Skip to main content
SpringerLink
Log in

Simultaneous size, shape, and topology optimization of truss structures using integrated particle swarm optimizer

  • RESEARCH PAPER
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

The current investigation deals with the weight minimization of truss structures accomplishing the simultaneous shape, size, and topology optimization. In this regard, this study presents an effective algorithm called integrated particle swarm optimizer (iPSO) as an optimization tool. The iPSO combines favorable features of the standard PSO with an efficient concept of ‘weighted particle’ to improve its performance. In addition, ‘improved fly-back’ technique is introduced to handle the problem constraints. The proposed methodology is tested on a series of benchmark problems and the obtained results are compared with those available in the technical literature. The iPSO achieves the results which are capable of competitive with those obtained by other techniques used for simultaneous optimization of truss structures and reported in the literature. Furthermore, the relative simplicity of the formulation can be considered as one of the significant features of this method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  • Ahrari A, Atai A (2013) Fully stressed design evolution strategy for shape and size optimization of truss structures. Comput Struct 123:58–67

    Article  Google Scholar 

  • Ahrari A, Atai A, Deb K (2014) Simultaneous topology, shape and size optimization of truss structures by fully stressed design based on evolution strategy. Eng Optim. doi:10.1080/0305215X.2014.947972

    MathSciNet  Google Scholar 

  • American Institute of Steel Construction (AISC) (1989) Manual of steel construction allowable stress design, 9th edn

  • Babu KSJ, Vijayalakshmi DP (2013) Self-adaptive PSO-GA hybrid model for combinatorial water distribution network design. Pipeline Syst Eng Pract 4:57–67

    Article  Google Scholar 

  • Balling RJ, Briggs RR, Gillman K (2006) Multiple optimum size/shape/topology designs for skeletal structures using a genetic algorithm. J Struct Eng ASCE 132:1158–1165

    Article  Google Scholar 

  • Camp CV, Bichon BJ (2004) Design of space trusses using ant colony optimization. J Struct Eng ASCE 130:741–751

    Article  Google Scholar 

  • Christensen PW, Klarbring A (2008) An introduction to structural optimization. Springer, Netherlands

    MATH  Google Scholar 

  • Coello CA (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

    Article  MathSciNet  MATH  Google Scholar 

  • Deb K, Gulati S (2001) Design of truss-structures for minimum weight using genetic algorithms. Finite Elem Anal Des 37:447–465

    Article  MATH  Google Scholar 

  • Dobbs MW, Felton LP (1969) Optimization of truss geometry. J Struct Div-ASCE 95:2105–2118

    Google Scholar 

  • Elsayed SM, Sarker RA, Mezura-Montes E (2014) Self-adaptive mix of particle swarm methodologies for constrained optimization. Inf Sci 277:216–233

    Article  MathSciNet  Google Scholar 

  • Fan Q, Yan X (2014) Self-adaptive particle swarm optimization with multiple velocity strategies and its application for p-xylene oxidation reaction process optimization. Chemom Intell Lab Syst 139:15–25

    Article  Google Scholar 

  • Gholizadeh S (2013) Layout optimization of truss structures by hybridizing cellular automata and particle swarm optimization. Comput Struct 125:86–99

    Article  Google Scholar 

  • Ghosh A, Mallik AK (1988) Theory of mechanisms and machines. Affiliated East–west Press, New Delhi

    Google Scholar 

  • Hasancebi O, Erbatur F (2001) Layout optimization of trusses using improved GA methodologies. Acta Mech 146:87–107

    Article  MATH  Google Scholar 

  • Hasancebi O, Erbatur F (2002) On efficient use of simulated annealing in complex structural optimization problems. Acta Mech 157:27–50

    Article  MATH  Google Scholar 

  • Hasançebi O, Çarbaş S, Doğan E, Erdal F, Saka MP (2009) Performance evaluation of metaheursitc search techniques in the optimum design of real size pin jointed structures. Comput Struct 87:284–302

    Article  Google Scholar 

  • Hasancebi O, Teke T, Pekcan O (2013) A bat-inspired algorithm for structural optimization. Comput Struct 128:77–90

  • Haug EJ, Arora JS (1989) Introduction to optimal design. McGraw Hill, New York

    Google Scholar 

  • He S, Prempain E, Wu QH (2004) An improved particle swarm optimizer for mechanical design optimization problems. Eng Optim 36:585–605

    Article  MathSciNet  Google Scholar 

  • Hu X, Eberhart R (2002). Solving constrained nonlinear optimization problems with particle swarm optimization. World 6th multiconference on systemics, cybernetics and informatics, p 203–206

  • Huang X, Xie YM (2007) Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elem Anal Des 43:1039–1049

    Article  Google Scholar 

  • Jansen PW, Perez RE (2011) Constrained structural design optimization via a parallel augmented lagrangian particle swarm optimization approach. Comput Struct 89:1352–1366

    Article  Google Scholar 

  • Kaveh A, Mahdavi VR (2014) Colliding bodies optimization method for optimum discrete design of truss structures. Comput Struct 139:43–53

    Article  Google Scholar 

  • Kaveh A, Talatahari S (2009) A particle swarm ant colony optimization for truss structures with discrete variables. J Constr Steel Res 65:1558–1568

    Article  Google Scholar 

  • Kennedy J, Eberhart RC (2001) Swarm intelligence. Morgan Kaufmann Publishers

  • Kirsch U (1989) Optimal topologies of truss structures. Comput Methods Appl Mech Eng 72:15–28

    Article  MathSciNet  MATH  Google Scholar 

  • Lee KS, Geem ZW, Lee SH, Bae KW (2005) The harmony search heuristic algorithm for discrete structural optimization. Eng Optim 37:663–684

    Article  MathSciNet  Google Scholar 

  • Li N, Wang W, Hsu C, Chang W, Chou H, Chang J (2014) Enhanced particle swarm optimizer incorporating a weighted particle. Neurocomputing 124:218–227

    Article  Google Scholar 

  • Luh GC, Lin CY (2008) Optimal design of truss structures using ant algorithm. Struct Multidiscip Optim 36:365–379

    Article  Google Scholar 

  • Luh GC, Lin CY (2011) Optimal design of truss-structures using particle swarm optimization. Comput Struct 89:2221–2232

    Article  Google Scholar 

  • Miguel Leandro FF, Lopez RH, Miguel Leticia FF (2013) Multimodal size, shape, and topology optimization of truss structures using the Firefly algorithm. Adv Eng Softw 56:23–37

    Article  Google Scholar 

  • Napoles G, Grau I, Bello R, Falcon, R, Abraham A (2013) Self-adaptive differential particle swarm using a ring topology for multimodal optimization. International Conference on Intelligent Systems Design and Applications ISDA, p 35–40

  • Ohsaki M (1995) Genetic algorithm for topology optimization of trusses. Comput Struct 57:219–225

    Article  MathSciNet  MATH  Google Scholar 

  • Ohsaki M (1998) Simultaneous optimization of topology and geometry of a regular plane truss. Comput Struct 66:69–71

    Article  MATH  Google Scholar 

  • Rahami H, Kaveh A, Gholipour Y (2008) Sizing, geometry, and topology optimization of trusses via force method and genetic algorithm. Eng Struct 30:2360–2369

    Article  Google Scholar 

  • Rajan SD (1995) Sizing, shape and topology design optimization of truss using genetic algorithm. J Struct Eng 121:1480–1487

    Article  Google Scholar 

  • Rajeev S, Krishnamoorthy CS (1992) Discrete optimization of structures using genetic algorithms. J Struct Eng 118:1233–1250

    Article  Google Scholar 

  • Reddy G, Cagan J (1993). Optimally directed truss topology generation using shape annealing. Technical Report, Carnegie Mellon University

  • Ringertz UT (1985) On topology optimization of trusses. Eng Optim 9:209–218

    Article  Google Scholar 

  • Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2012) Mine blast algorithm for optimization of truss structures with discrete variables. Comput Struct 102:49–63

    Article  Google Scholar 

  • Sadollah A, Eskandar H, Bahreininejad A, Kim JH (2015) Water cycle, mine blast and improved mine blast algorithms for discrete sizing optimization of truss structures. Comput Struct 149:1–16

    Article  Google Scholar 

  • Sönmez M (2011) Artificial Bee Colony algorithm for optimization of truss structures. Appl Soft Comput 11:2406–2418

    Article  Google Scholar 

  • Tang W, Tong L, Gu Y (2005) Improved genetic algorithm for design optimization of truss structures with sizing, shape and topology variables. Int J Numer Methods Eng 62:1737–1762

    Article  MATH  Google Scholar 

  • Toğan V (2012) Design of planar steel frames using teaching-learning based optimization. Eng Struct 34:225–232

    Article  Google Scholar 

  • Topping BHV (1983) Shape optimization of skeletal structures: a review. J Struct Eng 109(8):1933–1951

    Article  Google Scholar 

  • Van den Bergh F, Engelbrecht A (2003) Using neighborhood with the guaranteed convergence PSO. In: 2003 I.E. Swarm Intelligence Symposium, USA, p 235–242

  • Vanderplaat GN, Moses F (1972) Automated design of trusses for optimal geometry. J Struct Divisions 98:671–690

    Google Scholar 

  • Wei HL, Nor AMI (2014) An adaptive two-layer particle swarm optimization with elitist learning strategy. Inform Sci 273:49–72

    Article  MathSciNet  Google Scholar 

  • Wu SJ, Chow PT (1995) Integrated discrete and configuration optimization of trusses using genetic algorithms. Comput Struct 55(4):695–702

  • Wu CY, Tseng KY (2010) Truss structure optimization using adaptive multi-population differential evolution. Struct Multidiscip Optim 2:575–590

    Article  Google Scholar 

  • Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49:885–896

    Article  Google Scholar 

  • Zhang Y, Xiong X, Zhang Q (2013) An improved self-adaptive PSO algorithm with detection function for multimodal function optimization problems. Mathematical Problems in Engineering

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Ege University, Izmir, Turkey

    Ali Mortazavi

  2. Department of Civil Engineering, Karadeniz Technical University, 61080, Trabzon, Turkey

    Vedat Toğan

Authors
  1. Ali Mortazavi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vedat Toğan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vedat Toğan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mortazavi, A., Toğan, V. Simultaneous size, shape, and topology optimization of truss structures using integrated particle swarm optimizer. Struct Multidisc Optim 54, 715–736 (2016). https://doi.org/10.1007/s00158-016-1449-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-016-1449-7

Keywords

Search

Navigation