Skip to main content
SpringerLink
Log in

Truss structure optimization using adaptive multi-population differential evolution

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

This paper applies multi-population differential evolution (MPDE) with a penalty-based, self-adaptive strategy—the adaptive multi-population differential evolution (AMPDE)—to solve truss optimization problems with design constraints. The self-adaptive strategy developed in this study is a new adaptive approach that adjusts the control parameters of MPDE by monitoring the number of infeasible solutions generated during the evolution process. Multiple different minimum weight optimization problems of the truss structure subjected to allowable stress, deflection, and kinematic stability constraints are used to demonstrate that the proposed algorithm is an efficient approach to finding the best solution for truss optimization problems. The optimum designs obtained by AMPDE are better than those found in the current literature for problems that do not violate the design constraints. We also show that self-adaptive strategy can improve the performance of MPDE in constrained truss optimization problems, especially in the case of simultaneous optimization of the size, topology, and shape of truss structures.

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

Similar content being viewed by others

References

  • Becerra R, Coello Coello C (2006) Cultured differential evolution for constrained optimization. Comput Methods Appl Mech Eng 195:4303–4322

    Article  MATH  Google Scholar 

  • Deb K, Beyer HG (1999) Self-adaptation in real-parameter genetic algorithms with simulated binary crossover. In: Proceedings of the genetic and evolutionary computation conference, vol 1. Morgan Kaufmann, Orlando, pp 172–179

    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 

  • Dorigo M (1992) Optimization, learning and natural algorithms. PhD dissertation, Dipartimento di Elettronica, Politecnico di Milano

  • Fourie PC, Groenwold AA (2002) The particle swarm optimization algorithm in size and shape optimization. Struct Multidisc Optim 23:259–267

    Article  Google Scholar 

  • Ghasemi MR, Hinton E, Wood RD (1999) Optimization of trusses using genetic algorithm for discrete and continuous variables. Eng Comput 16(3):272–301

    Article  MATH  Google Scholar 

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

    Google Scholar 

  • Haftka RT, Gurdal Z (1992) Elements of structural optimization, 3rd edn. Kluwer Academic Publishers

    MATH  Google Scholar 

  • Hajela P, Lee E (1995) Genetic algorithms in truss topological optimization. Int J Solids Struct 32:3341–3357

    Article  MATH  MathSciNet  Google Scholar 

  • Hajela P, Lee E, Lin CY (1993) Genetic algorithms in structural topology optimization. In: Blendsoe M, Soares C (eds) Topology design of structures. NATO ASI Series, pp 117–133

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

    Google Scholar 

  • Kaelo P, Ali MM (2006) A numerical study of some modified differential evolution algorithms. Eur J Oper Res 169:1176–1184

    Article  MATH  MathSciNet  Google Scholar 

  • Krisch U (1989) Optimal topologies of truss structures. Comput Methods Appl Mech Eng 72(1):15–28

    Article  Google Scholar 

  • Lee KS, Geem ZW (2004) A new structural optimization method based on the harmony search. Comput Struct 82:781–798

    Article  Google Scholar 

  • Li L, Huang Z, Liu F (2007) An improved particle swarm optimizer for truss structure optimization. Lect Notes Comput Sci 4456:1–10

    Article  Google Scholar 

  • Liu J, Lampinen J (2005) A fuzzy adaptive differential evolution algorithm. Soft Computing—A Fusion of Foundations, Methodologies and Applications 9:448–462

    MATH  Google Scholar 

  • Liu X, Liu H, Duan H (2007) Particle swarm optimization based on dynamic niche technology with applications to conceptual design. Adv Eng Softw 38:668–676

    Article  Google Scholar 

  • Luh GC, Chueh CH (2004) Multi-objective optimal design of truss structure with immune algorithm. Comput Struct 82:829–844

    Article  MathSciNet  Google Scholar 

  • Luh GC, Lin CY (2008) Optimal design of truss structures using ant algorithm. Struct Multidisc Optim 36(4):365–379

    Article  Google Scholar 

  • Monmarché N, Venturini G, Slimane M (2000) On how Pachycondyla apicalis ants suggest a new search algorithm. Future Gener Comput Syst 16:937–946

    Article  Google Scholar 

  • Nanakorn P, Meesinklim K (2001) An adaptive penalty function in genetic algorithms for structural design optimization. Comput Struct 79:2527–2539

    Article  Google Scholar 

  • Paterlini S, Krink T (2006) Differential evolution and particle swarm optimization in partitional clustering. Comput Stat Data Anal 50:1220–1247

    Article  MathSciNet  Google Scholar 

  • Perez RE, Behdinan K (2007) Particle swarm approach for structural design optimization. Comput Struct 85(19–20):1579–1588

    Article  Google Scholar 

  • Potts JC, Giddens TD, Yadav SB (1994) The development and evaluation of an improved genetic algorithm based on migration and artificial selection. IEEE Trans Syst Man Cybern 24(1):73–86

    Article  Google Scholar 

  • Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. In: The 2005 IEEE congress on evolutionary computation CEC2005, pp 1785–1791

  • Rajeev S, Krishnamoorthy CS (1992) Discrete optimization of structures using genetic algorithms. J Struct Eng 118(5):1233–1250

    Article  Google Scholar 

  • Schmit L, Miura H (1976) A new structural analysis/synthesis capability—access 1. AIAA J 14:661-671

    Article  Google Scholar 

  • Storn R, Price K (1995) Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous space. Technical report TR-95-012

  • Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359

    Article  MATH  MathSciNet  Google Scholar 

  • Sun J, Zhang Q, Tsang EPK (2005) DE/EDA: a new evolutionary algorithm for global optimization. Inf Sci 169:249–262

    Article  MathSciNet  Google Scholar 

  • Tasoulis DK, Pavlidis NG, Plagianakos VP, Vrahatis MN (2004) Parallel differential evolution. Evolution, Evolutionary Computation 2:2023–2029

    Google Scholar 

  • Teo J (2006) Exploring dynamic self-adaptive populations in differential evolution. Soft Computing—A Fusion of Foundations, Methodologies and Applications 10:673–686

    Google Scholar 

  • Vanderplaats GN (1993) Thirty years of modern structural optimization. Adv Eng Softw 16:81–88

    Article  Google Scholar 

  • Vanderplaats GN, Miura H, Nagendra G, Wallerstein D (1989) Optimization of large scale structures using MSC/NASTRAN. In: Brebbia CA, Hernandez S (eds) Computer aided optimum design of structures: applications. Computational Mechanics Publications, Springer-Verlag, pp 51–68

  • Wu SJ, Chow PT (1995) Steady-state genetic algorithms for discrete optimization of trusses. Comput Struct 56:919–991

    Article  Google Scholar 

  • Yan B, Xiong W, Cheng M, Ye Q (2008) Multi-population binary ant colony algorithm with congestion control strategy. In: Proceedings of 27th control conference, 16–18 July 2008, Kunming, Yunnan, China, vol 26(4), pp 387–394

  • Zhou M, Rozvany G (1993) DCOC: an optimality criteria method for large systems, part II: algorithm. Struct Multidisc Optim 6(4):250–262

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Tatung University, Taipei, 104, Taiwan, Republic of China

    Chun-Yin Wu & Ko-Ying Tseng

Authors
  1. Chun-Yin Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ko-Ying Tseng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chun-Yin Wu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, CY., Tseng, KY. Truss structure optimization using adaptive multi-population differential evolution. Struct Multidisc Optim 42, 575–590 (2010). https://doi.org/10.1007/s00158-010-0507-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-010-0507-9

Keywords

Search

Navigation