Recent Reviews on Topology Optimization

Abstract

Gradient-based methods are utilized in traditional topology optimization studies. This approach is based on a point-by-point technique, which depends on the gradient information of the objective functions regarded as independent variables. Despite the fast response, this approach can lead them to find local optimal solutions, but it faces problems in defining the global optimal solutions in large-scale problems or high-degree functions. For this reason, non-gradient methods that give better solutions have been developed to solve these struggles. This study examines the nature-inspired methods developed over the last 25 years, which are called Genetic Algorithms, Ant Colony Optimization, Particle Swarm Optimization, and Artificial Neural Networks, and presents flowcharts to illustrate their principles. These methods are clarified via a cantilever beam. According to the results, methods are compared, and Particle Swarm Optimization can provide a reasonable solution to determine the optimal solution. These comparisons are tabulated and may be a guide for researchers.

Keywords

• Topology Optimization
• Optimization Algorithms
• Meta-heuristic Algorithms
• Continuum structural topology

Topoloji Optimizasyonunda Güncel Yaklaşımlar

Abstract

Geleneksel topoloji optimizasyon çalışmalarında eğimli yöntemler olarak belirtilen metotlar kullanılmaktadır. Bu yaklaşım, bir dizi bağımsız değişkene bağlı olarak amaç fonksiyonun türevine dayanan hesaplamalı nokta tekniğine bağlıdır. Bu metotlar, hızlı çözümler vermesine rağmen, kapsamlı işlemler, yüksek mertebeli fonksiyon gibi durumlarda yerel optimum çözümleri bulmakta; küresel sonuçlarda problemlerle karşılaşılmaktadır. Karşılaşılan sorunları çözmek amaçlı daha iyi sonuçlar elde edilen eğimsiz yöntemler geliştirilmiştir. Bu çalışmada, son 25 yılda yapılan eğimsiz yöntemler olarak belirtilen ve doğadan ilham alan Genetik Algoritmalar, Karınca Kolonisi Optimizasyonu, Parçacık Sürüsü Optimizasyonu ve Yapay Sinir Ağları adlı yöntemler hakkında araştırılmalar yapılmış ve çalışma prensipleri akış şeması ile belirtilmiştir. Bu yöntemler, özellikle kiriş örneği ile detaylandırılmıştır. Sonuçlara bağlı olarak, yöntemler karşılaştırılmakta ve Parçacık Sürü Optimizasyonu optimum çözümü belirlemek için uygun bir sonuç sunabilmektedir.Bu karşılaştırmalara dayanarak, araştırmacılara rehber olabilecek kıyaslama tablosu oluşturulmuştur.

Keywords

• Topoloji Optimizasyonu
• Optimizasyon Algoritmaları
• Sezgi üstü Algoritmalar
• Süreklilik yapısal topolojisi

References

1. [1] Mooneghi, M. A., Kargarmoakhar, R. Aerodynamic mitigation and shape optimization of buildings: review. Journal of Building Engineering, 6, (2016), 225-235. doi: 10.1016/j.jobe.2016.01.009
2. [2] Wang, S. Y., & Tai, K. Graph representation for structural topology optimization using genetic algorithms. Computers & Structures, 82(20–21), (2004), 1609–1622. doi: 10.1016/j.compstruc.2004.05.005
3. [3] Ahmed, F., Deb, K., Bhattacharya, B., Structural topology optimization using multi-objective genetic algorithm with constructive solid geometry representation. Applied Soft Computing, 39, (2016), 240-250. doi: 10.1016/j.asoc.2015.10.063
4. [4] Bendsøe, M.P. Optimal shape design as a material distribution problem. Structural Optimization 1, 193–202 (1989). doi: 10.1007/BF01650949
5. [5] Zhou, M., & Rozvany, G. I. N. The COC algorithm, part II: Topological, geometrical and generalized shape optimization. Computer Methods in Applied Mechanics and Engineering, 89(1–3),(1991), 309–336. doi: 10.1016/0045-7825(91)90046-9
6. [6] Allaire, G., Jouve, F., & Toader, A.-M. A level-set method for shape optimization. Comptes Rendus. Mathématique, 334(12), (2002),1125–1130. doi: 10.1016/s1631-073x(02)02412-3
7. [7] Wang, M. Y., Wang, X., & Guo, D.. A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering, 192(1–2), (2003), 227–246. doi: 10.1016/s0045-7825(02)00559-5
8. [8] Jan Sokolowski, Antoni Zochowski. On Topological Derivative in Shape Optimization. [Research Report] RR-3170, INRIA. (1997), pp.31.

9. [9] Bourdin, B., & Chambolle, A. Design-dependent loads in topology optimization. ESAIM: Control, Optimisation and Calculus of Variations, 9, (2003) 19–48. doi: 10.1051/cocv:2002070
10. [10] Xie, Y. M., & Steven, G. P. A simple evolutionary procedure for structural optimization. Computers & Structures, 49(5), (1993), 885–896. doi: 10.1016/0045-7949(93)90035-c
11. [11] Katoch, S., Chauhan, S.S. & Kumar, V. A review on genetic algorithm: past, present, and future. Multimed Tools Appl 80, (2021), 8091–8126. doi: 10.1007/s11042-020-10139-6
12. [12] A. Lambora, K. Gupta and K. Chopra, "Genetic Algorithm- A Literature Review," 2019 International Conference on Machine Learning, Big Data, Cloud and Parallel Computing (COMITCon), Faridabad, India, 2019, pp. 380-384, doi: 10.1109/COMITCon.2019.8862255.
13. [13] Lingaraj, Haldurai. A Study on Genetic Algorithm and its Applications. International Journal of Computer Sciences and Engineering, 4, (2016), 139-143.
14. [14] De Jong, K. Learning with genetic algorithms: An overview. Mach Learn 3, (1988), 121–138. doi: 10.1007/BF00113894
15. [15] Ohsaki, M., Genetic algorithm for topology optimization of trusses, Computers&Structures, 57(2), (1995), 219-225.
16. [16] Wang, S.Y., Tai, K., Wang, M, Y., An enhanced genetic algorithm for structural topology optimization. Int. J. Numer. Meth. Engng, 65, (2006), 18-44. doi : 10.1002/nme.1435
17. [17] Chapman, C.D., Structural topology optimization via the genetic algorithm, Master Thesis, Massachusetts Instıtute of Technology, Massachusetts, (1994).
18. [18] Kaveh, A., Kalatjari, V., Topology optimization of trusses using genetic algorithm, force method and graph theory. Int. J. Numer. Meth. Engng, 58, (2003), 771-791. doi: 10.1002/nme.800
19. [19] Kawamura, H., Ohmori, H. & Kito, N. Truss topology optimization by a modified genetic algorithm. Struct Multidisc Optim 23, (2002), 467–473. doi: 10.1007/s00158-002-0208-0
20. [20] Aguilar Maderia, J.F., Rodrigues, H. Pina, H., Multi-objective optimization of structures topology by genetic algorithms. Advances in Engineering Software, 36, (2005), 21-28. doi: 10.1016/j.advengsoft.2003.07.001
21. [21] Wang, S.Y., Tai, K., Structural topology design optimization using Genetic Algorithms with a bit-array representation, Comput. Methods Appl.Mech. Engrg, 194, (2005), 3749-3770. doi:10.1016/j.cma.2004.09.003
22. [22] Dorigo, M., Birattari., M., Stutzle, T., Ant colony optimization. IEEE Computational Intelligence Magazine, 1(4), 2006, 28-39. doi: 10.1109/MCI.2006.329691
23. [23] Dorigo, M.,Blum, C., Ant colony optimization theory: A survey, Theoretical Computer Science,344(2),(2005), 243-278. doi: 10.1016/j.tcs.2005.05.020.
24. [24] Hasançebi, O. & Çarbas, S., Ant colony search method in practical structural optimization. Int. J. Optim. Civil Eng, 1, (2011), 91-105.
25. [25] Socha, K., Sampels, M., Manfrin, M. Ant Algorithms for the University Course Timetabling Problem with Regard to the State-of-the-Art. In: Cagnoni, S., et al. Applications of Evolutionary Computing. EvoWorkshops 2003. Lecture Notes in Computer Science, 2611. Springer, (2003), Berlin, Heidelberg. doi: 10.1007/3-540-36605-9_31
26. [26] Parpinelli, R. S., Lopes, H. S., & Freitas, A. A., Data mining with an ant colony optimization algorithm. IEEE Transactions on Evolutionary Computation, 6(4), (2002), 321–332. doi: 10.1109/tevc.2002.802452
27. [27] Alupoaei, S., & Katkoori, S. Ant Colony System Application to macrocell overlap removal. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 12(10), (2004), 1118–1123. doi: 10.1109/tvlsi.2004.832926
28. [28] L. M. Gambardella, E. Taillard, and G. Agazzi. 1999. MACS-VRPTW: A Multiple Ant Colony System for Vehicle Routing Problems with Time Windows. Technical Report. Istituto Dalle Molle Di Studi Sull Intelligenza Artificiale.
29. [29] Guéret, C., Monmarché, N., Slimane, M. Ants Can Play Music. In: Dorigo, M., Birattari, M., Blum, C., Gambardella, L.M., Mondada, F., Stützle, T. (eds) Ant Colony Optimization and Swarm Intelligence. ANTS 2004. Lecture Notes in Computer Science, vol 3172. Springer, (2004), Berlin, Heidelberg. doi: 10.1007/978-3-540-28646-2_29
30. [30] Xu, Q., Mao, J., Jin, Z., Simulated annealing-based ant colony algorithm for tugboat scheduling optimization. Mathematical Problems in Engineering, (2012). doi: 10.1155/2012/246978.
31. [31] Kaveh, A., Hassani, B., Shojaee, S., & Tavakkoli, S. M. Structural topology optimization using ANT colony methodology. Engineering Structures, 30(9), (2008), 2559–2565. doi: 10.1016/j.engstruct.2008.02.012
32. [32] Luh, G.-C., & Lin, C.-Y. Structural topology optimization using ant colony optimization algorithm. Applied Soft Computing, 9(4), (2009), 1343–1353. doi: 10.1016/j.asoc.2009.06.001
33. [33] Kaveh, A., Talatahari, S., An improved ant colony optimization for the design of planar steel frames. Engineering Structures, 32, (2010), 864-873. doi: 10.1016/j.engstruct.2009.12012
34. [34] Angelo, J.S., Bernardino, H.S., Barbosa, H.J.C., Multi-objective ant colony approaches for structural optimization problems.Proceedings of the Eleventh International Conference on Computational Structures Technology, Stirlingshire, Scotland, 2012.
35. [35] Wang, D., Tan, D., & Liu, L. Particle Swarm Optimization Algorithm: An overview. Soft Computing, 22(2), (2018), 387–408. doi: 10.1007/s00500-016-2474-6
36. [36] Jain, N.K., Nangia, U., Jain, J., A Review of particle swarm optimization. J.Inst.Eng.India Ser. B, 99(4), (2018), 407-411. doi: 10.1007/s40031-018-0323-y
37. [37] Zeng, N., Qiu, H., Wang, Z., Liu, W., Zhang, H., & Li, Y. A new switching-delayed-PSO-based optimized SVM algorithm for diagnosis of alzheimer’s disease. Neurocomputing, 320, (2018), 195–202. doi: 10.1016/j.neucom.2018.09.001
38. [38] Jain, I., Jain, V. K., & Jain, R. Correlation feature selection based improved-binary particle swarm optimization for gene selection and cancer classification. Applied Soft Computing, 62, (2018), 203–215. doi: 10.1016/j.asoc.2017.09.038
39. [39] Zarei, A., Mousavi, SF., Eshaghi Gordji, M. et al. Optimal Reservoir Operation Using Bat and Particle Swarm Algorithm and Game Theory Based on Optimal Water Allocation among Consumers. Water Resour Manage 33, (2019), 3071–3093. doi: 10.1007/s11269-019-02286-9
40. [40] Cao, Y., Ye, Y., Zhao, H., Jiang, Y., Wang, H., Shang, Y., & Wang, J. Remote Sensing of water quality based on HJ-1A HSI imagery with modified discrete binary particle swarm optimization-partial least squares (MDBPSO-PLS) in inland waters: A case in Weishan Lake. Ecological Informatics, 44, (2018), 21–32. doi: 10.1016/j.ecoinf.2018.01.004
41. [41] Mohebbi, A., Achiche, S., & Baron, L. Integrated and concurrent detailed design of a mechatronic quadrotor system using a fuzzy-based particle swarm optimization. Engineering Applications of Artificial Intelligence, 82, (2019), 192–206. doi: 10.1016/j.engappai.2019.03.025
42. [42] Song, M., Chen, K., & Wang, J. Three-dimensional wind turbine positioning using gaussian particle swarm optimization with differential evolution. Journal of Wind Engineering and Industrial Aerodynamics, 172, (2018), 317–324. doi: 10.1016/j.jweia.2017.10.032
43. [43] Shen, J., Han, L. RETRACTED ARTICLE: Design process optimization and profit calculation module development simulation analysis of financial accounting information system based on particle swarm optimization (PSO). Inf Syst E-Bus Manage 18, (2020), 809–822. doi: 10.1007/s10257-018-00398-0
44. [44] Yi, T., Zheng, H., Tian, Y., & Liu, J. Intelligent prediction of transmission line project cost based on least squares support vector machine optimized by particle swarm optimization. Mathematical Problems in Engineering, (2018), 1–11. doi: 10.1155/2018/5458696
45. [45] Luh, G.-C., Lin, C.-Y., & Lin, Y.-S. A binary particle swarm optimization for continuum structural topology optimization. Applied Soft Computing, 11(2), (2011), 2833–2844. doi: 10.1016/j.asoc.2010.11.013
46. [46] Mortazavi, A., Toğan, V., Simuitaneous size, shape and topology optimization of truss structures using integrated particle swarm optimizer. Struct Multidisc Optim, 54, (2016), 715-736. doi: 10.1007/s00158-016-1449-7
47. [47] Dongare, A. D., Kharde, R. R., & Kachare, A. D. Introduction to artificial neural network. International Journal of Engineering and Innovative Technology (IJEIT), 2(1), (2012), 189-194.
48. [48] Abdolrasol, M.G.M., Hussain, S.M.S., Ustun, T.S., Sarker, M.R., Hannan, M.A., Mohamed, R., Ali, J.A., Mekhilef, S., Milad, A., Artificial neural networks based optimization techniques: a review. Electronics, 10, (2021), 2689. doi: 10.3390/electronics10212689
49. [49] Lee Sian Choon, Samsudin, A., & Budiarto, R. (n.d.). Lightweight and cost-effective MPEG video encryption. Proceedings. 2004 International Conference on Information and Communication Technologies: From Theory to Applications, 2004, 525–526. doi: 10.1109/ictta.2004.1307863
50. [50] D. Cho, Y. -W. Tai and I. S. Kweon, "Deep Convolutional Neural Network for Natural Image Matting Using Initial Alpha Mattes," in IEEE Transactions on Image Processing, vol. 28, no. 3, March 2019, pp. 1054-1067. doi: 10.1109/TIP.2018.2872925.
51. [51] LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, (2015), 436–444. doi: 10.1038/nature14539
52. [52] Himmelblau, D.M., Applications of artificial neural networks in chemical engineering. Korean J. Chem. Eng., 17(4), (2000), 373-392.
53. [53] Adeli, H., Neural networks in civil engineering 1989-2000. Computer-aided civil and infrastructure engineering, 16, (2001), 126-142.
54. [54] Banga, Saurabh & Gehani, Harsh & Bhilare, Sanket & Patel, Sagar & Kara, Levent. (2018). 3D Topology Optimization using Convolutional Neural Networks. 10.48550/arXiv.1808.07440.
55. [55] Meng, Z., Lv, S., Gao, Y., Zhong, C., & An, K. Data-driven reliability-based topology optimization by using the extended multi scale finite element method and neural network approach. Computer Methods in Applied Mechanics and Engineering, 438, (2025), 117837. doi: 10.1016/j.cma.2025.117837
56. [56] Chandrasekhar, A., Suresh, K. TOuNN: Topology Optimization using Neural Networks. Struct Multidisc Optim 63, (2021), 1135–1149. doi: 10.1007/s00158-020-02748-4
57. [57] Xing, Y., & Tong, L. A stochastic gradient online learning and prediction method for accelerating structural topology optimization using recurrent neural network. Engineering Structures, 338, (2025), 120507. doi: 10.1016/j.engstruct.2025.120507
58. [58] Nayak, J., Swapnarekha, H., Naik, B., Dhiman, G., Vimal, S. 25 years of particle swarm optimization: flourishing voyage of two decades. Archives of Computational Methods in Engineering, 30, (2023), 1663-1725. doi: 10.1007/s11831-022-09849-x.
59. [59] Alhijawi, B., Awajan, A. Genetic algorithms: theory, genetic operators, solutions, and applications. Evolutionary Intelligence, 17, (2024), 1245-1256. Doi: 10.1007/s12065-023-00822-6
60. [60] M. R. G. Meireles, P. E. M. Almeida and M. G. Simoes, A comprehensive review for industrial applicability of artificial neural networks, in IEEE Transactions on Industrial Electronics, 50(3), (2003), 585-601. doi: 10.1109/TIE.2003.812470.