji Dergisi(26), 466-471. https://doi.org/10.31590/ejosat.953349