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HYBRID THE ARITHMETIC OPTIMIZATION ALGORITHM FOR CONSTRAINED OPTIMIZATION PROBLEMS

Year 2021, Volume: 9 Issue: 3, 713 - 734, 01.09.2021
https://doi.org/10.36306/konjes.904335

Abstract

Since many real-world problems can be designed as optimization problems, heuristic algorithms are increasingly preferred by researchers. The Arithmetic Optimization Algorithm (AOA) is a newly developed heuristic algorithm. It uses four arithmetic operations in its structure. The addition and subtraction operators enhanced the AOA's local search capability, while the multiplication and division operators enhanced the AOA's global search capability. It has been hybridized with the Tree Seed Algorithm (TSA) to increase the success of AOA. Thus, hybrid AOA-TSA (HAOA) has been proposed. The seed production mechanism of TSA is placed in the random walking stage of AOA. New candidate solutions (seeds) have been produced with the arithmetic operators involved in AOA and the candidate solutions have been compared with the existing solutions. Thus, the performance of AOA has increased. In this study, the success of AOA and HAOA was tested in thirteen constrained optimization problems. The success of AOA and HAOA has been tested for their performance in six different population sizes. The Wilcoxon Signed-Rank test was applied to the obtained results and its success has been proved statistically. The results proved the superiority of HAOA. HAOA has been compared with other heuristic methods in the literature and the success of HAOA has been shown. Additionally, AOA and HAOA have also been tested on three different engineering design problems. The results are discussed and evaluated.

References

  • Abualigah, L., Diabat, A., Mirjalili, S., Elaziz, MA., Gandomi, A.H., (2021), The Arithmetic Optimization Algorithm, Comput. Methods Appl. Mech. Engrg. 376 (2021) 113609.
  • Aslan, M., Beskirli, M., Kodaz, H., Kiran, M.S., (2018), An Improved Tree Seed Algorithm for Optimization Problems, International Journal of Machine Learning and Computing, Vol. 8, No. 1.
  • Babalik, A., Cinar, A.C., Kiran, M.S., (2018), A modification of tree-seed algorithm using Deb’s rules for constrained optimization, Applied Soft Computing 63, 289–305.
  • Bansal, J.C., Joshi, S.K., Sharma, H., (2018), Modified global best artificial bee colony for constrained optimization problems, Computers and Electrical Engineering 67, 365–382.
  • Beşkirli, A., Özdemir, D., Temurtaş, H., (2020), A comparison of modified tree–seed algorithm for high- dimensional numerical functions, Neural Computing, and Applications, 32:6877–6911.
  • Braik, M.S., (2021), Chameleon Swarm Algorithm: A bio-inspired optimizer for solving engineering design problems, Expert Systems With Applications 174, 114685.
  • Cinar, A.C., Korkmaz, S., Kiran, M.S., (2020), A discrete tree-seed algorithm for solving symmetric traveling salesman problem, Volume 23, Issue 4, Pages 879-890.
  • Deb, K., (1991), Optimal design of a welded beam via genetic algorithms, AIAA J. 29(11) (1991) 2013– 2015.
  • El-Fergany, A., Hasanien, H.M., (2018), Tree-seed algorithm for solving optimal power flow problem in large-scale power systems incorporating validations and comparisons, Applied Soft Computing, Volume 64, Pages 307-316.
  • Garg, H., (2016), "A hybrid PSO-GA algorithm for constrained optimization problems", Applied Mathematics and Computation, 274, 292-305. doi:10.1016/j.amc.2015.11.001.
  • Haklı, H., (2019), A Novel Approach Based On Elephant Herding Optimization For Constrained Optimization Problems, Selcuk Univ. J. Eng. Sci. Tech., v.7, n.2, pp. 405-419.
  • Jiang, J., Meng, X., Chen, Y., Qiu, C., Liu, Y., Li, K., (2020), Enhancing tree-seed algorithm via feed-back mechanism for optimizing continuous problems, Applied Soft Computing, Volume 92, 106314.
  • Kiran, M.S., (2015), TSA: Tree-seed algorithm for continuous optimization, Volume 42, Issue 19, Pages 6686-6698.
  • Kohli, M., Arora, S., (2017), "Chaotic grey wolf optimization algorithm for constrained optimization problems", Journal of Computational Design and Engineering, In Press. Doi:10.1016/j.jcde.2017.02.005.
  • Lin, C. H., (2013), "A rough penalty genetic algorithm for constrained optimization", Information Sciences, 241, 119-137. Doi:10.1016/j.ins.2013.04.001.
  • Lee, K.S., Geem, Z.W., (2005), A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice, Comput.Methods Appl. Mech. Eng. 194 (36) (2005) 3902– 3933.
  • Mirjalili, S., Mirjalili, S.M., Lewis, A., (2014), Grey wolf optimizer, Adv. Eng. Software 69(2014) 46–61.
  • Mirjalili, S., (2015), Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm, Knowledge-Based Systems 89 (2015) 228–249.
  • Mirjalili, S., Lewis, A., (2016), The whale optimization algorithm, Adv. Eng. Software 95(2016) 51–67.
  • Runarsson, T.P., Yao, X., (2000), "Stochastic ranking for constrained evolutionary optimization", Ieee Transactions on Evolutionary Computation, 4(3), 284-294. Doi: 10.1109/4235.873238.
  • Strumberger, I., Bacanin, N., Tuba, M., (2018), "Hybridized Elephant Herding Optimization Algorithm for Constrained Optimization", Cham. 158-166.
  • Xu, B., Chen, X., Tao, L. L., (2018), "Differential evolution with adaptive trial vector generation strategy and cluster-replacement-based feasibility rule for constrained optimization", Information Sciences, 435, 240-262. Doi:10.1016/j.ins.2018.01.014.

Kısıtlı Optimizasyon Problemleri İçin Hibrit Aritmetik Optimizasyon Algoritması

Year 2021, Volume: 9 Issue: 3, 713 - 734, 01.09.2021
https://doi.org/10.36306/konjes.904335

Abstract

Pek çok gerçek dünya problemi optimizasyon problemleri olarak tasarlanabildiğinden, sezgisel algoritmalar araştırmacılar tarafından giderek daha fazla tercih edilmeye başlanmıştır. Aritmetik Optimizasyon Algoritması (AOA), yeni geliştirilmiş bir sezgisel algoritmadır. Yapısında dört aritmetik işlem kullanır. Toplama ve çıkarma operatörleri, AOA'nın yerel arama kabiliyetini geliştirirken, çarpma ve bölme operatörleri AOA'nın küresel arama kabiliyetini geliştirmiştir. AOA'nın başarısını artırmak için Ağaç Tohum Algoritması (TSA) ile hibritlenmiştir. Bu çalışmada, Hibrit AOA-TSA (HAOA) önerilmiştir. TSA'nın tohum üretim mekanizması, AOA'nın rastgele yürüme aşamasına yerleştirilmiştir. AOA'da yer alan aritmetik operatörler ile yeni aday çözümler (tohumlar) üretilmiş ve aday çözümler mevcut çözümlerle karşılaştırılmıştır. Böylece, AOA'nın performansı artmıştır. Bu çalışmada, AOA ve HAOA'nın başarısı on üç kısıtlı optimizasyon probleminde test edilmiştir. AOA ve HAOA'nın başarısı altı farklı popülasyon büyüklüğünde test edilmiştir. Elde edilen sonuçlara Wilcoxon Signed-Rank testi uygulanmış ve başarısı istatistiksel olarak kanıtlanmıştır. Sonuçlar HAOA'nın üstünlüğünü kanıtlamıştır. HAOA, literatürdeki diğer sezgisel yöntemlerle karşılaştırılmış ve HAOA'nın başarısı gösterilmiştir. Ek olarak, AOA ve HAOA, üç farklı mühendislik tasarım probleminde de test edilmiştir.

References

  • Abualigah, L., Diabat, A., Mirjalili, S., Elaziz, MA., Gandomi, A.H., (2021), The Arithmetic Optimization Algorithm, Comput. Methods Appl. Mech. Engrg. 376 (2021) 113609.
  • Aslan, M., Beskirli, M., Kodaz, H., Kiran, M.S., (2018), An Improved Tree Seed Algorithm for Optimization Problems, International Journal of Machine Learning and Computing, Vol. 8, No. 1.
  • Babalik, A., Cinar, A.C., Kiran, M.S., (2018), A modification of tree-seed algorithm using Deb’s rules for constrained optimization, Applied Soft Computing 63, 289–305.
  • Bansal, J.C., Joshi, S.K., Sharma, H., (2018), Modified global best artificial bee colony for constrained optimization problems, Computers and Electrical Engineering 67, 365–382.
  • Beşkirli, A., Özdemir, D., Temurtaş, H., (2020), A comparison of modified tree–seed algorithm for high- dimensional numerical functions, Neural Computing, and Applications, 32:6877–6911.
  • Braik, M.S., (2021), Chameleon Swarm Algorithm: A bio-inspired optimizer for solving engineering design problems, Expert Systems With Applications 174, 114685.
  • Cinar, A.C., Korkmaz, S., Kiran, M.S., (2020), A discrete tree-seed algorithm for solving symmetric traveling salesman problem, Volume 23, Issue 4, Pages 879-890.
  • Deb, K., (1991), Optimal design of a welded beam via genetic algorithms, AIAA J. 29(11) (1991) 2013– 2015.
  • El-Fergany, A., Hasanien, H.M., (2018), Tree-seed algorithm for solving optimal power flow problem in large-scale power systems incorporating validations and comparisons, Applied Soft Computing, Volume 64, Pages 307-316.
  • Garg, H., (2016), "A hybrid PSO-GA algorithm for constrained optimization problems", Applied Mathematics and Computation, 274, 292-305. doi:10.1016/j.amc.2015.11.001.
  • Haklı, H., (2019), A Novel Approach Based On Elephant Herding Optimization For Constrained Optimization Problems, Selcuk Univ. J. Eng. Sci. Tech., v.7, n.2, pp. 405-419.
  • Jiang, J., Meng, X., Chen, Y., Qiu, C., Liu, Y., Li, K., (2020), Enhancing tree-seed algorithm via feed-back mechanism for optimizing continuous problems, Applied Soft Computing, Volume 92, 106314.
  • Kiran, M.S., (2015), TSA: Tree-seed algorithm for continuous optimization, Volume 42, Issue 19, Pages 6686-6698.
  • Kohli, M., Arora, S., (2017), "Chaotic grey wolf optimization algorithm for constrained optimization problems", Journal of Computational Design and Engineering, In Press. Doi:10.1016/j.jcde.2017.02.005.
  • Lin, C. H., (2013), "A rough penalty genetic algorithm for constrained optimization", Information Sciences, 241, 119-137. Doi:10.1016/j.ins.2013.04.001.
  • Lee, K.S., Geem, Z.W., (2005), A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice, Comput.Methods Appl. Mech. Eng. 194 (36) (2005) 3902– 3933.
  • Mirjalili, S., Mirjalili, S.M., Lewis, A., (2014), Grey wolf optimizer, Adv. Eng. Software 69(2014) 46–61.
  • Mirjalili, S., (2015), Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm, Knowledge-Based Systems 89 (2015) 228–249.
  • Mirjalili, S., Lewis, A., (2016), The whale optimization algorithm, Adv. Eng. Software 95(2016) 51–67.
  • Runarsson, T.P., Yao, X., (2000), "Stochastic ranking for constrained evolutionary optimization", Ieee Transactions on Evolutionary Computation, 4(3), 284-294. Doi: 10.1109/4235.873238.
  • Strumberger, I., Bacanin, N., Tuba, M., (2018), "Hybridized Elephant Herding Optimization Algorithm for Constrained Optimization", Cham. 158-166.
  • Xu, B., Chen, X., Tao, L. L., (2018), "Differential evolution with adaptive trial vector generation strategy and cluster-replacement-based feasibility rule for constrained optimization", Information Sciences, 435, 240-262. Doi:10.1016/j.ins.2018.01.014.
There are 22 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Emine Baş 0000-0003-4322-6010

Publication Date September 1, 2021
Submission Date March 27, 2021
Acceptance Date July 29, 2021
Published in Issue Year 2021 Volume: 9 Issue: 3

Cite

IEEE E. Baş, “HYBRID THE ARITHMETIC OPTIMIZATION ALGORITHM FOR CONSTRAINED OPTIMIZATION PROBLEMS”, KONJES, vol. 9, no. 3, pp. 713–734, 2021, doi: 10.36306/konjes.904335.