Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems

In this study, a new metaheuristic optimization algorithm, called cuckoo search (CS), is introduced for solving structural optimization tasks. The new CS algorithm in combination with Lévy flights is first verified using a benchmark nonlinear constrained optimization problem. For the validation against structural engineering optimization problems, CS is subsequently applied to 13 design problems reported in the specialized literature. The performance of the CS algorithm is further compared with various algorithms representative of the state of the art in the area. The optimal solutions obtained by CS are mostly far better than the best solutions obtained by the existing methods. The unique search features used in CS and the implications for future research are finally discussed in detail.

[1]  Xiaohui Hu,et al.  Engineering optimization with particle swarm , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[2]  El-Ghazali Talbi,et al.  Metaheuristics - From Design to Implementation , 2009 .

[3]  G. G. Wang,et al.  Adaptive Response Surface Method Using Inherited Latin Hypercube Design Points , 2003 .

[4]  Geoffrey T. Parks,et al.  Engineering design optimization using species-conserving genetic algorithms , 2007 .

[5]  Carlos A. Coello Coello,et al.  Engineering optimization using simple evolutionary algorithm , 2003, Proceedings. 15th IEEE International Conference on Tools with Artificial Intelligence.

[6]  Shang He,et al.  An improved particle swarm optimizer for mechanical design optimization problems , 2004 .

[7]  Leandro dos Santos Coelho,et al.  Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems , 2010, Expert Syst. Appl..

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

[9]  Kyung K. Choi,et al.  Reliability-based design optimization for crashworthiness of vehicle side impact , 2004 .

[10]  C. A. Coello Coello,et al.  Multiple trial vectors in differential evolution for engineering design , 2007 .

[11]  Carlos A. Coello Coello,et al.  Solving Engineering Optimization Problems with the Simple Constrained Particle Swarm Optimizer , 2008, Informatica.

[12]  A. Ravindran,et al.  Engineering Optimization: Methods and Applications , 2006 .

[13]  Han-Lin Li,et al.  An approximate approach of global optimization for polynomial programming problems , 1998, Eur. J. Oper. Res..

[14]  Kalyanmoy Deb,et al.  GeneAS: A Robust Optimal Design Technique for Mechanical Component Design , 1997 .

[15]  V. Braibant,et al.  Structural optimization: A new dual method using mixed variables , 1986 .

[16]  E. Sandgren,et al.  Nonlinear Integer and Discrete Programming in Mechanical Design Optimization , 1990 .

[17]  Carlos A. Coello Coello,et al.  Self-adaptive penalties for GA-based optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[18]  Hae Chang Gea,et al.  STRUCTURAL OPTIMIZATION USING A NEW LOCAL APPROXIMATION METHOD , 1996 .

[19]  Kalyanmoy Deb,et al.  A combined genetic adaptive search (GeneAS) for engineering design , 1996 .

[20]  H Nowacki,et al.  OPTIMIZATION IN PRE-CONTRACT SHIP DESIGN , 1973 .

[21]  David Mautner Himmelblau,et al.  Applied Nonlinear Programming , 1972 .

[22]  Abdollah Homaifar,et al.  Constrained Optimization Via Genetic Algorithms , 1994, Simul..

[23]  V. Litinetski,et al.  MARS - A MULTISTART ADAPTIVE RANDOM SEARCH METHOD FOR GLOBAL CONSTRAINED OPTIMIZATION IN ENGINEERING APPLICATIONS , 1998 .

[24]  C. J. Shih,et al.  MIXED-DISCRETE FUZZY PROGRAMMING FOR NONLINEAR ENGINEERING OPTIMIZATION , 1995 .

[25]  James C. Bean,et al.  A Genetic Algorithm for the Multiple-Choice Integer Program , 1997, Oper. Res..

[26]  Yun Li,et al.  Optimization and robustness for crashworthiness of side impact , 2001 .

[27]  Keigo Watanabe,et al.  Evolutionary Optimization of Constrained Problems , 2004 .

[28]  P. Barthelemy,et al.  A Lévy flight for light , 2008, Nature.

[29]  S. N. Kramer,et al.  An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design , 1994 .

[30]  Siamak Talatahari,et al.  An improved ant colony optimization for constrained engineering design problems , 2010 .

[31]  Mahamed G. H. Omran,et al.  Constrained optimization using CODEQ , 2009 .

[32]  Xin-She Yang,et al.  Cuckoo Search via Lévy flights , 2009, 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC).

[33]  M. Shlesinger.  Mathematical physics: Search research , 2006, Nature.

[34]  Xin-She Yang.  Harmony Search as a Metaheuristic Algorithm , 2009 .

[35]  K I Majid,et al.  Optimum design of structures , 1974 .

[36]  A. Reynolds,et al.  Free-Flight Odor Tracking in Drosophila Is Consistent with an Optimal Intermittent Scale-Free Search , 2007, PloS one.

[37]  K. Lee,et al.  A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice , 2005 .

[38]  Georg Thierauf,et al.  EVOLUTION STRATEGIES IN ENGINEERING OPTIMIZATION , 1997 .

[39]  Chun Zhang,et al.  Mixed-discrete nonlinear optimization with simulated annealing , 1993 .

[40]  C. J. Shih,et al.  Generalized Hopfield network based structural optimization using sequential unconstrained minimization technique with additional penalty strategy , 2002 .

[41]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[42]  R. G. Fenton,et al.  A MIXED INTEGER-DISCRETE-CONTINUOUS PROGRAMMING METHOD AND ITS APPLICATION TO ENGINEERING DESIGN OPTIMIZATION , 1991 .

[43]  Tapabrata Ray,et al.  Society and civilization: An optimization algorithm based on the simulation of social behavior , 2003, IEEE Trans. Evol. Comput..

[44]  Erwie Zahara,et al.  Hybrid Nelder-Mead simplex search and particle swarm optimization for constrained engineering design problems , 2009, Expert Syst. Appl..

[45]  Jung-Fa Tsai,et al.  Global optimization of nonlinear fractional programming problems in engineering design , 2005 .

[46]  Yeh-Liang Hsu,et al.  Developing a fuzzy proportional–derivative controller optimization engine for engineering design optimization problems , 2007 .

[47]  尹 泳秀,et al.  Study on adaptive hybrid genetic algorithm and its applications to engineering design problems , 2005 .

[48]  Carlos A. Coello Coello,et al.  Use of a self-adaptive penalty approach for engineering optimization problems , 2000 .

[49]  Carlos A. Coello Coello,et al.  Constraint-handling in genetic algorithms through the use of dominance-based tournament selection , 2002, Adv. Eng. Informatics.

[50]  Singiresu S. Rao.  Engineering Optimization : Theory and Practice , 2010 .

[51]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms in Engineering Applications , 1997, Springer Berlin Heidelberg.

[52]  Ling Wang,et al.  An effective co-evolutionary differential evolution for constrained optimization , 2007, Appl. Math. Comput..

[53]  Jung-Fa Tsai,et al.  Global optimization for signomial discrete programming problems in engineering design , 2002 .

[54]  H. Amir,et al.  Nonlinear Mixed-Discrete Structural Optimization , 1989 .

[55]  Michael N. Vrahatis,et al.  Unified Particle Swarm Optimization for Solving Constrained Engineering Optimization Problems , 2005, ICNC.

[56]  S. Wu,et al.  GENETIC ALGORITHMS FOR NONLINEAR MIXED DISCRETE-INTEGER OPTIMIZATION PROBLEMS VIA META-GENETIC PARAMETER OPTIMIZATION , 1995 .

[57]  Carlos A. Coello Coello,et al.  Hybridizing a genetic algorithm with an artificial immune system for global optimization , 2004 .

[58]  Jongsoo Lee,et al.  An integrated method of particle swarm optimization and differential evolution , 2009 .

[59]  Christopher R. Houck,et al.  On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[60]  Judith S. Liebman,et al.  Discrete Structural Optimization , 1981 .

[61]  Amir Hossein Gandomi,et al.  Benchmark Problems in Structural Optimization , 2011, Computational Optimization, Methods and Algorithms.

[62]  A. Gandomi,et al.  Mixed variable structural optimization using Firefly Algorithm , 2011 .

[63]  Tapabrata Ray,et al.  A socio-behavioural simulation model for engineering design optimization , 2002 .

[64]  Han-Lin Li,et al.  A GLOBAL APPROACH FOR NONLINEAR MIXED DISCRETE PROGRAMMING IN DESIGN OPTIMIZATION , 1993 .

[65]  Xin-She Yang,et al.  Nature-Inspired Metaheuristic Algorithms , 2008 .

[66]  C. Coello,et al.  CONSTRAINT-HANDLING USING AN EVOLUTIONARY MULTIOBJECTIVE OPTIMIZATION TECHNIQUE , 2000 .

[67]  Li Chen,et al.  TAGUCHI-AIDED SEARCH METHOD FOR DESIGN OPTIMIZATION OF ENGINEERING SYSTEMS , 1998 .

[68]  Clifford T. Brown,et al.  Lévy Flights in Dobe Ju/’hoansi Foraging Patterns , 2007 .

[69]  Xinwei Wang,et al.  Nanoparticles Formed in Picosecond Laser Argon Crystal Interaction , 2003 .

[70]  Ling Wang,et al.  An effective co-evolutionary particle swarm optimization for constrained engineering design problems , 2007, Eng. Appl. Artif. Intell..

[71]  M. Mahdavi,et al.  ARTICLE IN PRESS Available online at www.sciencedirect.com , 2007 .

[72]  Masoud Sanayei,et al.  Parameter Estimation of Structures from Static Strain Measurements. I: Formulation , 1996 .

[73]  Ilya Pavlyukevich.  Lévy flights, non-local search and simulated annealing , 2007, J. Comput. Phys..