A fast hybrid refining optimization with sensitivity-based partitioning approach for truss structures

Document Type : Civil Article


1 PhD Student, Civil Engineering Department, University of Sistan and Baluchestan, Zahedan, Iran

2 Professor, Civil Engineering Department, University of Sistan and Baluchestan, Zahedan, Iran

3 Associate Professor, Civil Engineering Department, University of Sistan and Baluchestan, Zahedan, Iran


So far, several methods have been utilized for truss optimization where metaheuristic thechniqes have been used as one of the most common methods for such purpose. These thechniqes have received much attention due to their independence from gradient information and efficient global search property. In some of the metaheuristic thechniqes, random generation of the preliminary population leads to creation of repetitive population, dependency of final optimum solution on preliminary population, increasing of the number of analyses and reduction of the algorithm efficiency. To overcome these disadvantages, the present study employs some intelligent thechniqes for the generation and the selection of the population. So, a new metaheuristic algorithm called SPR is proposed for discrete truss optimization problems. The SPR algorithm is based on the sensitivity of the elements, the partitioning of the search space and the rebirthing of the optimization procedure. The structural members which are more sensitive to changing the cross-sectional areas are recognized through the procedure. In order to find the best approximate solution for any design variable, the search space is discritized to some partitions. Rebirthing technique searches for better optimum solutions around the last local optimum point for any design variable to end the stagnation states. The performance of the proposed algorithm is investigated using several benchmark size optimization problems of truss structures from the literature. In comparison to the available results in the literature, the proposed SPR algorithm showed capable of obtaining the optimum design with much lesser computational attempt.


Main Subjects


[1] M. Sonmez, “Discrete optimum design of truss structures using artificial bee colony algorithm”, Struct. Multidisc. Opt., Vol. 43, No. 1, January 2011, pp. 85-97.
[2] L.J. Li, Z.B. Huang and F. Liu, “A heuristic particle swarm optimization method for truss structures with discrete variables”, Comput. Struct., Vol. 87, No. 7-8, April 2009, pp. 435-443.
[3] S.J. Wu and P.T. Chow, “Steady-state genetic algorithms for discrete optimization of trusses”, Comput. Struct., Vol. 56, No. 6, September 1995, pp. 979-991.
[4] A. Sadollah, A. Bahreininejad, H. Eskandar and M. Hamdi, “Mine blast algorithm for optimization of truss structures with discrete variables”, Comput. Struct., Vol. 102-103, July 2012, pp. 49-63.
]5[ محمد رضا رضایی پژند و خسرو خالقی، "الگوی هندسه‌ی بهینه‌ی شکل سدهای قوسی بتنی"، نشریه مدل‌سازی در مهندسی، دوره 8، شماره 20، بهار 1389، صفحه 1-15.
]6[ علی قدوسیان، مجتبی شیخی و محمد رضا رستمی، "بهینه سازی شکل سطح تماس برای سازه ها تحت بارگذاری چندگانه به کمک روش تکاملی دوطرفه"، نشریه مدل‌سازی در مهندسی، دوره 10، شماره 30، پاییز 1391، صفحه 77-86.
]7[ علی قدوسیان و مجتبی شیخی، "بهینه کردن موقعیت تکیه گاه های سازه جهت حداقل کردن ممان خمشی با الگوریتم گروه ذرات تحت بارگذاری چندگانه"، نشریه مدل‌سازی در مهندسی، دوره 8، شماره 22، پاییز 1389، صفحه 59-67.
[8] O. Hasancebi and S.K. Azad, “Adaptive dimensional search: A new metaheuristic algorithm for discrete truss sizing optimization”, Comput. Struct., Vol. 154, July 2015, pp. 1-16.
]9[ علی قدوسیان، امین نیکوبین و مجتبی ریاحی وزواری، "بهینه سازی شکل و اندازه -شکل سازه‌های خرپا با روش بهینه سازی الگوریتم مثلث بهینه‌گر"، نشریه مدل‌سازی در مهندسی، دوره 14، شماره 46، پاییز 1395، صفحه 51-60.
[10] J.S. Arora and E.J. Haug, “Methods of design sensitivity analysis in structural optimization”, American Institute of Aeronautics and Astronautics, Vol. 17, No. 9, September 1979, pp. 970-974.
[11] J.L.T. Santos and K.K. Choi, “Sizing design sensitivity analysis of non-linear structural systems. Part II: Numerical method”, Int. J. for Numer. Meth. Eng., Vol. 26, No. 9, September 1988, pp. 2097-2114.
[12] C.C. Wu and J.S. Arora, “Design sensitivity analysis of non-linear buckling load”, Comput. Mech., Vol. 3, No. 2, March 1988, pp. 129-140.
[13] M. Ohsaki, “Simultaneous optimization of topology and geometry of a regular plane truss”, Comput. Struct., Vol. 66, No. 1, January 1998, pp. 69-77.
[14] P. Kolakowski and J. Holnicki-Szulc, “Sensitivity analysis of truss structures (virtual distortion method approach)”, Int. J. Numer. Meth. Engng., Vol. 43, No. 6, November 1998, pp. 1085-1108.
[15] M. Ohsaki, “Sensitivity analysis and optimization corresponding to a degenerate critical point”, Int. J. Solids Struct., Vol. 38, No. 28-29, July 2001, pp. 4955-4967.
[16] D. Wang, W.H. Zhang and J.S. Jiang, “Combined shape and sizing optimization of truss structures”, Comput. Mech., Vol. 29, No. 4-5, October 2002, pp. 307-312.
[17] D. Wang, W.H. Zhang and J.S. Jiang, “Truss shape optimization with multiple displacement constraints” Comput. Methods Appl. Mech. Engrg., Vol. 191, No. 33, June 2002, pp. 3597-3612.
[18] N.L. Pedersen and A.K. Nielsen, “Optimization of practical trusses with constraints on eigenfrequencies, displacements, stresses, and buckling” Struct. Multidisc. Optim., Vol. 25, No. 5-6, December 2003, pp. 436-445.
[19] B. Dizangian and M.R. Ghasem, “A fast marginal feasibility search method in size optimization of truss structures”, Asian Journal of Civil Engineering (BHRC), Vol. 16, No. 5, October 2015, pp. 567-585.
[20] B. Dizangian and M.R. Ghasem, “Ranked-based sensitivity analysis for size optimization of structures”, J. Mech. Design., Vol. 137, No. 12, October 2015, Paper No. MD-15-1022.
[21] S.K. Azad, O. Hasancebi and M.P. Saka, “Guided stochastic search technique for discrete sizing optimization of steel trusses: A design-driven heuristic approach”, Comput. Struct., Vol. 134, April 2014, pp. 62-74.
[22] V. Ho-Huu, T. Nguyen-Thoi, T. Vo-Duy and T. Nguyen-Trang, “An adaptive elitist differential evolution for optimization of truss structures with discrete design variables”, Comput. Struct., Vol. 165, No. C, March 2016, pp. 59-75.
[23] M.Y. Cheng, D. Prayogo, Y.W. Wu and M.M. Lukito, “A Hybrid Harmony Search algorithm for discrete sizing optimization of truss structure”, Automat. Constr., Vol. 69, September 2016, pp. 21-33.
[24] D.T. Le, D.K. Bui, T.D. Ngo, Q.H. Nguyen and H. Nguyen-Xuan, “A novel hybrid method combining electromagnetism-like mechanism and firefly algorithms for constrained design optimization of discrete truss structures”, Comput. Struct., Vol. 212, February 2019, pp. 20-42.
[25] S. Gholizadeh, “Optimum design of structures by an improved particle swarm algorithm”, Asian J. Civil Eng., Vol. 11, No. 6, December 2010, pp. 777-793.
[26] H. Eskandar, A. Sadollah and A. Bahreininejad, “Weight optimization of truss structures using water cycle algorithm”, Int. J. Optim. Civil Eng., Vol. 3, No. 1, March 2013, pp. 115-129.
[27] S. Mirjalili and A. Lewis, “The Whale Optimization Algorithm”, Adv. Eng. Softw., Vol. 95, May 2016, pp. 51-67.
]28[ سید مجتبی سیدزاده اطاقسرائی، مجتبی جعفری صمیمی و سید رضا سیدزاده اطاقسرائی ، "بهینه سازی وزن خرپای فولادی توسط الگوریتم بهینه سازی مبتنی بر آموزش-یادگیری"، نشریه نشریه علمی و پژوهشی سازه و فولاد، سال 12، شماره 19، بهار و تابستان 1395، صفحه 27-39.
[29] J. Cai and G. Thierauf, “Evolution strategies for solving discrete optimization problems” Adv. Eng. Softw., Vol. 25, No. 2-3, March–April 1996, pp. 177-183.
[30] M.R. Ghasemi, E. Hinton and R.D. Wood, “Optimization of trusses using genetic algorithms for discrete and continuous variables”, Eng. Comput., Vol. 16, No. 3, March 1999, pp. 272-301.
[31] T. Dede, S. Bekiroglu and Y. Ayvaz, “Weight minimization of trusses with genetic algorithm”, Appl. Soft Comput., Vol. 11, No. 2, March 2011, pp. 2565-2575.
[32] Y. Zhang, Y. Hou and S. Liu, “A new method of discrete optimization for cross-section selection of truss structures”, Engineering Optimization, Vol. 46, No. 8, October 2013, pp. 1052-1073.
[33] K. Grygierek, “Optimization of trusses with self-adaptive approach in genetic algorithms”, Architecture Civil Engineering Environment, Vol. 9, No. 4, December 2016, pp. 67-78.
[34] M.H. Talebpour, A. Kaveh and V.R. Kalatjari, “Optimization of skeletal structures using a hybridized ant colony–harmony search-genetic algorithm”, Iran J. Sci. Technol. Trans. Civ. Eng., Vol. 38, No. C1, February 2014, pp. 1-20.
[35] S.K. Azad and O. Hasançebi, “An elitist self-adaptive step-size search for structural design optimization”, Appl. Soft Comput., Vol. 19, June 2014, pp. 226-235.
[36] S. Gholizade and R. Sojoudizadeh, “Modified Sine-Cosine Algorithm for Sizing Optimization of Truss Structures with Discrete Design Variables”, Int. J. Optim. Civil Eng., Vol. 9, No. 2, April 2019, pp. 195-212.
[37] C.M. Paramo, “Modified simulated annealing algorithm for discrete sizing optimization of truss structure”, Jordan Journal of Civil Engineering, Vol. 12, No. 4, January 2018, pp. 683-697.
[38] S.O. Degertekin, “Improved harmony search algorithms for sizing optimization of truss structures”, Comput. Struct., Vol. 92-93, February 2012, pp. 229-241.