Bat algorithm for constrained optimization tasks

In this study, we use a new metaheuristic optimization algorithm, called bat algorithm (BA), to solve constraint optimization tasks. BA is verified using several classical benchmark constraint problems. For further validation, BA is applied to three benchmark constraint engineering problems reported in the specialized literature. The performance of the bat algorithm is compared with various existing algorithms. The optimal solutions obtained by BA are found to be better than the best solutions provided by the existing methods. Finally, the unique search features used in BA are analyzed, and their implications for future research are discussed in detail.

[1]  Rong-Song He,et al.  A hybrid real-parameter genetic algorithm for function optimization , 2006, Adv. Eng. Informatics.

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

[3]  Zbigniew Michalewicz,et al.  Evolutionary optimization of constrained problems , 1994 .

[4]  James N. Siddall,et al.  Analytical decision-making in engineering design , 1972 .

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

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

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

[8]  Ricardo Landa Becerra,et al.  Efficient evolutionary optimization through the use of a cultural algorithm , 2004 .

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

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

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

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

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

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

[15]  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).

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

[17]  Jasbir S. Arora,et al.  Introduction to Optimum Design , 1988 .

[18]  J. Altringham Bats: Biology and Behaviour , 1996 .

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

[20]  Klaus Schittkowski,et al.  Test examples for nonlinear programming codes , 1980 .

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

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

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

[24]  C. Coello,et al.  Cultured differential evolution for constrained optimization , 2006 .

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

[26]  Kalyanmoy Deb,et al.  Optimal design of a welded beam via genetic algorithms , 1991 .

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

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

[29]  Y. J. Cao,et al.  Evolutionary programming , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

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

[31]  Changyong Liang,et al.  An effective multiagent evolutionary algorithm integrating a novel roulette inversion operator for engineering optimization , 2009, Appl. Math. Comput..

[32]  A. Amirjanov The development of a changing range genetic algorithm , 2006 .

[33]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[34]  Xin-She Yang,et al.  A New Metaheuristic Bat-Inspired Algorithm , 2010, NICSO.

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

[36]  Mir M. Atiqullah,et al.  SIMULATED ANNEALING AND PARALLEL PROCESSING: AN IMPLEMENTATION FOR CONSTRAINED GLOBAL DESIGN OPTIMIZATION , 2000 .

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

[38]  M. Montaz Ali,et al.  Solving nonlinearly constrained global optimization problem via an auxiliary function method , 2009 .

[39]  Heder S. Bernardino,et al.  Constraint Handling in Genetic Algorithms via Artificial Immune Systems , 2006 .

[40]  Carlos A. Coello Coello,et al.  An empirical study about the usefulness of evolution strategies to solve constrained optimization problems , 2008, Int. J. Gen. Syst..

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

[42]  Heder S. Bernardino,et al.  A hybrid genetic algorithm for constrained optimization problems in mechanical engineering , 2007, 2007 IEEE Congress on Evolutionary Computation.

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

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

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

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

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

[48]  C. Coello,et al.  USE OF DOMINANCE-BASED TOURNAMENT SELECTION TO HANDLE CONSTRAINTS IN GENETIC ALGORITHMS , 2001 .

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

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

[51]  Barry Hilary Valentine Topping,et al.  Improved genetic operators for structural engineering optimization , 1998 .

[52]  Li Cheng,et al.  A New Metaheuristic Bat-Inspired Algorithm , 2010 .

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

[54]  K. M. Ragsdell,et al.  Optimal Design of a Class of Welded Structures Using Geometric Programming , 1976 .

[55]  Amir Hossein Gandomi,et al.  Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems , 2011, Engineering with Computers.

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

[57]  Helio J. C. Barbosa,et al.  An adaptive penalty scheme for genetic algorithms in structural optimization , 2004 .

[58]  Carlos A. Coello Coello,et al.  Handling Constraints in Global Optimization Using an Artificial Immune System , 2005, ICARIS.

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

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

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

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

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

[64]  Carlos A. Coello Coello,et al.  A simple multimembered evolution strategy to solve constrained optimization problems , 2005, IEEE Transactions on Evolutionary Computation.

[65]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization , 1999, Evolutionary Computation.

[66]  Masao Fukushima,et al.  Derivative-Free Filter Simulated Annealing Method for Constrained Continuous Global Optimization , 2006, J. Glob. Optim..

[67]  Klaus Schittkowski,et al.  More test examples for nonlinear programming codes , 1981 .

[68]  Gary G. Yen,et al.  A generic framework for constrained optimization using genetic algorithms , 2005, IEEE Transactions on Evolutionary Computation.

[69]  Helio J. C. Barbosa,et al.  An Adaptive Penalty Scheme In Genetic Algorithms For Constrained Optimiazation Problems , 2002, GECCO.

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

[71]  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.

[72]  Carlos A. Coello Coello,et al.  Handling Constraints in Particle Swarm Optimization Using a Small Population Size , 2007, MICAI.

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

[74]  Amir Hossein Gandomi,et al.  Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization , 2012, Comput. Math. Appl..

[75]  A. Kaveh,et al.  A novel heuristic optimization method: charged system search , 2010 .

[76]  Ashok Dhondu Belegundu,et al.  A Study of Mathematical Programming Methods for Structural Optimization , 1985 .

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

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

[79]  Heder S. Bernardino,et al.  A new hybrid AIS-GA for constrained optimization problems in mechanical engineering , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

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

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

[82]  Jenn-Long Liu,et al.  Novel orthogonal simulated annealing with fractional factorial analysis to solve global optimization problems , 2005 .

[83]  B. Hernández-Ocaña,et al.  Bacterial Foraging for Engineering Design Problems: Preliminary Results , 2008 .

[84]  Wenjian Luo,et al.  Differential evolution with dynamic stochastic selection for constrained optimization , 2008, Inf. Sci..

[85]  Carlos A. Coello Coello,et al.  A modified version of a T‐Cell Algorithm for constrained optimization problems , 2010 .

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