Critical Evaluation of Metaheuristic Algorithms for Weight Minimization of Truss Structures

This study critically compares variants of Genetic Algorithms, Particle Swarm Optimization, Artificial Bee Colony, Differential Evolution and Simulated Annealing used in truss sizing optimization problems including displacement and stress constraints. The comparison is based on several benchmark problems of varying complexity number of design variables. i.e. the number of design variables, and the degree of static indeterminacy. Most of these problems have been studied by numerous researchers using a large variety of methods; this allows for absolute rather than relative comparison. Rigorous statistical analysis based on large sample size, as well as monitoring of the success rate throughout the optimization process, reveal and explain the convergence behavior observed for each method. The results indicate that, for the problem at hand, Differential Evolution is the best algorithm in terms of robustness, performance, and scalability.

[1]  M. Géradin,et al.  Optimality criteria and mathematical programming in structural weight optimization , 1978 .

[2]  Ali Kaveh,et al.  A comparative study of CBO and ECBO for optimal design of skeletal structures , 2015 .

[3]  V. K. Koumousis,et al.  Reliability-Based Optimal Design of Truss Structures Using Particle Swarm Optimization , 2009 .

[4]  Nielen Stander,et al.  Structural optimization using augmented Lagrangian methods with secant Hessian updating , 1996 .

[5]  K. Lee,et al.  A new structural optimization method based on the harmony search algorithm , 2004 .

[6]  Kamran Behdinan,et al.  Particle swarm approach for structural design optimization , 2007 .

[7]  Ali Kaveh,et al.  ENHANCED BAT ALGORITHM FOR OPTIMAL DESIGN OF SKELETAL STRUCTURES , 2014 .

[8]  V. K. Koumousis,et al.  Identification of Bouc-Wen hysteretic systems by a hybrid evolutionary algorithm , 2008 .

[9]  A. Z. Baraniecki,et al.  Computationally efficient discrete wavelet transform model , 1996 .

[10]  T. Bakhshpoori,et al.  An efficient hybrid Particle Swarm and Swallow Swarm Optimization algorithm , 2014 .

[11]  Q. H. Wu,et al.  A heuristic particle swarm optimizer for optimization of pin connected structures , 2007 .

[12]  Tapabrata Ray,et al.  ENGINEERING DESIGN OPTIMIZATION USING A SWARM WITH AN INTELLIGENT INFORMATION SHARING AMONG INDIVIDUALS , 2001 .

[13]  A. Charalampakis,et al.  Analytical solutions for the minimum weight design of trusses by cylindrical algebraic decomposition , 2018 .

[14]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[15]  Siamak Talatahari,et al.  Optimal design of skeletal structures via the charged system search algorithm , 2010 .

[16]  Amir Hossein Gandomi,et al.  A multi-stage particle swarm for optimum design of truss structures , 2013, Neural Computing and Applications.

[17]  Andy J. Keane,et al.  A brief comparison of some evolutionary optimization methods , 1996 .

[18]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[19]  P. Fourie,et al.  The particle swarm optimization algorithm in size and shape optimization , 2002 .

[20]  C. K. Dimou,et al.  Comparison of Evolutionary Algorithms for the Identification of Bouc-Wen Hysteretic Systems , 2015, J. Comput. Civ. Eng..

[21]  Alan D. Christiansen,et al.  Multiobjective optimization of trusses using genetic algorithms , 2000 .

[22]  Giuseppe Quaranta,et al.  Modified Genetic Algorithm for the Dynamic Identification of Structural Systems Using Incomplete Measurements , 2011, Comput. Aided Civ. Infrastructure Eng..

[23]  Kong Fah Tee,et al.  Combined size and shape optimization of truss structures using subset simulation optimization , 2018, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering.

[24]  Subramaniam Rajan,et al.  Sizing, Shape, and Topology Design Optimization of Trusses Using Genetic Algorithm , 1995 .

[25]  Charles V. Camp DESIGN OF SPACE TRUSSES USING BIG BANG–BIG CRUNCH OPTIMIZATION , 2007 .

[26]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[27]  Ali Kaveh,et al.  Ray optimization for size and shape optimization of truss structures , 2013 .

[28]  Carlos Artemio Coello-Coello,et al.  Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art , 2002 .

[29]  D. Karaboga,et al.  On the performance of artificial bee colony (ABC) algorithm , 2008, Appl. Soft Comput..

[30]  O. Hasançebi,et al.  Performance evaluation of metaheuristic search techniques in the optimum design of real size pin jointed structures , 2009 .

[31]  A. Groenwold,et al.  Comparison of linear and classical velocity update rules in particle swarm optimization: notes on diversity , 2007 .

[32]  Sean R Eddy,et al.  What is dynamic programming? , 2004, Nature Biotechnology.

[33]  Saku Kukkonen,et al.  Real-parameter optimization with differential evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

[34]  A. Kaveh,et al.  Size optimization of space trusses using Big Bang-Big Crunch algorithm , 2009 .

[35]  Michael Frankfurter,et al.  Numerical Recipes In C The Art Of Scientific Computing , 2016 .

[36]  Xin Yao,et al.  Self-adaptive differential evolution with neighborhood search , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[37]  A. Kaveh,et al.  Two-dimensional colliding bodies algorithm for optimal design of truss structures , 2015, Adv. Eng. Softw..

[38]  David A. Wood,et al.  What a performance , 2004 .

[39]  Luciano Lamberti,et al.  AN IMPROVED HARMONY-SEARCH ALGORITHM FOR TRUSS STRUCTURE OPTIMIZATION , 2009 .

[40]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[41]  Luciano Lamberti,et al.  An efficient simulated annealing algorithm for design optimization of truss structures , 2008 .

[42]  Albert A. Groenwold,et al.  Sizing design of truss structures using particle swarms , 2003 .

[43]  Hojjat Adeli,et al.  Distributed Genetic Algorithm for Structural Optimization , 1995 .

[44]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[45]  A. E. Eiben,et al.  Introduction to Evolutionary Computing , 2003, Natural Computing Series.

[46]  V. K. Koumousis,et al.  Genetic Algorithms in Discrete Optimization of Steel Truss Roofs , 1994 .

[47]  Zong Woo Geem,et al.  A New Heuristic Optimization Algorithm: Harmony Search , 2001, Simul..

[48]  Mustafa Sonmez,et al.  Artificial Bee Colony algorithm for optimization of truss structures , 2011, Appl. Soft Comput..

[49]  Ali Kaveh,et al.  Colliding bodies optimization for size and topology optimization of truss structures , 2015 .

[50]  Charles V. Camp,et al.  Design of space trusses using modified teaching–learning based optimization , 2014 .

[51]  S. O. Degertekin Improved harmony search algorithms for sizing optimization of truss structures , 2012 .

[52]  O. Hasançebi,et al.  Computationally efficient discrete sizing of steel frames via guided stochastic search heuristic , 2015 .

[53]  S. O. Degertekin,et al.  Sizing truss structures using teaching-learning-based optimization , 2013 .

[54]  L. Berke,et al.  Structural optimization using optimality criteria , 1987 .

[55]  Ibrahim Eksin,et al.  A new optimization method: Big Bang-Big Crunch , 2006, Adv. Eng. Softw..

[56]  R. Venkata Rao,et al.  Teaching-learning-based optimization: A novel method for constrained mechanical design optimization problems , 2011, Comput. Aided Des..

[57]  A. Kaveh,et al.  Chaotic swarming of particles: A new method for size optimization of truss structures , 2014, Adv. Eng. Softw..

[58]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[59]  Siamak Talatahari,et al.  Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures , 2009 .

[60]  M. Ehrgott Multiobjective Optimization , 2008, AI Mag..

[61]  Arthur C. Sanderson,et al.  JADE: Adaptive Differential Evolution With Optional External Archive , 2009, IEEE Transactions on Evolutionary Computation.

[62]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[63]  Richard J. Balling,et al.  Optimal Steel Frame Design by Simulated Annealing , 1991 .

[64]  Chun-Yin Wu,et al.  Truss structure optimization using adaptive multi-population differential evolution , 2010 .

[65]  Nantiwat Pholdee,et al.  Optimal Truss Sizing Using an Adaptive Differential Evolution Algorithm , 2016, J. Comput. Civ. Eng..

[66]  Yusuf Ayvaz,et al.  Combined size and shape optimization of structures with a new meta-heuristic algorithm , 2015, Appl. Soft Comput..

[67]  C. K. Dimou,et al.  Identification of Bouc-Wen hysteretic systems using particle swarm optimization , 2010 .

[68]  Saeid Kazemzadeh Azad,et al.  Adaptive dimensional search: A new metaheuristic algorithm for discrete truss sizing optimization , 2015 .