Improved bat algorithm for structural reliability assessment: application and challenges

Purpose – The first order reliability method requires optimization algorithms to find the minimum distance from the origin to the limit state surface in the normal space. The purpose of this paper is to develop an improved version of the new metaheuristic algorithm inspired from echolocation behaviour of bats, namely, the bat algorithm (BA) dedicated to perform structural reliability analysis. Design/methodology/approach – Modifications have been embedded to the standard BA to enhance its efficiency, robustness and reliability. In addition, a new adaptive penalty equation dedicated to solve the problem of the determination of the reliability index and a proposition on the limit state formulation are presented. Findings – The comparisons between the improved bat algorithm (iBA) presented in this paper and other standard algorithms on benchmark functions show that the iBA is highly efficient, and the application to structural reliability problems such as the reliability analysis of overhead crane girder pro...

[1]  Saeed Tavakoli,et al.  Improved cuckoo search for reliability optimization problems , 2013, Comput. Ind. Eng..

[2]  G. Cheng,et al.  Convergence analysis of first order reliability method using chaos theory , 2006, Computers & Structures.

[3]  Xin-She Yang,et al.  Design optimization of truss structures using cuckoo search algorithm , 2013 .

[4]  Hao Yan,et al.  Structural Reliability Analysis Based on Imperialist Competitive Algorithm , 2013, 2013 Fourth International Conference on Intelligent Systems Design and Engineering Applications.

[5]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[6]  Jin Cheng,et al.  Reliability analysis of structures using artificial neural network based genetic algorithms , 2008 .

[7]  Károly Jármai,et al.  Decision support system on IBM PC for design of economic steel structures applied to crane girders , 1990 .

[8]  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.

[9]  A. Kiureghian,et al.  Optimization algorithms for structural reliability , 1991 .

[10]  K. Breitung.  Asymptotic approximations for multinormal integrals , 1984 .

[11]  A. Rezaee Jordehi,et al.  Chaotic bat swarm optimisation (CBSO) , 2015, Appl. Soft Comput..

[12]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[13]  Yu Liu,et al.  A New Bio-inspired Algorithm: Chicken Swarm Optimization , 2014, ICSI.

[14]  Tetsuyuki Takahama,et al.  Constrained Optimization by the ε Constrained Differential Evolution with Gradient-Based Mutation and Feasible Elites , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[15]  Nicolas Devictor.  Fiabilite et mecanique : methodes form/sorm et couplages avec des codes d'elements finis par des surfaces de reponse adaptatives , 1996 .

[16]  Ehsan Valian,et al.  Solving Reliability Optimization Problems by Cuckoo Search , 2014 .

[17]  Xin-She Yang,et al.  Bat algorithm for multi-objective optimisation , 2011, Int. J. Bio Inspired Comput..

[18]  Yaacob Ibrahim,et al.  Observations on applications of importance sampling in structural reliability analysis , 1991 .

[19]  Dexuan Zou,et al.  A novel global harmony search algorithm for reliability problems , 2010, Comput. Ind. Eng..

[20]  Xin-She Yang,et al.  Bat algorithm: a novel approach for global engineering optimization , 2012, 1211.6663.

[21]  Dixiong Yang.  Chaos control for numerical instability of first order reliability method , 2010 .

[22]  Jeng-Shyang Pan,et al.  Bat Algorithm Inspired Algorithm for Solving Numerical Optimization Problems , 2011 .

[23]  Amir Hossein Gandomi,et al.  Bat algorithm for constrained optimization tasks , 2012, Neural Computing and Applications.

[24]  Zhen Wang,et al.  A new constraint handling method based on the modified Alopex-based evolutionary algorithm , 2014, Comput. Ind. Eng..

[25]  Ramana V. Grandhi,et al.  Reliability-based Structural Design , 2006 .

[26]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[27]  Hongbo Zhao,et al.  Reliability Analysis Using Chaotic Particle Swarm Optimization , 2015, Qual. Reliab. Eng. Int..

[28]  N. Gayton,et al.  CQ2RS: a new statistical approach to the response surface method for reliability analysis , 2003 .

[29]  S. Rahman,et al.  A univariate approximation at most probable point for higher-order reliability analysis , 2006 .

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

[31]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

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

[33]  Yongquan Zhou,et al.  A novel complex-valued bat algorithm , 2014, Neural Computing and Applications.

[34]  Byeng D. Youn,et al.  Performance Moment Integration (PMI) Method for Quality Assessment in Reliability-Based Robust Design Optimization , 2005 .

[35]  Robert E. Melchers,et al.  General multi-dimensional probability integration by directional simulation , 1990 .

[36]  Caro Lucas,et al.  A novel numerical optimization algorithm inspired from weed colonization , 2006, Ecol. Informatics.

[37]  Mohammad Shafiul Alam,et al.  Bat Algorithm with Self-adaptive Mutation: A Comparative Study on Numerical Optimization Problems , 2014 .

[38]  Byung Chai Lee,et al.  Development of a simple and efficient method for robust optimization , 2002 .

[39]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

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

[41]  R. Melchers.  Search-based importance sampling , 1990 .

[42]  F. Grooteman.  Adaptive radial-based importance sampling method for structural reliability , 2008 .

[43]  T. V. Santosh,et al.  Optimum step length selection rule in modified HL-RF method for structural reliability , 2006 .

[44]  S. Rahman,et al.  A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics , 2004 .

[45]  Gary G. Yen,et al.  A Self Adaptive Penalty Function Based Algorithm for Constrained Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[46]  Trong-The Nguyen,et al.  Parallelized Bat Algorithm with a Communication Strategy , 2014, IEA/AIE.

[47]  J. Beck,et al.  A new adaptive importance sampling scheme for reliability calculations , 1999 .

[48]  Andrzej S. Nowak,et al.  Reliability of Structures , 2000 .

[49]  Nostrand Reinhold,et al.  the utility of using the genetic algorithm approach on the problem of Davis, L. (1991), Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York. , 1991 .

[50]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[51]  B. Ellingwood,et al.  Directional methods for structural reliability analysis , 2000 .

[52]  O. Hasançebi,et al.  A bat-inspired algorithm for structural optimization , 2013 .

[53]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

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

[55]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[56]  Ling Wang,et al.  A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization , 2007, Appl. Math. Comput..

[57]  Trong-The Nguyen,et al.  Hybrid Particle Swarm Optimization with Bat Algorithm , 2014, ICGEC.

[58]  A. M. Hasofer,et al.  Exact and Invariant Second-Moment Code Format , 1974 .

[59]  A. E. Eiben,et al.  Adaptive Penalties for Evolutionary Graph Coloring , 1997, Artificial Evolution.

[60]  M. Miri,et al.  A new efficient simulation method to approximate the probability of failure and most probable point , 2012 .

[61]  Xin-She Yang,et al.  Bat algorithm based on simulated annealing and Gaussian perturbations , 2013, Neural Computing and Applications.

[62]  Xin-She Yang,et al.  Binary bat algorithm , 2013, Neural Computing and Applications.

[63]  Selim Yilmaz,et al.  A new modification approach on bat algorithm for solving optimization problems , 2015, Appl. Soft Comput..

[64]  Alice E. Smith,et al.  Genetic Optimization Using A Penalty Function , 1993, ICGA.

[65]  Jian Wang,et al.  Linkage-shredding genetic algorithm for reliability assessment of structural systems , 2005 .

[66]  Iztok Fister,et al.  A hybrid bat algorithm , 2013, ArXiv.

[67]  Jian Xie,et al.  A Novel Bat Algorithm Based on Differential Operator and Lévy Flights Trajectory , 2013, Comput. Intell. Neurosci..

[68]  Robert E. Melchers,et al.  Structural Reliability: Analysis and Prediction , 1987 .

[69]  Niels C. Lind,et al.  Methods of structural safety , 2006 .

[70]  R. Rackwitz.  Reliability analysis—a review and some perspectives , 2001 .

[71]  Yan Zhang,et al.  Two Improved Algorithms for Reliability Analysis , 1995 .

[72]  Charles Elegbede,et al.  Structural reliability assessment based on particles swarm optimization , 2005 .

[73]  Sharif Rahman,et al.  A multi-point univariate decomposition method for structural reliability analysis , 2010 .

[74]  Manolis Papadrakakis,et al.  Reliability-based structural optimization using neural networks and Monte Carlo simulation , 2002 .

[75]  Carlos A. Coello Coello,et al.  THEORETICAL AND NUMERICAL CONSTRAINT-HANDLING TECHNIQUES USED WITH EVOLUTIONARY ALGORITHMS: A SURVEY OF THE STATE OF THE ART , 2002 .

[76]  A. Sellier,et al.  Adaptive response surface method based on a double weighted regression technique , 2009 .

[77]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

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

[79]  L. C. Matioli,et al.  New Optimization Algorithms for Structural Reliability Analysis , 2012 .

[80]  B. Youn,et al.  Eigenvector dimension reduction (EDR) method for sensitivity-free probability analysis , 2008 .

[81]  Selim Yilmaz,et al.  Modified Bat Algorithm , 2014 .

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

[83]  P. N. Suganthan,et al.  Ensemble of Constraint Handling Techniques , 2010, IEEE Transactions on Evolutionary Computation.

[84]  Simon Fong,et al.  A Novel Hybrid Self-Adaptive Bat Algorithm , 2014, TheScientificWorldJournal.

[85]  Wei-Hsin Huang,et al.  Study of an assembly tolerance allocation model based on Monte Carlo simulation , 1997 .

[86]  A. Olsson,et al.  On Latin hypercube sampling for structural reliability analysis , 2003 .

[87]  Ali Kaveh,et al.  STRUCTURAL RELIABILITY ASSESSMENT UTILIZING FOUR METAHEURISTIC ALGORITHMS , 2015 .

[88]  L. Tvedt.  Distribution of quadratic forms in normal space-application to structural reliability , 1990 .

[89]  Ali Osman Kusakci,et al.  Constrained Optimization with Evolutionary Algorithms: A Comprehensive Review , 2012, SOCO 2012.

[90]  V. I. Weingarten,et al.  Buckling of thin-walled truncated cones , 1968 .

[91]  J. Farkas.  Economy of higher-strength steels in overhead travelling cranes with double-box girders , 1986 .

[92]  D. Huntington,et al.  Improvements to and limitations of Latin hypercube sampling , 1998 .

[93]  Antonio Borri,et al.  Structural reliability analysis using a standard deterministic finite element code , 1997 .

[94]  P. Seide,et al.  Buckling of thin-walled truncated cones, NASA SPACE VEHICLE DESIGN CRITERIA (Structures) , 1968 .

[95]  Amir Hossein Alavi,et al.  Krill herd: A new bio-inspired optimization algorithm , 2012 .