Skip to main content
Top
Published in: Neural Computing and Applications 10/2019

02-03-2018 | Original Article

Multi-objective sizing and topology optimization of truss structures using genetic programming based on a new adaptive mutant operator

Authors: Hirad Assimi, Ali Jamali, Nader Nariman-zadeh

Published in: Neural Computing and Applications | Issue 10/2019

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Most real-world engineering problems deal with multiple conflicting objectives simultaneously. In order to address this issue in truss optimization, this paper presents a multi-objective genetic programming approach for sizing and topology optimization of trusses. It aims to find the optimal cross-sectional areas and connectivities between the nodes to achieve a set of trade-off solutions to satisfy all the optimization objective functions subjected to some constraints such as kinematic stability, maximum allowable stress in members and nodal deflections. It also uses the variable-length representation of potential solutions in the shape of computer programs and evolves to the potential final set of solutions. This approach also employs an adaptive mutant factor besides the classical genetic operators to improve the exploring capabilities of Genetic Programming in structural optimization. The intrinsic features of genetic programming help to identify redundant truss members and nodes in the design space, while no violation of constraints occurs. Our approach applied to some numerical examples and found a better non-dominated solution set in the most cases in comparison with the competent methods available in the literature.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Kicinger R, Arciszewski T, De Jong K (2005) Evolutionary computation and structural design: a survey of the state-of-the-art. Comput Struct 83(23–24):1943–1978CrossRef Kicinger R, Arciszewski T, De Jong K (2005) Evolutionary computation and structural design: a survey of the state-of-the-art. Comput Struct 83(23–24):1943–1978CrossRef
2.
go back to reference Dorn WS (1964) Automatic design of optimal structures. J Mech 3:25–52 Dorn WS (1964) Automatic design of optimal structures. J Mech 3:25–52
3.
go back to reference Deb K (2001) Design of truss-structures for minimum weight using genetic algorithms. Finite Elem Anal Des 37(5):447–465MATHCrossRef Deb K (2001) Design of truss-structures for minimum weight using genetic algorithms. Finite Elem Anal Des 37(5):447–465MATHCrossRef
4.
go back to reference Chun-Yin W, Tseng K-Y (2010) Truss structure optimization using adaptive multi-population differential evolution. Struct Multidiscip Optim 42(4):575–590CrossRef Chun-Yin W, Tseng K-Y (2010) Truss structure optimization using adaptive multi-population differential evolution. Struct Multidiscip Optim 42(4):575–590CrossRef
5.
go back to reference Hare W, Nutini J, Tesfamariam S (2013) A survey of non-gradient optimization methods in structural engineering. Adv Eng Softw 59:19–28CrossRef Hare W, Nutini J, Tesfamariam S (2013) A survey of non-gradient optimization methods in structural engineering. Adv Eng Softw 59:19–28CrossRef
9.
go back to reference Hajela P, Lin C-Y (1992) Genetic search strategies in multicriterion optimal design. Struct Optim 4(2):99–107CrossRef Hajela P, Lin C-Y (1992) Genetic search strategies in multicriterion optimal design. Struct Optim 4(2):99–107CrossRef
10.
go back to reference Coello CA, Christiansen AD (2000) Multiobjective optimization of trusses using genetic algorithms. Comput Struct 75(6):647–660CrossRef Coello CA, Christiansen AD (2000) Multiobjective optimization of trusses using genetic algorithms. Comput Struct 75(6):647–660CrossRef
11.
go back to reference Büche D, Dornberger R (2001) New evolutionary algorithm for multi-objective optimization and its application to engineering design problems. In: Proceedings of the fourth world congress of structural and multidisciplinary optimization, Dalian, China Büche D, Dornberger R (2001) New evolutionary algorithm for multi-objective optimization and its application to engineering design problems. In: Proceedings of the fourth world congress of structural and multidisciplinary optimization, Dalian, China
12.
go back to reference Deb K, Pratap A, Agarwal S, Meyarivan TAMT (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRef Deb K, Pratap A, Agarwal S, Meyarivan TAMT (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRef
13.
go back to reference Deb K, Goel T (2001) A hybrid multi-objective evolutionary approach to engineering shape design. In: Zitzler E, Thiele L, Deb K, Coello Coello CA, Corne D (eds) Evolutionary multi-criterion optimization. Springer, Berlin, pp 385–399. ISBN: 978-3-540-44719-1 Deb K, Goel T (2001) A hybrid multi-objective evolutionary approach to engineering shape design. In: Zitzler E, Thiele L, Deb K, Coello Coello CA, Corne D (eds) Evolutionary multi-criterion optimization. Springer, Berlin, pp 385–399. ISBN: 978-3-540-44719-1
14.
go back to reference Hamda H, Roudenko O, Schoenauer M (2002) Application of a multi-objective evolutionary algorithm to topology optimum design. In: Fifth international conference on adaptive computing in design and manufacture (ACDM02), Exeter, UK, pp 16–18 Hamda H, Roudenko O, Schoenauer M (2002) Application of a multi-objective evolutionary algorithm to topology optimum design. In: Fifth international conference on adaptive computing in design and manufacture (ACDM02), Exeter, UK, pp 16–18
15.
go back to reference Luh G-C, Chueh C-H (2004) Multi-objective optimal design of truss structure with immune algorithm. Comput Struct 82(11–12):829–844MathSciNetCrossRef Luh G-C, Chueh C-H (2004) Multi-objective optimal design of truss structure with immune algorithm. Comput Struct 82(11–12):829–844MathSciNetCrossRef
16.
go back to reference Kelesoglu O (2007) Fuzzy multiobjective optimization of truss-structures using genetic algorithm. Adv Eng Softw 38(10):717–721CrossRef Kelesoglu O (2007) Fuzzy multiobjective optimization of truss-structures using genetic algorithm. Adv Eng Softw 38(10):717–721CrossRef
17.
go back to reference Izui K, Nishiwaki S, Yoshimura M, Nakamura M, Renaud JE (2008) Enhanced multiobjective particle swarm optimization in combination with adaptive weighted gradient-based searching. Eng Optim 40(9):789–804MathSciNetCrossRef Izui K, Nishiwaki S, Yoshimura M, Nakamura M, Renaud JE (2008) Enhanced multiobjective particle swarm optimization in combination with adaptive weighted gradient-based searching. Eng Optim 40(9):789–804MathSciNetCrossRef
18.
go back to reference Ruiyi S, Wang X, Gui L, Fan Z (2010) Multi-objective topology and sizing optimization of truss structures based on adaptive multi-island search strategy. Struct Multidiscip Optim 43(2):275–286 Ruiyi S, Wang X, Gui L, Fan Z (2010) Multi-objective topology and sizing optimization of truss structures based on adaptive multi-island search strategy. Struct Multidiscip Optim 43(2):275–286
19.
go back to reference Greiner D, Hajela P (2011) Truss topology optimization for mass and reliability considerations? Co-evolutionary multiobjective formulations. Struct Multidiscip Optim 45(4):589–613MathSciNetMATHCrossRef Greiner D, Hajela P (2011) Truss topology optimization for mass and reliability considerations? Co-evolutionary multiobjective formulations. Struct Multidiscip Optim 45(4):589–613MathSciNetMATHCrossRef
20.
go back to reference Noilublao N, Bureerat S (2011) Simultaneous topology, shape and sizing optimisation of a three-dimensional slender truss tower using multiobjective evolutionary algorithms. Comput Struct 89(23–24):2531–2538CrossRef Noilublao N, Bureerat S (2011) Simultaneous topology, shape and sizing optimisation of a three-dimensional slender truss tower using multiobjective evolutionary algorithms. Comput Struct 89(23–24):2531–2538CrossRef
21.
go back to reference Takada T (2012) Multiobjective optimization of truss topology by linear/sequential linear programming method. J Mech Eng Autom 2:585–593 Takada T (2012) Multiobjective optimization of truss topology by linear/sequential linear programming method. J Mech Eng Autom 2:585–593
22.
go back to reference Kaveh A, Laknejadi K (2012) A hybrid multi-objective optimization and decision making procedure for optimal design of truss structures. Iranian J Sci Technol Trans Civ Eng 35(2):137–154 Kaveh A, Laknejadi K (2012) A hybrid multi-objective optimization and decision making procedure for optimal design of truss structures. Iranian J Sci Technol Trans Civ Eng 35(2):137–154
23.
go back to reference Pholdee N, Bureerat S (2012) Performance enhancement of multiobjective evolutionary optimisers for truss design using an approximate gradient. Comput Struct 106–107(C):115–124CrossRef Pholdee N, Bureerat S (2012) Performance enhancement of multiobjective evolutionary optimisers for truss design using an approximate gradient. Comput Struct 106–107(C):115–124CrossRef
24.
go back to reference Richardson JN, Adriaenssens S, Bouillard P, Coelho RF (2012) Multiobjective topology optimization of truss structures with kinematic stability repair. Struct Multidiscip Optim 46(4):513–532MATHCrossRef Richardson JN, Adriaenssens S, Bouillard P, Coelho RF (2012) Multiobjective topology optimization of truss structures with kinematic stability repair. Struct Multidiscip Optim 46(4):513–532MATHCrossRef
25.
go back to reference Kaveh A, Laknejadi K (2012) A hybrid evolutionary graph-based multi-objective algorithm for layout optimization of truss structures. Acta Mech 224(2):343–364MathSciNetMATHCrossRef Kaveh A, Laknejadi K (2012) A hybrid evolutionary graph-based multi-objective algorithm for layout optimization of truss structures. Acta Mech 224(2):343–364MathSciNetMATHCrossRef
26.
go back to reference Kaveh A, Laknejadi K (2013) A new multi-swarm multi-objective optimization method for structural design. Adv Eng Softw 58(C):54–69MATHCrossRef Kaveh A, Laknejadi K (2013) A new multi-swarm multi-objective optimization method for structural design. Adv Eng Softw 58(C):54–69MATHCrossRef
27.
go back to reference Pholdee N, Bureerat S (2013) Hybrid real-code population-based incremental learning and approximate gradients for multi-objective truss design. Eng Optim 46(8):1032–1051MathSciNetCrossRef Pholdee N, Bureerat S (2013) Hybrid real-code population-based incremental learning and approximate gradients for multi-objective truss design. Eng Optim 46(8):1032–1051MathSciNetCrossRef
28.
go back to reference Coelho RF (2013) Co-evolutionary optimization for multi-objective design under uncertainty. J Mech Des 135(2):021006–021008CrossRef Coelho RF (2013) Co-evolutionary optimization for multi-objective design under uncertainty. J Mech Des 135(2):021006–021008CrossRef
29.
go back to reference Zavala GR, Nebro AJ, Luna F, Coello Coello CA (2013) A survey of multi-objective metaheuristics applied to structural optimization. Struct Multidiscip Optim 49(4):537–558MathSciNetCrossRef Zavala GR, Nebro AJ, Luna F, Coello Coello CA (2013) A survey of multi-objective metaheuristics applied to structural optimization. Struct Multidiscip Optim 49(4):537–558MathSciNetCrossRef
30.
go back to reference Zavala GR, Nebro AJ, Durillo JJ, Luna F (2014) Integrating a multi-objective optimization framework into a structural design software. Adv Eng Softw 76(C):161–170CrossRef Zavala GR, Nebro AJ, Durillo JJ, Luna F (2014) Integrating a multi-objective optimization framework into a structural design software. Adv Eng Softw 76(C):161–170CrossRef
31.
go back to reference Xu B, Jin YJ (2014) Multiobjective dynamic topology optimization of truss with interval parameters based on interval possibility degree. J Vib Control 20(1):66–81MathSciNetMATHCrossRef Xu B, Jin YJ (2014) Multiobjective dynamic topology optimization of truss with interval parameters based on interval possibility degree. J Vib Control 20(1):66–81MathSciNetMATHCrossRef
32.
go back to reference Angelo JS, Bernardino HS, Barbosa HJC (2015) Ant colony approaches for multiobjective structural optimization problems with a cardinality constraint. Adv Eng Softw 80:101–115CrossRef Angelo JS, Bernardino HS, Barbosa HJC (2015) Ant colony approaches for multiobjective structural optimization problems with a cardinality constraint. Adv Eng Softw 80:101–115CrossRef
33.
go back to reference Richardson JN, Coelho RF, Adriaenssens S (2015) Robust topology optimization of truss structures with random loading and material properties: a multiobjective perspective. Comput Struct 154(C):41–47CrossRef Richardson JN, Coelho RF, Adriaenssens S (2015) Robust topology optimization of truss structures with random loading and material properties: a multiobjective perspective. Comput Struct 154(C):41–47CrossRef
34.
go back to reference Hosseini SS, Hamidi SA, Mansuri M, Ghoddosian A (2015) Multi objective particle swarm optimization (MOPSO) for size and shape optimization of 2D truss structures. Period Polytech Civ Eng 59(1):9–14CrossRef Hosseini SS, Hamidi SA, Mansuri M, Ghoddosian A (2015) Multi objective particle swarm optimization (MOPSO) for size and shape optimization of 2D truss structures. Period Polytech Civ Eng 59(1):9–14CrossRef
35.
go back to reference Milajić A, Beljaković D, Solovev V, Murgul V (2016) Multi-objective truss optimization using different types of the BB–BC algorithm. Proc Eng 165:947–953CrossRef Milajić A, Beljaković D, Solovev V, Murgul V (2016) Multi-objective truss optimization using different types of the BB–BC algorithm. Proc Eng 165:947–953CrossRef
36.
go back to reference Dey S, Kumar Roy T (2016) Multi-objective structural design problem optimization using parameterized t-norm based fuzzy optimization programming technique. J Intell Fuzzy Syst 30(2):971–982MATHCrossRef Dey S, Kumar Roy T (2016) Multi-objective structural design problem optimization using parameterized t-norm based fuzzy optimization programming technique. J Intell Fuzzy Syst 30(2):971–982MATHCrossRef
37.
go back to reference Yang I-T, Hsieh Y-H, Kuo C-G (2016) Integrated multiobjective framework for reliability-based design optimization with discrete design variables. Autom Constr 63:162–172CrossRef Yang I-T, Hsieh Y-H, Kuo C-G (2016) Integrated multiobjective framework for reliability-based design optimization with discrete design variables. Autom Constr 63:162–172CrossRef
38.
go back to reference Luis Mroginski J, Alejandro Beneyto P, Gutierrez GJ, Di Rado A (2016) A selective genetic algorithm for multiobjective optimization of cross sections in 3D trussed structures based on a spatial sensitivity analysis. Multidiscip Model Mater Struct 12(2):423–435CrossRef Luis Mroginski J, Alejandro Beneyto P, Gutierrez GJ, Di Rado A (2016) A selective genetic algorithm for multiobjective optimization of cross sections in 3D trussed structures based on a spatial sensitivity analysis. Multidiscip Model Mater Struct 12(2):423–435CrossRef
39.
go back to reference Yu S, Tang H, Xue S, Li D (2016) Multi-objective differential evolution for truss design optimization with epistemic uncertainty. Adv Struct Eng 19(9):1403–1419CrossRef Yu S, Tang H, Xue S, Li D (2016) Multi-objective differential evolution for truss design optimization with epistemic uncertainty. Adv Struct Eng 19(9):1403–1419CrossRef
40.
go back to reference Xie L, Tang H, Changyuan H, Xue S (2016) An adaptive multi-objective immune algorithm for optimal design of truss structures. J Asian Archit Build Eng 15(3):557–564CrossRef Xie L, Tang H, Changyuan H, Xue S (2016) An adaptive multi-objective immune algorithm for optimal design of truss structures. J Asian Archit Build Eng 15(3):557–564CrossRef
41.
go back to reference Martini K (2016) Multiobjective structural optimization of frameworks using enumerative topology. Comput Struct 173(C):61–70CrossRef Martini K (2016) Multiobjective structural optimization of frameworks using enumerative topology. Comput Struct 173(C):61–70CrossRef
42.
go back to reference Gholizadeh S (2017) Multi-objective seismic design optimization of steel frames by a chaotic meta-heuristic algorithm. Eng Comput 33:1045–1060CrossRef Gholizadeh S (2017) Multi-objective seismic design optimization of steel frames by a chaotic meta-heuristic algorithm. Eng Comput 33:1045–1060CrossRef
43.
go back to reference Tawhid MA, Savsani V (2018) \(\varepsilon\)-constraint heat transfer search (\(\varepsilon\)-hts) algorithm for solving multi-objective engineering design problems. J Comput Des Eng 5(1):104–119 Tawhid MA, Savsani V (2018) \(\varepsilon\)-constraint heat transfer search (\(\varepsilon\)-hts) algorithm for solving multi-objective engineering design problems. J Comput Des Eng 5(1):104–119
44.
go back to reference Pedroso DM, Bonyadi MR, Gallagher M (2017) Parallel evolutionary algorithm for single and multi-objective optimisation: differential evolution and constraints handling. Appl Soft Comput 61(Supplement C):995–1012CrossRef Pedroso DM, Bonyadi MR, Gallagher M (2017) Parallel evolutionary algorithm for single and multi-objective optimisation: differential evolution and constraints handling. Appl Soft Comput 61(Supplement C):995–1012CrossRef
46.
go back to reference Koza JR (1992) Genetic programming—on the programming of computer programs by natural selection. MIT Press, CambridgeMATH Koza JR (1992) Genetic programming—on the programming of computer programs by natural selection. MIT Press, CambridgeMATH
47.
48.
go back to reference Soh CK, Yang Y (2000) Genetic programming-based approach for structural optimization. J Comput Civ Eng 14(1):31–37CrossRef Soh CK, Yang Y (2000) Genetic programming-based approach for structural optimization. J Comput Civ Eng 14(1):31–37CrossRef
49.
go back to reference Yang Y, Soh CK (2002) Automated optimum design of structures using genetic programming. Comput Struct 80(18–19):1537–1546CrossRef Yang Y, Soh CK (2002) Automated optimum design of structures using genetic programming. Comput Struct 80(18–19):1537–1546CrossRef
50.
go back to reference Yang Y, Soh KC (2000) Fuzzy logic integrated genetic programming for optimization and design. J Comput Civ Eng 14(4):249–254CrossRef Yang Y, Soh KC (2000) Fuzzy logic integrated genetic programming for optimization and design. J Comput Civ Eng 14(4):249–254CrossRef
51.
go back to reference Zheng QZ, Querin OM, Barton DC (2006) Geometry and sizing optimisation of discrete structure using the genetic programming method. Struct Multidiscip Optim 31(6):452–461CrossRef Zheng QZ, Querin OM, Barton DC (2006) Geometry and sizing optimisation of discrete structure using the genetic programming method. Struct Multidiscip Optim 31(6):452–461CrossRef
52.
go back to reference Fenton M, McNally C, Byrne J, Hemberg E, McDermott J, O’Neill M (2014) Automatic innovative truss design using grammatical evolution. Autom Constr 39(C):59–69CrossRef Fenton M, McNally C, Byrne J, Hemberg E, McDermott J, O’Neill M (2014) Automatic innovative truss design using grammatical evolution. Autom Constr 39(C):59–69CrossRef
53.
go back to reference Fenton M, McNally C, Byrne J, Hemberg E, McDermott J, O’Neill M (2015) Discrete planar truss optimization by node position variation using grammatical evolution. IEEE Trans Evol Comput 20(4):577–589CrossRef Fenton M, McNally C, Byrne J, Hemberg E, McDermott J, O’Neill M (2015) Discrete planar truss optimization by node position variation using grammatical evolution. IEEE Trans Evol Comput 20(4):577–589CrossRef
54.
go back to reference Assimi H, Jamali A, Nariman-zadeh N (2017) Sizing and topology optimization of truss structures using genetic programming. Swarm Evol Comput 37(Supplement C):90–103CrossRef Assimi H, Jamali A, Nariman-zadeh N (2017) Sizing and topology optimization of truss structures using genetic programming. Swarm Evol Comput 37(Supplement C):90–103CrossRef
55.
go back to reference Assimi H, Jamali A (2018) A hybrid algorithm coupling genetic programming and Nelder–Mead for topology and size optimization of trusses with static and dynamic constraints. Expert Syst Appl 95(Supplement C):127–141CrossRef Assimi H, Jamali A (2018) A hybrid algorithm coupling genetic programming and Nelder–Mead for topology and size optimization of trusses with static and dynamic constraints. Expert Syst Appl 95(Supplement C):127–141CrossRef
57.
go back to reference Jamali A, Ghamati M, Ahmadi B, Nariman-zadeh N (2013) Probability of failure for uncertain control systems using neural networks and multi-objective uniform-diversity genetic algorithms (MUGA). Eng Appl Artif Intell 26(2):714–723CrossRef Jamali A, Ghamati M, Ahmadi B, Nariman-zadeh N (2013) Probability of failure for uncertain control systems using neural networks and multi-objective uniform-diversity genetic algorithms (MUGA). Eng Appl Artif Intell 26(2):714–723CrossRef
58.
go back to reference Jamali A, Khaleghi E, Gholaminezhad I, Nariman-zadeh N, Gholaminia B, Jamal-Omidi A (2014) Multi-objective genetic programming approach for robust modeling of complex manufacturing processes having probabilistic uncertainty in experimental data. J Intell Manuf 28(1):149–163CrossRef Jamali A, Khaleghi E, Gholaminezhad I, Nariman-zadeh N, Gholaminia B, Jamal-Omidi A (2014) Multi-objective genetic programming approach for robust modeling of complex manufacturing processes having probabilistic uncertainty in experimental data. J Intell Manuf 28(1):149–163CrossRef
59.
go back to reference Jamali A, Khaleghi E, Gholaminezhad I, Nariman-zadeh N (2014) Modelling and prediction of complex non-linear processes by using Pareto multi-objective genetic programming. Int J Syst Sci 47(7):1675–1688MATHCrossRef Jamali A, Khaleghi E, Gholaminezhad I, Nariman-zadeh N (2014) Modelling and prediction of complex non-linear processes by using Pareto multi-objective genetic programming. Int J Syst Sci 47(7):1675–1688MATHCrossRef
60.
go back to reference Gholaminezhad I, Assimi H, Jamali A, Vajari DA (2016) Uncertainty quantification and robust modeling of selective laser melting process using stochastic multi-objective approach. Int J Adv Manuf Technol 86(5–8):1425–1441CrossRef Gholaminezhad I, Assimi H, Jamali A, Vajari DA (2016) Uncertainty quantification and robust modeling of selective laser melting process using stochastic multi-objective approach. Int J Adv Manuf Technol 86(5–8):1425–1441CrossRef
61.
go back to reference Gholaminezhad I, Jamali A, Assimi H (2016) Multi-objective reliability-based robust design optimization of robot gripper mechanism with probabilistically uncertain parameters. Neural Comput Appl 28(1):659–670 Gholaminezhad I, Jamali A, Assimi H (2016) Multi-objective reliability-based robust design optimization of robot gripper mechanism with probabilistically uncertain parameters. Neural Comput Appl 28(1):659–670
62.
go back to reference Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, LondonMATH Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, LondonMATH
63.
go back to reference Mazzoni S, McKenna F, Scott MH, Fenves GL et al (2006) OpenSees command language manual. Pacific Earthquake Engineering Research (PEER) Center, Berkeley Mazzoni S, McKenna F, Scott MH, Fenves GL et al (2006) OpenSees command language manual. Pacific Earthquake Engineering Research (PEER) Center, Berkeley
64.
go back to reference Usmani A, Zhang J, Jiang J, Jiang Y, May I (2012) Using Opensees for structures in fire. J Struct Fire Eng 3(1):57–70CrossRef Usmani A, Zhang J, Jiang J, Jiang Y, May I (2012) Using Opensees for structures in fire. J Struct Fire Eng 3(1):57–70CrossRef
65.
go back to reference Yuan L, Panagiotou M (2014) Three-dimensional cyclic beam-truss model for nonplanar reinforced concrete walls. J Struct Eng 140(3):04013071CrossRef Yuan L, Panagiotou M (2014) Three-dimensional cyclic beam-truss model for nonplanar reinforced concrete walls. J Struct Eng 140(3):04013071CrossRef
66.
go back to reference Gholaminezhad I (2015) A multi-objective differential evolution approach based on \(\varepsilon\)-elimination uniform-diversity for mechanism design. Struct Multidiscip Optim 52(5):861–877CrossRef Gholaminezhad I (2015) A multi-objective differential evolution approach based on \(\varepsilon\)-elimination uniform-diversity for mechanism design. Struct Multidiscip Optim 52(5):861–877CrossRef
67.
go back to reference Salehpour M, Jamali A, Bagheri A, Nariman-zadeh N (2017) A new adaptive differential evolution optimization algorithm based on fuzzy inference system. Int J Eng Sci Technol 20(2):587–597CrossRef Salehpour M, Jamali A, Bagheri A, Nariman-zadeh N (2017) A new adaptive differential evolution optimization algorithm based on fuzzy inference system. Int J Eng Sci Technol 20(2):587–597CrossRef
68.
go back to reference Das S, Subhra Mullick S, Suganthan PN (2016) Recent advances in differential evolution? An updated survey. Swarm Evol Comput 27:1–30CrossRef Das S, Subhra Mullick S, Suganthan PN (2016) Recent advances in differential evolution? An updated survey. Swarm Evol Comput 27:1–30CrossRef
69.
go back to reference Seok Lee K, Woo Geem Z (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82(9–10):781–798 Seok Lee K, Woo Geem Z (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82(9–10):781–798
70.
go back to reference Li LJ, Huang ZB, Liu F, Wu QH (2007) A heuristic particle swarm optimizer for optimization of pin connected structures. Comput Struct 85(7–8):340–349CrossRef Li LJ, Huang ZB, Liu F, Wu QH (2007) A heuristic particle swarm optimizer for optimization of pin connected structures. Comput Struct 85(7–8):340–349CrossRef
71.
go back to reference Li LJ, Huang ZB, Liu F (2009) A heuristic particle swarm optimization method for truss structures with discrete variables. Comput Struct 87(7–8):435–443CrossRef Li LJ, Huang ZB, Liu F (2009) A heuristic particle swarm optimization method for truss structures with discrete variables. Comput Struct 87(7–8):435–443CrossRef
72.
go back to reference Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2012) Mine blast algorithm for optimization of truss structures with discrete variables. Comput Struct 102–103(C):49–63CrossRef Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2012) Mine blast algorithm for optimization of truss structures with discrete variables. Comput Struct 102–103(C):49–63CrossRef
73.
go back to reference Degertekin SO, Hayalioglu MS (2013) Sizing truss structures using teaching–learning-based optimization. Comput Struct 119(C):177–188CrossRef Degertekin SO, Hayalioglu MS (2013) Sizing truss structures using teaching–learning-based optimization. Comput Struct 119(C):177–188CrossRef
74.
go back to reference Kaveh A, Bakhshpoori T, Afshari E (2014) An efficient hybrid particle swarm and swallow swarm optimization algorithm. Comput Struct 143(C):40–59CrossRef Kaveh A, Bakhshpoori T, Afshari E (2014) An efficient hybrid particle swarm and swallow swarm optimization algorithm. Comput Struct 143(C):40–59CrossRef
Metadata
Title
Multi-objective sizing and topology optimization of truss structures using genetic programming based on a new adaptive mutant operator
Authors
Hirad Assimi
Ali Jamali
Nader Nariman-zadeh
Publication date
02-03-2018
Publisher
Springer London
Published in
Neural Computing and Applications / Issue 10/2019
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-018-3401-9

Other articles of this Issue 10/2019

Neural Computing and Applications 10/2019 Go to the issue

Premium Partner