Abstract
The truss sizing optimization problem, where the cross-sectional areas of truss members are optimized, is a nonlinear and complex problem. The problem becomes quite challenging especially when a large number of variables exist. Metaheuristics proved to be working efficiently for this problem type. Flower pollination algorithm (FPA) is a recently developed metaheuristic search algorithm, and it has been successfully applied to structural optimization problems in the literature. In this paper, the formulation of FPA is enhanced to improve its local and global searching capabilities for better performance. For this purpose, a hybrid algorithm is developed by imitating the algorithmic structure of FPA while the mutation and crossover operators of differential evolution (DE) with elitism strategy are replaced with Levy flights of FPA to explore search space more efficiently and exploitation ability of FPA is improved with the addition of mutation factor and crossover operator of DE working in the local search formula of FPA. The performance of the proposed algorithm is tested with benchmark truss sizing optimization problems and the results are compared with other metaheuristics. The results show that hybrid FPA improves the capabilities of the original one, produces more robust solutions than both FPA and DE, generates quite competitive results for the test problems compared to the previous studies with different algorithms. Therefore, the hybrid FPA proves to be a promising optimization algorithm alternative for engineering practice.
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References
Erbatur F, Hasançebi O, Tütüncü İ, Kılıç H (2000) Optimal design of planar and space structures with genetic algorithms. Comput Struct Struct 75:209–224
Rajan SD (1995) Sizing, shape, and topology design optimization of trusses using Genetic Algorithm. J Struct Eng 121:1480–1487
Lee KS, Geem ZW (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82:781–798
Altun M, Pekcan O (2017) A modified approach to cross entropy method: elitist stepped distribution algorithm. Appl Soft Comput J 58
Goldberg DE (1989) Genetic algorithms in search, pptimization, and machine learning. Addison Wesley, Boston
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE international conference on neural networks, 1995. Proceedings, vol 4, pp 1942–1948
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science (80-) 220:671–680
Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci (Ny) 179:2232–2248
Rao RV, Savsani VJ, Vakharia DP (2011) Teaching–learning-based optimization: A novel method for constrained mechanical design optimization problems. Comput Des 43:303–315
Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simul 76:60–68
Dorigo M, Stützle T (2004) Ant colony optimization
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471
Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: Proceedings of 2009 world congress on nature and biologically inspired computing, NABIC 2009, pp 210–214
Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2013) Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems. Appl Soft Comput 13:2592–2612
Kaveh A, Mahdavi VR (2014) Colliding bodies optimization: a novel meta-heuristic method. Comput Struct 139:18–27
Yalcin Y, Pekcan O (2020) Nuclear fission-nuclear fusion algorithm for global optimization: a modified Big Bang-Big Crunch algorithm. Neural Comput Appl 32:2751–2783
Hasançebi O, Azad SK (2015) Adaptive dimensional search: a new metaheuristic algorithm for discrete truss sizing optimization. Comput Struct 154:1–16
Hasançebi O, Azad K (2012) An efficient metaheuristic algorithm for engineering optimization: SOPT. Int J Optim Civ Eng 2:479–487
Erol OK, Eksin I (2006) A new optimization method: big bang-big crunch. Adv Eng Softw 37:106–111
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61
Venkata Rao R (2016) Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int J Ind Eng Comput 7:19–34
Cheng M-Y, Prayogo D (2014) Symbiotic organisms search: a new metaheuristic optimization algorithm. Comput Struct 139:98–112
Kaveh A, Dadras Eslamlou A (2020) Water strider algorithm: a new metaheuristic and applications. Structures 25:520–541
Zhang Y, Jin Z (2020) Group teaching optimization algorithm: a novel metaheuristic method for solving global optimization problems. Expert Syst Appl 148:113246
Toğan V, Daloğlu AT (2016) Genetic algorithms for optimization of 3D truss structures. In: Metaheuristics and optimization in civil engineering, pp 115–134
Gomes HM (2011) Truss optimization with dynamic constraints using a particle swarm algorithm. Expert Syst Appl 38:957–968
Sonmez M (2011) Artificial Bee Colony algorithm for optimization of truss structures. Appl Soft Comput 11:2406–2418
Wang Z, Tang H, Li P (2009) Optimum design of truss structures based on differential evolution strategy. In: International conference on information engineering and computer science, pp 1–5
Camp CV, Bichon BJ (2004) Design of space trusses using ant colony optimization. J Struct Eng 130:741–751
Degertekin SO, Hayalioglu MS (2013) Sizing truss structures using teaching-learning-based optimization. Comput Struct 119:177–188
Camp CV (2007) Design of space trusses using big bang-big crunch optimization. J Struct Eng 133:999–1008
Gandomi AH, Talatahari S, Yang X-S, Deb S (2013) Design optimization of truss structures using cuckoo search algorithm. Struct Des Tall Spec Build 22:1330–1349
Hasançebi O, Teke T, Pekcan O (2013) A bat-inspired algorithm for structural optimization. Comput Struct 128:77–90
Gonçalves MS, Lopez RH, Miguel LFF (2015) Search group algorithm: a new metaheuristic method for the optimization of truss structures. Comput Struct 153:165–184
Toğan V, Daloğlu AT (2008) An improved genetic algorithm with initial population strategy and self-adaptive member grouping. Comput Struct 86:1204–1218
Ho-Huu V, Nguyen-Thoi T, Vo-Duy T, Nguyen-Trang T (2016) An adaptive elitist differential evolution for optimization of truss structures with discrete design variables. Comput Struct 165:59–75
Hadidi A, Kazemzadeh Azad S, Kazemzadeh Azad S (2010) Structural optimization using artificial bee colony algorithm. In: 2nd international conference on engineering optimization (EngOpt)
Kumar S, Tejani GG, Mirjalili S (2019) Modified symbiotic organisms search for structural optimization. Eng Comput 35:1269–1296
Hasançebi O, Kazemzadeh Azad S, Kazemzadeh Azad S (2013) Automated sizing of truss structures using a computationally improved SOPT algorithm. Int J Optim Civ Eng 3:209–221
Kaveh A, Bakhshpoori T, Afshari E (2014) An efficient hybrid particle swarm and swallow swarm optimization algorithm. Comput Struct 143:40–59
Cheng M-Y, Prayogo D, Wu Y-W, Lukito MM (2016) A hybrid harmony search algorithm for discrete sizing optimization of truss structure. Autom Constr 69:21–33
Yang XS (2012) Flower pollination algorithm for global optimization. Lect Notes Comput Sci (including Subser Lect Notes Artif Intell Lect Notes Bioinformatics) 7445 LNCS:240–249
Abdel-Basset M, Shawky LA (2019) Flower pollination algorithm: a comprehensive review. Artif Intell Rev 52:2533–2557
Kayabekir AE, Bekdaş G, Nigdeli SM, Yang X-S (2018) A comprehensive review of the flower pollination algorithm for solving engineering problems. In: Yang X-S (ed) Nature-inspired algorithms and applied optimization. Springer International Publishing, Cham, pp 171–188
Alyasseri ZAA, Khader AT, Al-Betar MA et al (2018) Variants of the flower pollination algorithm: a review. In: Yang X-S (ed) Nature-inspired algorithms and applied optimization. Springer International Publishing, Cham, pp 91–118
Bekdaş G, Niğdeli SM, Yang X-S (2015) Sizing optimization of truss structures using flower pollination algorithm. Appl Soft Comput 37:322–331
Abdel-Basset M, El-Shahat D, El-Henawy I (2019) Solving 0–1 knapsack problem by binary flower pollination algorithm. Neural Comput Appl 31:5477–5495
Strange R, Yang AY, Cheng L (2019) Discrete flower pollination algorithm for solving the symmetric travelling salesman problem. In: 2019 IEEE symposium series on computational intelligence, pp 2130–2137
Salgotra R, Singh U (2017) Application of mutation operators to flower pollination algorithm. Expert Syst Appl 79:112–129
Dubey HM, Pandit M, Panigrahi BK (2015) A biologically inspired modified flower pollination algorithm for solving economic dispatch problems in modern power systems. Cognit Comput 7:594–608
Zhang W, Yang Y, Zhang S et al (2016) A new manufacturing service selection and composition method using improved flower pollination algorithm. Math Probl Eng 2016:7343794
Chakraborty D, Saha S, Dutta O (2014) DE-FPA: a hybrid differential evolution-flower pollination algorithm for function minimization. In: 2014 international conference on high performance computing and applications (ICHPCA), pp 1–6
Zhou Y, Wang R, Luo Q (2016) Elite opposition-based flower pollination algorithm. Neurocomputing 188:294–310
Ku-Mahamud KR (2015) Hybrid ant colony system and flower pollination algorithms for global optimization. In: 2015 9th international conference on IT in Asia (CITA), pp 1–9
Yang XS, Deb S, He X (2013) Eagle strategy with flower algorithm. In: International conference on advances in computing, communications and informatics. Mysore, India, pp 1213–1217
Wang R, Zhou Y, Zhao C, Wu H (2015) A hybrid flower pollination algorithm based modified randomized location for multi-threshold medical image segmentation. Biomed Mater Eng 26:S1345–S1351
Wang R, Zhou Y, Qiao S, Huang K (2016) Flower pollination algorithm with bee pollinator for cluster analysis. Inf Process Lett 116:1–14
Chakraborty D, Saha S, Maity S (2015) Training feedforward neural networks using hybrid flower pollination-gravitational search algorithm. In: 2015 international conference on futuristic trends on computational analysis and knowledge management (ABLAZE), pp 261–266
Dubey HM, Pandit M, Panigrahi BK (2015) Hybrid flower pollination algorithm with time-varying fuzzy selection mechanism for wind integrated multi-objective dynamic economic dispatch. Renew Energy 83:188–202
Abdel-Baset, Mohamed Hezam IM (2015) An effective hybrid flower pollination and genetic algorithm for constrained optimization problems. Adv Eng Technol Appl 4:27–34
Altun M, Yalcin Y, Pekcan O (2020) A hybrid cuckoo search algorithm for cost optimization of mechanically stabilized earth walls. In: Dey N (ed) Applications of cuckoo search algorithm and its variants. Springer STNIC Series
Rajeev S, Krishnamoorthy CS (1992) Discrete optimization of structures using genetic algorithms. J Struct Eng 118:1233–1250
Dede T (2014) Application of teaching-learning-based-optimization algorithm for the discrete optimization of truss structures. KSCE J Civ Eng 18:1759–1767
Li LJ, Huang ZB, Liu F, Wu QH (2007) A heuristic particle swarm optimizer for optimization of pin connected structures. Comput Struct 85:340–349
Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2012) Mine blast algorithm for optimization of truss structures with discrete variables. Comput Struct 102–103:49–63
Xiang B, Chen R, Zhang T (2009) Optimization of trusses using simulated annealing for discrete variables. In: 2009 international conference on image analysis and signal processing, pp 410–414
Sonmez M (2011) Discrete optimum design of truss structures using artificial bee colony algorithm. Struct Multidiscip Optim 43:85–97
Capriles PVSZ, Fonseca LG, Barbosa HJC, Lemonge ACC (2007) Rank-based ant colony algorithms for truss weight minimization with discrete variables. Commun Numer Methods Eng 23:553–575
Kale IR, Kulkarni AJ (2018) Cohort intelligence algorithm for discrete and mixed variable engineering problems. Int J Parallel Emergent Distrib Syst 33:627–662
Degertekin SO (2012) Improved harmony search algorithms for sizing optimization of truss structures. Comput Struct 92–93:229–241
Lu YC, Jan JC, Hung SL, Hung GH (2013) Enhancing particle swarm optimization algorithm using two new strategies for optimizing design of truss structures. Eng Optim 45:1251–1271
Koohestani K, Kazemzadeh Azad S (2009) An adaptive real-coded genetic algorithm for size and shape optimization of truss structures. In: Topping BHV, Tsompanakis Y (eds) The first international conference on soft computing technology in civil, structural and environmental engineering. Civil-Comp Press, Stirlingshire
Azad SK, Hasançebi O, Azad SK, Erol OK (2013) Upper bound strategy in optimum design of truss structures: a big bang-big crunch algorithm based application. Adv Struct Eng 16:1035–1046
Li L, Huang Z, Liu F (2006) An improved particle swarm optimizer for truss structure optimization. In: Wang Y, Cheung Y, Liu H (eds) Computational intelligence and security. Springer, Berlin Heidelberg, pp 1–10
Talatahari S, Kheirollahi M, Farahmandpour C, Gandomi AH (2013) A multi-stage particle swarm for optimum design of truss structures. Neural Comput Appl 23:1297–1309
Berke L, Khot NS (1987) Structural optimization using optimality criteria. In: Mota Soares CA (ed) Computer aided optimal design: structural and mechanical systems. Springer, Berlin Heidelberg, pp 271–311
Pouriyanezhad E, Rahami H, Mirhosseini SM (2020) Truss optimization using eigenvectors of the covariance matrix. Eng Comput
Adeli H, Kumar S (1995) Distributed genetic algorithm for structural optimization. J Aerosp Eng 8:156–163
Barakat S, Ibrahim H (2011) Application of shuffled complex evolution global optimization technique in the design of truss structures. In: 2011 fourth international conference on modeling, simulation and applied optimization, pp 1–6
Baghlani A, Makiabadi MH (2014) Weight optimization of truss structures by a new feasible boundary search technique hybridized with firefly algorithm. KSCE J Civ Eng 18:1105–1118
Kaveh A, Ilchi Ghazaan M (2014) Enhanced colliding bodies optimization for design problems with continuous and discrete variables. Adv Eng Softw 77:66–75
Azad SK, Hasançebi O (2014) An elitist self-adaptive step-size search for structural design optimization. Appl Soft Comput 19:226–235
Kazemzadeh Azad S, Kazemzadeh Azad S, Hasançebi O (2016) Structural optimization problems of the ISCSO 2011–2015: a test set. Int J Optim Civ Eng 6:629–638
Kulkarni AJ, Kale IR, Tai K, Azad SK (2012) Discrete optimization of truss structure using probability collectives. In: 2012 12th international conference on hybrid intelligent systems (HIS), pp 225–230
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The authors greatly acknowledge the help provided by Dr. Oguzhan Hasancebi and Dr. Saeid Kazemzadeh Azad.
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Altun, M., Pekcan, O. (2021). Optimum Sizing of Truss Structures Using a Hybrid Flower Pollinations. In: Dey, N. (eds) Applications of Flower Pollination Algorithm and its Variants. Springer Tracts in Nature-Inspired Computing. Springer, Singapore. https://doi.org/10.1007/978-981-33-6104-1_6
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