Improved Runge Kutta Optimizer with Fitness Distance Balance-Based Guiding Mechanism for Global Optimization of High-Dimensional Problems

Yıl 2021, , 135 - 149, 31.12.2021

Enes Cengiz , Cemal Yılmaz , Hamdi Kahraman , Çağrı Suiçmez

https://doi.org/10.29130/dubited.1014947

Cited By: 8

Öz

Runge Kutta (RUN) is an up-to-date and well-founded metaheuristic algorithm. The RUN algorithm aims to find the global best in solving problems by going beyond the traps of metaphors. For this purpose, enhanced solution quality mechanism is used to avoid local optimum solutions and increase the convergence speed. Although the RUN algorithm offers promising solutions, it is seen that this algorithm has shortcomings, especially in solving high dimensional multimodal problems. In this study, the solution candidates that guide the search process in the RUN algorithm are developed using the Fitness-Distance Balance (FDB) method. Thus, using the FDB-based RUN algorithm, the global optimum value of many optimization problems will be obtained in the future. CEC 2020 which has current benchmark problems was used to test the performance of the developed FDB-RUN algorithm. 10 different unconstrained benchmark problems taken from CEC 2020 were designed by arranging them in 30/50/100 dimensions. Experimental studies were carried out using the designed benchmark problems and analyzed with Friedman and Wilcoxon statistical test methods. According to the results of the analysis, it was seen that the FDB-RUN variations showed a superior performance compared to the base algorithm (RUN) in all experimental studies. In particular, it has been shown to provide more effective results for the continuous optimization of high-dimensional problems.

Anahtar Kelimeler

Meta-heuristic search, runge kutta algorithm, fitness-distance balance (FDB), benchmark problems

Yüksek Boyutlu Problemlerin Global Optimizasyonu için Uygunluk Mesafe Dengesi Tabanlı Rehber Mekanizmasıyla Runge Kutta Optimize Edicinin İyileştirilmesi

Öz

Runge Kutta (RUN), güncel ve sağlam temellere sahip bir metasezgisel algoritmadır. RUN algoritması, metaforların tuzaklarının ötesine geçerek problemlerin çözümünde küresel en iyiyi bulmayı amaçlar. Bu amaçla, yerel optimum çözümlerden kaçınmak ve yakınsama hızını artırmak için geliştirilmiş çözüm kalitesi mekanizması kullanılmaktadır. RUN algoritması umut verici çözümler sunsa da bu algoritmanın özellikle yüksek boyutlu multimodal problemlerin çözümünde eksiklikleri olduğu görülmektedir. Bu çalışmada, Uygunluk-Mesafe Dengesi (FDB) yöntemi kullanılarak RUN algoritmasında arama sürecine rehberlik eden çözüm adayları geliştirilmiştir. Böylece FDB tabanlı RUN algoritması kullanılarak gelecekte birçok optimizasyon probleminin global optimum değeri elde edilecektir. Geliştirilen FDB-RUN algoritmasının performansını test etmek için güncel benchmark sorunları olan CEC 2020 kullanılmıştır. CEC 2020'den alınan 10 farklı kısıtsız kıyaslama problemi 30/50/100 boyutlarında düzenlenerek tasarlanmıştır. Deneysel çalışmalar tasarlanan kıyaslama problemleri kullanılarak gerçekleştirilmiş ve Friedman ve Wilcoxon istatistiksel test yöntemleri ile analiz edilmiştir. Analiz sonuçlarına göre FDB-RUN varyasyonlarının tüm deneysel çalışmalarda temel algoritmaya (RUN) göre daha üstün bir performans gösterdiği görülmüştür. Özellikle yüksek boyutlu problemlerin sürekli optimizasyonu için daha etkili sonuçlar sağladığı gösterilmiştir.

Anahtar Kelimeler

Meta-sezgisel arama, Runge Kutta algoritması, uygunluk-mesafe dengesi (FDB), kıyaslama problemleri

Kaynakça

• [1] A. H. Halim, I. Ismail, and S. Das, “Performance assessment of the metaheuristic optimization algorithms: an exhaustive review,” Artificial Intelligence Review, vol. 54, no. 3, pp. 2323-2409, 2021.
• [2] X. S. Yang, “Metaheuristic optimization”. Scholarpedia, vol. 6, no. 8, 11472, 2011.
• [3] D. E. Goldberg and J. H. Holland, “Genetic algorithms and machine learning,” Mach Learn, vol. 3, pp. 95-99, 1988.
• [4] S. Mirjalili, “Genetic algorithm,” In Evolutionary algorithms and neural networks, Springer, Cham, 2019, pp. 43-55.
• [5] D. Bertsimas, and J. Tsitsiklis, “Simulated annealing,” Statistical science, vol. 8, no. 1, pp. 10-15, 1993.
• [6] A. Franzin and T. Stützle, “Revisiting simulated annealing: A component-based analysis”. Computers & operations research, vol. 104, pp. 191-206, 2019.
• [7] L. Xing, Y. Liu, H. Li, C. C. Wu, W. C. Lin, and X. Chen, “A novel tabu search algorithm for multi-AGV routing problem,” Mathematics, vol. 8, no. 2, 279, 2020.
• [8] K. L. Du and M. N. S. Swamy, “Ant colony optimization,” In Search and optimization by metaheuristics. Birkhäuser, Cham, 2016, pp. 191-199.
• [9] J. Kennedy and R. Eberhart, “Particle swarm optimization,” In Proceedings of ICNN'95-international conference on neural networks, 1995, pp. 1942-1948.
• [10] K. L. Du and M. N. S. Swamy, “Particle swarm optimization,” Search and optimization by metaheuristics, Birkhäuser, Cham, 2016, pp. 153-173.
• [11] Z. W. Geem, J. H. Kim, and G. V. Loganathan, “A new heuristic optimization algorithm: harmony search,” simulation, vol. 76, no. 2, pp. 60-68, 2001.
• [12] D. Karaboga, and B. Basturk, “A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm,” Journal of global optimization, vol. 39, no. 3, pp. 459-471, 2007.
• [13] E. Rashedi, H. Nezamabadi-Pour, and S. Saryazdi, “GSA: a gravitational search algorithm”. Information sciences, vol. 179, no. 13, pp. 2232-2248, 2009.
• [14] X. S. Yang, and S. Deb, “Cuckoo search via Lévy flights,” In 2009 World congress on nature & biologically inspired computing, 2009, pp. 210-214.
• [15] R. L. Rardin, and R. Uzsoy “Experimental evaluation of heuristic optimization algorithm: a tutorial”. J Heuristics, vol. 7, no. 3, pp. 261–304, 2018.
• [16] V. Beiranvand, W. Hare, and Y. Lucet, “Best practices for comparing optimization algorithms,” Optimization and Engineering, vol. 18, no. 4, pp. 815-848, 2017.
• [17] T. T. Nguyen, S. Yang, and J. Branke, “Evolutionary dynamic optimization: A survey of the state of the art,” Swarm and Evolutionary Computation, vol. 6, pp. 1-24, 2012.
• [18] J. Tian, C. Sun, Y. Tan, and J. Zeng, “Granularity-based surrogate-assisted particle swarm optimization for high-dimensional expensive optimization,” Knowledge-Based Systems, vol. 187, 104815, 2020.
• [19] L. Cui, G. Li, Q. Lin, Z. Du, W. Gao, J. Chen, and N. Lu, “A novel artificial bee colony algorithm with depth-first search framework and elite-guided search equation,” Information Sciences, vol. 367, pp. 1012-1044, 2016.
• [20] K. H. Truong, P. Nallagownden, Z. Baharudin, and D. N. Vo, “A quasi-oppositional-chaotic symbiotic organisms search algorithm for global optimization problems,” Applied Soft Computing, vol. 77, pp. 567-583, 2019.
• [21] A. W. Mohamed and A. K. Mohamed, “Adaptive guided differential evolution algorithm with novel mutation for numerical optimization,” International Journal of Machine Learning and Cybernetics, vol. 10, no. 2, pp. 253-277, 2019.
• [22] R. Salgotra, U. Singh, and S. Saha, “New cuckoo search algorithms with enhanced exploration and exploitation properties,”.Expert Systems with Applications, vol. 95, pp. 384-420, 2018.
• [23] H. T. Kahraman, S. Aras, and E. Gedikli, “Fitness-distance balance (FDB): a new selection method for meta-heuristic search algorithms,” Knowledge-Based Systems, vol. 190, 105169, 2020.
• [24] U. Guvenc, S. Duman, H. T. Kahraman, S. Aras, and M. Katı, “Fitness–Distance Balance based adaptive guided differential evolution algorithm for security-constrained optimal power flow problem incorporating renewable energy sources,” Applied Soft Computing, vol. 108, 107421, 2021.
• [25] S. Duman, H. T. Kahraman, U. Guvenc, and S.Aras, “Development of a Lévy flight and FDB-based coyote optimization algorithm for global optimization and real-world ACOPF problems,” Soft Computing, vol. 25, no. 8, pp. 6577-6617, 2021.
• [26] S. Aras, E. Gedikli, and H. T. Kahraman, “A novel stochastic fractal search algorithm with fitness-Distance balance for global numerical optimization,” Swarm and Evolutionary Computation, vol. 61, 100821, 2021.
• [27] Katı M., Kahraman, H. T. “Arz-Talep tabanlı optimizasyon algoritmasinin FDB yöntemi ile iyileştirilmesi: Mühendislik tasarim problemleri üzerine kapsamli bir araştirma,” Mühendislik Bilimleri ve Tasarım Dergisi, c. 8, s. 5, ss. 156-172, 2020.
• [28] I. Ahmadianfar, A. A. Heidari, A. H. Gandomi, X. Chu, and H. Chen, “RUN beyond the metaphor: an efficient optimization algorithm based on Runge Kutta method,” Expert Systems with Applications, vol. 181, 115079, 2021.
• [29] H. Buch, I. N. Trivedi, and P. Jangir, “Moth flame optimization to solve optimal power flow with non-parametric statistical evaluation validation,” Cogent Engineering, vol. 4, no. 1, 1286731, 2017.
• [30] X. Cai, X. Z. Gao, and Y. Xue, “Improved bat algorithm with optimal forage strategy and random disturbance strategy,” International Journal of Bio-Inspired Computation, vol. 8, no. 4, pp. 205-214, 2016.
• [31] Kahraman, H. T. “Rulet elektromanyetik alan optimizasyon (R-EFO) algoritması,” Düzce Üniversitesi Bilim ve Teknoloji Dergisi, c. 8, s.1, ss. 69-80, 2020.
• [32] C. T. Yue, K. V. Price, P. N. Suganthan, J. J. Liang, M. Z. Ali, B. Y. Qu, et al., "Problem Definitions and Evaluation Criteria for the CEC 2020 Special Session and Competition on Single Objective Bound Constrained Numerical Optimization,” Tech. Rep. Zhengzhou University and Nanyang Technological University, 2019.
• [33] F. A. Hashim, K. Hussain, E. H. Houssein, M. S. Mabrouk, and W. Al-Atabany, “Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems,” Applied Intelligence, vol. 51, no. 3, pp. 1531-1551, 2021.
• [34] Q. Chen, B. Liu, Q. Zhang, J. Liang, P. Suganthan, and B. Qu, “Problem definitions and evaluation criteria for CEC 2015 special session on bound constrained single-objective computationally expensive numerical optimization”. Tech. Rep. Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou, China and Technical Report, Nanyang Technological University, 2014.