Kafes Yapıların NSGA-II ve SHAMODE Algoritmaları ile Çok-amaçlı Optimizasyonu

Yıl 2025, Cilt: 41 Sayı: 2, 432 - 446, 30.08.2025

İbrahim Behram Uğur

Öz

Bu çalışmada, büyük ölçekli çok-amaçlı kafes yapı optimizasyonunda Başarı Geçmişine Dayalı Uyarlamalı Çok Amaçlı Diferansiyel Evrim (SHAMODE) ve İkinci Nesil Sıralamalı Genetik Algoritma (NSGA-II) yöntemlerinin performansları incelenmiştir. Amaç, kafes sistemin yapısal ağırlığını ve maksimum düğüm noktası deplasmanlarını minimize ederken, gerilme ve deplasman sınırlayıcılarını da sağlamaktır. Bu iki yöntem ile yapılan optimizasyon sonucunda elde edilen Pareto çözümlerin kalitesi ve dağılımı, Hiperhacim (HV), Nesilsel Uzaklık (GD), Ters Nesilsel Uzaklık (IGD) ve Aralık-Uzunluk Oranı (STE) performans ölçütleri kullanılarak değerlendirilmiştir. Farklı çalıştırmalar sonucu elde edilen en iyi ve ortalama değerler incelendiğinde, SHAMODE’un, NSGA-II’ye kıyasla daha yüksek HV ve daha düşük GD ve IGD değerleri ürettiği görülmüştür. Ayrıca, SHAMODE daha düşük STE değeri ile daha dengeli bir çözüm dağılımı sağlamıştır. Bu sonuçlar, SHAMODE’un karmaşık yapısal optimizasyon problemleri için etkili ve sağlam bir yöntem olduğunu ortaya koymaktadır.

Anahtar Kelimeler

SHAMODE , NSGA-II , Çok amaçlı optimizasyon , Kafes yapı

Multi-Objective Optimization of Truss Structures Using NSGA-II and SHAMODE Algorithms

Öz

This study investigates the performance of Success-History Adaptive Multi-Objective Differential Evolution (SHAMODE) and Non-dominated Sorting Genetic Algorithm II (NSGA-II), methods in solving a large-scale, multi-objective truss optimization problem. The objective is to minimize the structural weight while maximizing displacement performance, subject to stress and displacement constraints. Four widely used performance metrics including Hypervolume, Generational Distance (GD), Inverted Generational Distance (IGD), and Spacing-to-Extent (STE) are employed to evaluate the quality and distribution of the Pareto fronts obtained. Results from independent runs show that SHAMODE consistently produces superior Pareto fronts, as evidenced by higher HV values and significantly lower GD and IGD scores compared to NSGA-II. Furthermore, SHAMODE achieves a more uniform distribution of solutions, indicated by its lower STE values. These findings demonstrate SHAMODE's effectiveness and robustness in handling complex structural optimization problems

Anahtar Kelimeler

SHAMODE , NSGA-II , Multi-objective optimization , Truss

Kaynakça

• K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput., vol. 6, no. 2, 2002, doi: 10.1109/4235.996017.
• F. Zhao, W. Lei, W. Ma, Y. Liu, and C. Zhang, “An improved SPEA2 algorithm with adaptive selection of evolutionary operators scheme for multiobjective optimization problems,” Mathematical Problems in Engineering, vol. 2016. 2016. doi: 10.1155/2016/8010346.
• S. Rostami and F. Neri, “Covariance matrix adaptation pareto archived evolution strategy with hypervolume-sorted adaptive grid algorithm,” Integr. Comput. Aided. Eng., vol. 23, no. 4, 2016, doi: 10.3233/ICA-160529.
• S. Mirjalili, “Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems,” Neural Comput. Appl., vol. 27, no. 4, 2016, doi: 10.1007/s00521-015-1920-1.
• S. Z. Mirjalili, S. Mirjalili, S. Saremi, H. Faris, and I. Aljarah, “Grasshopper optimization algorithm for multi-objective optimization problems,” Appl. Intell., vol. 48, no. 4, 2018, doi: 10.1007/s10489-017-1019-8.
• S. Mirjalili, A. H. Gandomi, S. Z. Mirjalili, S. Saremi, H. Faris, and S. M. Mirjalili, “Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems,” Adv. Eng. Softw., vol. 114, 2017, doi: 10.1016/j.advengsoft.2017.07.002.
• T. Aittokoski and K. Miettinen, “Efficient evolutionary approach to approximate the Pareto-optimal set in multiobjective optimization, UPS-EMOA,” in Optimization Methods and Software, 2010, vol. 25, no. 6. doi: 10.1080/10556780903548265.
• S. Mirjalili, P. Jangir, S. Z. Mirjalili, S. Saremi, and I. N. Trivedi, “Optimization of problems with multiple objectives using the multi-verse optimization algorithm,” Knowledge-Based Syst., vol. 134, 2017, doi: 10.1016/j.knosys.2017.07.018.
• N. Panagant, S. Bureerat, and K. Tai, “A novel self-adaptive hybrid multi-objective meta-heuristic for reliability design of trusses with simultaneous topology, shape and sizing optimisation design variables,” Struct. Multidiscip. Optim., vol. 60, no. 5, 2019, doi: 10.1007/s00158-019-02302-x.
• K. Wansasueb, N. Pholdee, N. Panagant, and S. Bureerat, “Multiobjective meta-heuristic with iterative parameter distribution estimation for aeroelastic design of an aircraft wing,” Eng. Comput., vol. 38, no. 1, 2022, doi: 10.1007/s00366-020-01077-w.
• N. Noilublao and S. Bureerat, “Simultaneous topology, shape and sizing optimisation of a three-dimensional slender truss tower using multiobjective evolutionary algorithms,” Comput. Struct., vol. 89, no. 23–24, 2011, doi: 10.1016/j.compstruc.2011.08.010.
• A. Kaveh and K. Laknejadi, “A hybrid evolutionary graph-based multi-objective algorithm for layout optimization of truss structures,” Acta Mech., vol. 224, no. 2, 2013, doi: 10.1007/s00707-012-0754-5.
• G. G. Tejani, N. Pholdee, S. Bureerat, and D. Prayogo, “Multiobjective adaptive symbiotic organisms search for truss optimization problems,” Knowledge-Based Syst., vol. 161, 2018, doi: 10.1016/j.knosys.2018.08.005.
• V. Mokarram and M. R. Banan, “A new PSO-based algorithm for multi-objective optimization with continuous and discrete design variables,” Struct. Multidiscip. Optim., vol. 57, no. 2, 2018, doi: 10.1007/s00158-017-1764-7.
• T. Techasen, K. Wansasueb, N. Panagant, N. Pholdee, and S. Bureerat, “Simultaneous topology, shape, and size optimization of trusses, taking account of uncertainties using multi-objective evolutionary algorithms,” Eng. Comput., vol. 35, no. 2, 2019, doi: 10.1007/s00366-018-0629-z.
• D. E. C. Vargas, A. C. C. Lemonge, H. J. C. Barbosa, and H. S. Bernardino, “Differential evolution with the adaptive penalty method for structural multi-objective optimization,” Optim. Eng., vol. 20, no. 1, 2019, doi: 10.1007/s11081-018-9395-4.
• A. Kaveh and V. R. Mahdavi, “Multi-objective colliding bodies optimization algorithm for design of trusses,” J. Comput. Des. Eng., vol. 6, no. 1, 2019, doi: 10.1016/j.jcde.2018.04.001.
• N. Panagant, N. Pholdee, S. Bureerat, A. R. Yildiz, and S. Mirjalili, “A Comparative Study of Recent Multi-objective Metaheuristics for Solving Constrained Truss Optimisation Problems,” Arch. Comput. Methods Eng., vol. 28, no. 5, 2021, doi: 10.1007/s11831-021-09531-8.
• J. P. G. Carvalho, É. C. R. Carvalho, D. E. C. Vargas, P. H. Hallak, B. S. L. P. Lima, and A. C. C. Lemonge, “Multi-objective optimum design of truss structures using differential evolution algorithms,” Comput. Struct., vol. 252, 2021, doi: 10.1016/j.compstruc.2021.106544.
• A. C. C. Lemonge, J. P. G. Carvalho, P. H. Hallak, and D. E. C. Vargas, “Multi-objective truss structural optimization considering natural frequencies of vibration and global stability,” Expert Syst. Appl., vol. 165, 2021, doi: 10.1016/j.eswa.2020.113777.
• H. F. Eid, L. Garcia-Hernandez, and A. Abraham, “Spiral water cycle algorithm for solving multi-objective optimization and truss optimization problems,” Eng. Comput., vol. 38, 2022, doi: 10.1007/s00366-020-01237-y.
• S. Kumar et al., “A two-archive multi-objective multi-verse optimizer for truss design,” Knowledge-Based Syst., vol. 270, 2023, doi: 10.1016/j.knosys.2023.110529.
• ISCSO-2024,” International Student competition in Structural optimization.
• J. M. P. Vieira, J. P. G. Carvalho, D. E. C. Vargas, É. C. R. Carvalho, P. H. Hallak, and A. C. C. Lemonge, “Many-Objective Truss Structural Optimization Considering Dynamic and Stability Behaviors,” Dynamics, vol. 5, no. 1, p. 3, 2025.
• R. Tanabe and A. Fukunaga, “Success-history based parameter adaptation for Differential Evolution,” in 2013 IEEE Congress on Evolutionary Computation, CEC 2013, 2013. doi: 10.1109/CEC.2013.6557555.
• R. Tanabe and A. S. Fukunaga, “Improving the search performance of SHADE using linear population size reduction,” in Proceedings of the 2014 IEEE Congress on Evolutionary Computation, CEC 2014, 2014. doi: 10.1109/CEC.2014.6900380