Abstract
This study investigates the search capability, stability, and computational efficiency of four improved penalty-free constraint-handling techniques (CHTs), including the death penalty, the Deb rule, the filter method, and the mapping strategy, in structural optimization using harmony search (HS). The first three general-purpose CHTs have been improved by hybridizing with a structural analysis filter strategy to enhance their computational efficiency based on the characteristics of structural optimization and the solution updating rule of the HS. This study also has modified the mapping operator of the mapping strategy to handle size and shape optimization with Euler buckling constraints. Four numerical examples examine the performances of these CHTs. The comparative results show that the mapping strategy exhibits apparent superiority both in search capability and stability among the four. However, it also demands the most computational cost, and the improved Deb rule becomes the most competitive method while considering computational efficiency. The difference between the death penalty and the Deb rule method is that the feasible solution initialization process required by the death penalty method will deteriorate its computational efficiency in problems with small feasible space. The filter method always reserves some infeasible solutions to guide the search in the iteration process. However, its performances are inferior to the other three approaches in four benchmark problems.
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References
Li L, Huang Z, Liu F (2009) A heuristic particle swarm optimization method for truss structures with discrete variables. Comput Struct 87:435–443
Farshchin M, Camp CV, Maniat M (2016) Optimal design of truss structures for size and shape with frequency constraints using a collaborative optimization strategy. Expert Syst Appl 66:203–218
Kanarachos S, Griffin J, Fitzpatrick ME (2017) Efficient truss optimization using the contrast-based fruit fly optimization algorithm. Comput Struct 182:137–148
Lieu QX, Do DT, Lee J (2018) An adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures with frequency constraints. Comput Struct 195:99–112
Tejani GG, Saysani VJ, Patel VK, Mirjalili S (2018) Truss optimization with natural frequency bounds using improved symbiotic organisms search. Knowl-Based Syst 143:162–178
Tejani GG, Savsani V, Patel V (2016) Adaptive symbiotic organisms search (SOS) algorithm for structural design optimization. J Comput Design Eng 3:226–249
Tejani GG, Savsani V, Bureerat S, Patel V (2018) Topology and size optimization of trusses with static and dynamic bounds by modified symbiotic organisms search. J Comput Civil Eng 32:04017085
Tejani GG, Pholdee N, Bureerat S, Prayogo D, Gandomi AH (2019) Structural optimization using multi-objective modified adaptive symbiotic organisms search. Expert Syst Appl 125:425–441
Tejani GG, Pholdee N, Bureerat S, Prayogo D (2018) Multiobjective adaptive symbiotic organisms search for truss optimization problems. Knowl Based Syst 161:398–414
Tejani GG, Savsani V, Patel V, Mirjalili S (2019) An improved heat transfer search algorithm for unconstrained optimization problems. J Comput Design Eng 6:13–32
Tejani GG, Kumar S, Gandomi AH (2019) Multi-objective heat transfer search algorithm for truss optimization. Eng Comput 1–22
Tejani GG, Savsani VJ, Bureerat S, Patel VK, Savsani P (2019) Topology optimization of truss subjected to static and dynamic constraints by integrating simulated annealing into passing vehicle search algorithms. Eng Comput 35:499–517
Farshchin M, Maniat M, Camp CV, Pezeshk S (2018) School based optimization algorithm for design of steel frames. Eng Struct 171:326–335
Cao H, Qian X, Chen Z, Zhu H (2017) Enhanced particle swarm optimization for size and shape optimization of truss structures. Eng Optim 1–18
Cao H, Qian X, Zhou Y-L, Yang H (2018) Applicability of subspace harmony search hybrid with improved deb rule in optimizing Trusses. J Comput Civil Eng 32:04018021
Kaveh A, Ilchi GM (2018) A new hybrid meta-heuristic algorithm for optimal design of large-scale dome structures. Eng Optim 50:235–252
Kaveh A, Moghanni RM, Javadi SM (2019) Optimum design of large steel skeletal structures using chaotic firefly optimization algorithm based on the Gaussian map. Struct Multidiscip Optim 60:879–894
Wang ZM, Luo QF, Zhou YQ (2020) Hybrid metaheuristic algorithm using butterfly and flower pollination base on mutualism mechanism for global optimization problems. Eng Comput 34
Adil B, Cengiz B (2019) Optimal design of truss structures using weighted superposition attraction algorithm. Eng Comput 1–15
Kumar S, Tejani GG, Mirjalili S (2018) Modified symbiotic organisms search for structural optimization. Eng Comput 1–28
Jafari M, Salajegheh E, Salajegheh J (2019) An efficient hybrid of elephant herding optimization and cultural algorithm for optimal design of trusses. Eng Comput 35:781–801
Kaveh A, Zakian P (2018) Improved GWO algorithm for optimal design of truss structures. Eng Comput 34:685–707
Mezura-Montes E (2009) Constraint-handling in evolutionary optimization. Springer, Berlin
Coello CAC (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput Methods Appl Mech Eng 191:1245–1287
Mezura-Montes E, Coello CAC (2011) Constraint-handling in nature-inspired numerical optimization: past, present and future. Swarm Evol Comput 1:173–194
Liu Z, Hui Q (2012) A constraint-handling technique for particle swarm optimization. World Automation Congress IEEE 1–6
Deb K, Datta R (2013) A bi-objective constrained optimization algorithm using a hybrid evolutionary and penalty function approach. Eng Optim 45:503–527
Bureerat S, Pholdee N (2015) Optimal truss sizing using an adaptive differential evolution algorithm. J Comput Civil Eng 30:04015019
de Castro RM, Guimarães S, de Lima BSLP (2018) E-BRM: a constraint handling technique to solve optimization problems with evolutionary algorithms. Appl Soft Comput 72:14–29
Balande U, Shrimankar D (2019) SRIFA: stochastic ranking with improved-firefly-algorithm for constrained optimization engineering design problems. Mathematics 7:250
Savsani V, Tejani GG, Patel V, Savsani P (2017) Modified meta-heuristics using random mutation for truss topology optimization with static and dynamic constraints. J Comput Design Eng 4:106–130
Tejani GG, Savsani V, Patel V, Savsani P (2018) Size, shape, and topology optimization of planar and space trusses using mutation-based improved metaheuristics. J Comput Design Eng 5:198–214
Tang J, Wang W (2015) A filter-genetic algorithm for constrained optimization problems. Advances in global optimization. Springer, Berlin, pp 355–362
Hu T, Mao J, Tian M, Dai H, Rong G (2017) New constraint-handling technique for evolutionary optimization of reservoir operation. J Water Resour Plan Manage 144:04017097
Schwefel H-P (1981) Numerical optimization of computer models. Wiley, USA
Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186:311–338
Fletcher R, Leyffer S (2002) Nonlinear programming without a penalty function. Math Program 91:239–269
Clevenger L, Ferguson L, Hart WE (2005) A filter-based evolutionary algorithm for constrained optimization. Evol Comput 13:329–352
Hedar A-R, Fukushima M (2006) Derivative-free filter simulated annealing method for constrained continuous global optimization. J Global Optim 35:521–549
Rocha AMA, Costa MFP, Fernandes EM (2014) A filter-based artificial fish swarm algorithm for constrained global optimization: theoretical and practical issues. J Global Optim 60:239–263
Kazemzadeh Azad S, Hasançebi O, Kazemzadeh AS (2013) Upper bound strategy for metaheuristic based design optimization of steel frames. Adv Eng Softw 57:19–32
Cao H, Qian X, Zhou Y (2018) Large-scale structural optimization using metaheuristic algorithms with elitism and a filter strategy. Struct Multidiscip Optim 57:799–814
Liu S, Zhu H, Chen Z, Cao H (2019) Frequency-constrained truss optimization using the fruit fly optimization algorithm with an adaptive vision search strategy. Eng Optim 1–21
Baghlani A, Makiabadi M, Maheri M (2017) Sizing optimization of truss structures by an efficient constraint-handling strategy in TLBO. J Comput Civil Eng 2017:04017004
Geem ZW, Kim JH, Loganathan G (2001) A new heuristic optimization algorithm: harmony search. Simulation 76:60–68
Arora JS, Wang Q (2005) Review of formulations for structural and mechanical system optimization. Struct Multidiscip Optim 30:251–272
Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188:1567–1579
Cassis JH, Sepulveda A (1985) Optimum design of trusses with buckling constraints. J Struct Eng Asce 111:1573–1589
Acknowledgements
The authors would like to acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 51708436, 51629801), the Hubei Provincial Natural Science Foundation of China (2018CFB609) and the Fundamental Research Funds for the Central Universities (WUT: 2018IVB028).
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Cao, H., Chen, Y., Zhou, Y. et al. Comparative study of four penalty-free constraint-handling techniques in structural optimization using harmony search. Engineering with Computers 38 (Suppl 1), 561–581 (2022). https://doi.org/10.1007/s00366-020-01162-0
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DOI: https://doi.org/10.1007/s00366-020-01162-0