July  2014, 10(3): 777-794. doi: 10.3934/jimo.2014.10.777

Solving structural engineering design optimization problems using an artificial bee colony algorithm

1. 

School of Mathematics and Computer Applications, Thapar University Patiala, Patiala - 147004, Punjab, India

Received  June 2012 Revised  June 2013 Published  November 2013

The main goal of the present paper is to solve structural engineering design optimization problems with nonlinear resource constraints. Real world problems in engineering domain are generally large scale or nonlinear or constrained optimization problems. Since heuristic methods are powerful than the traditional numerical methods, as they don't requires the derivatives of the functions and provides near to the global solution. Hence, in this article, a penalty guided artificial bee colony (ABC) algorithm is presented to search the optimal solution of the problem in the feasible region of the entire search space. Numerical results of the structural design optimization problems are reported and compared. As shown, the solutions by the proposed approach are all superior to those best solutions by typical approaches in the literature. Also we can say, our results indicate that the proposed approach may yield better solutions to engineering problems than those obtained using current algorithms.
Citation: Harish Garg. Solving structural engineering design optimization problems using an artificial bee colony algorithm. Journal of Industrial & Management Optimization, 2014, 10 (3) : 777-794. doi: 10.3934/jimo.2014.10.777
References:
[1]

B. Akay and D. Karaboga, Artificial bee colony algorithm for large-scale problems and engineering design optimization,, Journal of Intelligent Manufacturing, 23 (2012), 1001.  doi: 10.1007/s10845-010-0393-4.  Google Scholar

[2]

J. S. Arora, Introduction to Optimum Design,, McGraw-Hill, (1989).   Google Scholar

[3]

A. D. Belegundu, A Study of Mathematical Programming Methods for Structural Optimization,, PhD thesis, (1982).   Google Scholar

[4]

L. C. Cagnina, S. C. Esquivel and C. A. C. Coello, Solving engineering optimization problems with the simple constrained particle swarm optimizer,, Informatica, 32 (2008), 319.   Google Scholar

[5]

L. S. Coelho, Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems,, Expert Systems with Applications, 37 (2010), 1676.  doi: 10.1016/j.eswa.2009.06.044.  Google Scholar

[6]

C. A. C. Coello, Treating constraints as objectives for single-objective evolutionary optimization,, Engineering Optimization, 32 (2000), 275.  doi: 10.1080/03052150008941301.  Google Scholar

[7]

C. A. C. Coello, Use of a self -adaptive penalty approach for engineering optimization problems,, Computers in Industry, 41 (2000), 113.  doi: 10.1016/S0166-3615(99)00046-9.  Google Scholar

[8]

C. A. C. Coello and E. M. Montes, Constraint- handling in genetic algorithms through the use of dominance-based tournament selection,, Advanced Engineering Informatics, 16 (2002), 193.  doi: 10.1016/S1474-0346(02)00011-3.  Google Scholar

[9]

K. Deb, Optimal design of a welded beam via genetic algorithms,, AIAA Journal, 29 (1991), 2013.   Google Scholar

[10]

K. Deb, An efficient constraint handling method for genetic algorithms,, Computer Methods in Applied Mechanics and Engineering, 186 (2000), 311.  doi: 10.1016/S0045-7825(99)00389-8.  Google Scholar

[11]

K. Deb and A. S. Gene, A robust optimal design technique for mechanical component design,, (Eds. D. Dasgupta, (1997), 497.  doi: 10.1007/978-3-662-03423-1_27.  Google Scholar

[12]

K. Deb and M. Goyal, A combined genetic adaptive search (GeneAS) for engineering design,, Computer Science and Informatics, 26 (1986), 30.   Google Scholar

[13]

G. G. Dimopoulos, Mixed-variable engineering optimization based on evolutionary and social metaphors,, Computer Methods in Applied Mechanics and Engineering, 196 (2007), 803.  doi: 10.1016/j.cma.2006.06.010.  Google Scholar

[14]

M. Fesanghary, M. Mahdavi, M. Minary-Jolandan and Y. Alizadeh, Hybridizing harmony search algorithm with sequential quadratic programming for engineering optimization problems,, Computer Methods in Applied Mechanics and Engineering, 197 (2008), 3080.  doi: 10.1016/j.cma.2008.02.006.  Google Scholar

[15]

A. H. Gandomi, X. S. Yang, and A. H. Alavi, Mixed variable structural optimization using firefly algorithm,, Computers & Structures, 89 (): 2325.   Google Scholar

[16]

A. H. Gandomi, X. S. Yang and A. Alavi, Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems,, Engineering with Computers, 29 (2003), 17.  doi: 10.1007/s00366-011-0241-y.  Google Scholar

[17]

Q. He and L. Wang, An effective co - evolutionary particle swarm optimization for constrained engineering design problems,, Engineering Applications of Artificial Intelligence, 20 (2007), 89.  doi: 10.1016/j.engappai.2006.03.003.  Google Scholar

[18]

S. He, E. Prempain and Q. H. Wu, An improved particle swarm optimizer for mechanical design optimization problems,, Engineering Optimization, 36 (2004), 585.  doi: 10.1080/03052150410001704854.  Google Scholar

[19]

A. R. Hedar and M. Fukushima, Derivative - free filter simulated annealing method for constrained continuous global optimization,, Journal of Global Optimization, 35 (2006), 521.  doi: 10.1007/s10898-005-3693-z.  Google Scholar

[20]

D. M. Himmelblau, Applied Nonlinear Programming,, McGraw-Hill, (1972).   Google Scholar

[21]

A. Homaifar, S. H. Y. Lai and X. Qi, Constrained optimization via genetic algorithms,, Simulation, 62 (1994), 242.  doi: 10.1177/003754979406200405.  Google Scholar

[22]

Y. L. Hsu and T. C. Liu, Developing a fuzzy proportional derivative controller optimization engine for engineering design optimization problems,, Engineering Optimization, 39 (2007), 679.  doi: 10.1080/03052150701252664.  Google Scholar

[23]

X. H. Hu, R. C. Eberhart and Y. H. Shi, Engineering optimization with particle swarm,, Proceedings of the 2003 IEEE Swarm Intelligence Symposium, (2003), 53.   Google Scholar

[24]

S. F. Hwang and R. S. He, A hybrid real-parameter genetic algorithm for function optimization,, Advanced Engineering Informatics, 20 (2006), 7.  doi: 10.1016/j.aei.2005.09.001.  Google Scholar

[25]

B. K. Kannan and S. N. Kramer, An augmented lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design,, Transactions of the ASME, 116 (1994), 405.  doi: 10.1115/1.2919393.  Google Scholar

[26]

D. Karaboga, An Idea Based on Honey Bee Swarm for Numerical Optimization,, Technical report, (2005).   Google Scholar

[27]

D. Karaboga and B. Akay, A comparative study of artificial bee colony algorithm,, Applied Mathematics and Computation, 214 (2009), 108.  doi: 10.1016/j.amc.2009.03.090.  Google Scholar

[28]

D. Karaboga, B. Gorkemli, C. Ozturk and N. Karaboga, A comprehensive survey: Artificial bee colony (abc) algorithm and applications,, Artificial Intelligence Review, (2012), 1.  doi: 10.1007/s10462-012-9328-0.  Google Scholar

[29]

D. Karaboga and C. Ozturk, A novel clustering approach: Artificial bee colony (ABC) algorithm,, Applied Soft Computing, 11 (2011), 652.  doi: 10.1016/j.asoc.2009.12.025.  Google Scholar

[30]

A. Kaveh and S. Talatahari, Engineering optimization with hybrid particle swarm and ant colony optimization,, Asian journal of civil engineering (building and housing), 10 (2009), 611.   Google Scholar

[31]

A. Kaveh and S. Talatahari, An improved ant colony optimization for constrained engineering design problems,, Engineering Computations, 27 (2010), 155.  doi: 10.1108/02644401011008577.  Google Scholar

[32]

K. S. Lee and Z. W. Geem, A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice,, Computer Methods in Applied Mechanics and Engineering, 194 (2005), 3902.  doi: 10.1016/j.cma.2004.09.007.  Google Scholar

[33]

M. Mahdavi, M. Fesanghary and E. Damangir, An improved harmony search algorithm for solving optimization problems,, Applied Mathematics and Computation, 188 (2007), 1567.  doi: 10.1016/j.amc.2006.11.033.  Google Scholar

[34]

V. K. Mehta and B. Dasgupta, A constrained optimization algorithm based on the simplex search method,, Engineering Optimization, 44 (2012), 537.  doi: 10.1080/0305215X.2011.598520.  Google Scholar

[35]

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs,, Springer - Verlag, (1994).   Google Scholar

[36]

E. M. Montes and C. A. C. Coello, An empirical study about the usefulness of evolution strategies to solve constrained optimization problems,, International Journal of General Systems, 37 (2008), 443.  doi: 10.1080/03081070701303470.  Google Scholar

[37]

E. M. Montes, C. A. C. Coello, J. V. Reyes and L. M. Davila, Multiple trial vectors in differential evolution for engineering design,, Engineering Optimization, 39 (2007), 567.  doi: 10.1080/03052150701364022.  Google Scholar

[38]

M. G. H. Omran and A. Salman, Constrained optimization using CODEQ,, Chaos, 42 (2009), 662.   Google Scholar

[39]

K. M. Ragsdell and D. T. Phillips, Optimal design of a class of welded structures using geometric programming,, ASME Journal of Engineering for Industries, 98 (1976), 1021.  doi: 10.1115/1.3438995.  Google Scholar

[40]

K. H. Raj, R. S. Sharma, G. S. Mishra, A. Dua and C. Patvardhan, An evolutionary computational technique for constrained optimisation in engineering design,, Journal of the Institution of Engineers India Part Me Mechanical Engineering Division, 86 (2005), 121.   Google Scholar

[41]

S. S. Rao, Engineering Optimization: Theory and Practice,, 3rd edition, (1996).   Google Scholar

[42]

T. Ray and K. M. Liew, Society and civilization : An optimization algorithm based on the simulation of social behavior,, IEEE Transactions on Evolutionary Computation, 7 (2003), 386.  doi: 10.1109/TEVC.2003.814902.  Google Scholar

[43]

T. Ray and P. Saini, Engineering design optimization using a swarm with an intelligent information sharing among individuals,, Engineering Optimization, 33 (2001), 735.  doi: 10.1080/03052150108940941.  Google Scholar

[44]

E. Sandgren, Nonlinear integer and discrete programming in mechanical design,, Proceedings of the ASME Design Technology Conference, (1988), 95.   Google Scholar

[45]

Y. Shi and R. C. Eberhart, A modified particle swarm optimizer,, IEEE International Conference on Evolutionary Computation, (1998), 69.   Google Scholar

[46]

J. Tsai, Global optimization of nonlinear fractional programming problems in engineering design,, Engineering Optimization, 37 (2005), 399.  doi: 10.1080/03052150500066737.  Google Scholar

[47]

C. Zhang and H. P. Wang, Mixed-discrete nonlinear optimization with simulated annealing,, Engineering Optimization, 21 (1993), 277.  doi: 10.1080/03052159308940980.  Google Scholar

[48]

M. Zhang, W. Luo and X. Wang, Differential evolution with dynamic stochastic selection for constrained optimization,, Information Sciences, 178 (2008), 3043.  doi: 10.1016/j.ins.2008.02.014.  Google Scholar

show all references

References:
[1]

B. Akay and D. Karaboga, Artificial bee colony algorithm for large-scale problems and engineering design optimization,, Journal of Intelligent Manufacturing, 23 (2012), 1001.  doi: 10.1007/s10845-010-0393-4.  Google Scholar

[2]

J. S. Arora, Introduction to Optimum Design,, McGraw-Hill, (1989).   Google Scholar

[3]

A. D. Belegundu, A Study of Mathematical Programming Methods for Structural Optimization,, PhD thesis, (1982).   Google Scholar

[4]

L. C. Cagnina, S. C. Esquivel and C. A. C. Coello, Solving engineering optimization problems with the simple constrained particle swarm optimizer,, Informatica, 32 (2008), 319.   Google Scholar

[5]

L. S. Coelho, Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems,, Expert Systems with Applications, 37 (2010), 1676.  doi: 10.1016/j.eswa.2009.06.044.  Google Scholar

[6]

C. A. C. Coello, Treating constraints as objectives for single-objective evolutionary optimization,, Engineering Optimization, 32 (2000), 275.  doi: 10.1080/03052150008941301.  Google Scholar

[7]

C. A. C. Coello, Use of a self -adaptive penalty approach for engineering optimization problems,, Computers in Industry, 41 (2000), 113.  doi: 10.1016/S0166-3615(99)00046-9.  Google Scholar

[8]

C. A. C. Coello and E. M. Montes, Constraint- handling in genetic algorithms through the use of dominance-based tournament selection,, Advanced Engineering Informatics, 16 (2002), 193.  doi: 10.1016/S1474-0346(02)00011-3.  Google Scholar

[9]

K. Deb, Optimal design of a welded beam via genetic algorithms,, AIAA Journal, 29 (1991), 2013.   Google Scholar

[10]

K. Deb, An efficient constraint handling method for genetic algorithms,, Computer Methods in Applied Mechanics and Engineering, 186 (2000), 311.  doi: 10.1016/S0045-7825(99)00389-8.  Google Scholar

[11]

K. Deb and A. S. Gene, A robust optimal design technique for mechanical component design,, (Eds. D. Dasgupta, (1997), 497.  doi: 10.1007/978-3-662-03423-1_27.  Google Scholar

[12]

K. Deb and M. Goyal, A combined genetic adaptive search (GeneAS) for engineering design,, Computer Science and Informatics, 26 (1986), 30.   Google Scholar

[13]

G. G. Dimopoulos, Mixed-variable engineering optimization based on evolutionary and social metaphors,, Computer Methods in Applied Mechanics and Engineering, 196 (2007), 803.  doi: 10.1016/j.cma.2006.06.010.  Google Scholar

[14]

M. Fesanghary, M. Mahdavi, M. Minary-Jolandan and Y. Alizadeh, Hybridizing harmony search algorithm with sequential quadratic programming for engineering optimization problems,, Computer Methods in Applied Mechanics and Engineering, 197 (2008), 3080.  doi: 10.1016/j.cma.2008.02.006.  Google Scholar

[15]

A. H. Gandomi, X. S. Yang, and A. H. Alavi, Mixed variable structural optimization using firefly algorithm,, Computers & Structures, 89 (): 2325.   Google Scholar

[16]

A. H. Gandomi, X. S. Yang and A. Alavi, Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems,, Engineering with Computers, 29 (2003), 17.  doi: 10.1007/s00366-011-0241-y.  Google Scholar

[17]

Q. He and L. Wang, An effective co - evolutionary particle swarm optimization for constrained engineering design problems,, Engineering Applications of Artificial Intelligence, 20 (2007), 89.  doi: 10.1016/j.engappai.2006.03.003.  Google Scholar

[18]

S. He, E. Prempain and Q. H. Wu, An improved particle swarm optimizer for mechanical design optimization problems,, Engineering Optimization, 36 (2004), 585.  doi: 10.1080/03052150410001704854.  Google Scholar

[19]

A. R. Hedar and M. Fukushima, Derivative - free filter simulated annealing method for constrained continuous global optimization,, Journal of Global Optimization, 35 (2006), 521.  doi: 10.1007/s10898-005-3693-z.  Google Scholar

[20]

D. M. Himmelblau, Applied Nonlinear Programming,, McGraw-Hill, (1972).   Google Scholar

[21]

A. Homaifar, S. H. Y. Lai and X. Qi, Constrained optimization via genetic algorithms,, Simulation, 62 (1994), 242.  doi: 10.1177/003754979406200405.  Google Scholar

[22]

Y. L. Hsu and T. C. Liu, Developing a fuzzy proportional derivative controller optimization engine for engineering design optimization problems,, Engineering Optimization, 39 (2007), 679.  doi: 10.1080/03052150701252664.  Google Scholar

[23]

X. H. Hu, R. C. Eberhart and Y. H. Shi, Engineering optimization with particle swarm,, Proceedings of the 2003 IEEE Swarm Intelligence Symposium, (2003), 53.   Google Scholar

[24]

S. F. Hwang and R. S. He, A hybrid real-parameter genetic algorithm for function optimization,, Advanced Engineering Informatics, 20 (2006), 7.  doi: 10.1016/j.aei.2005.09.001.  Google Scholar

[25]

B. K. Kannan and S. N. Kramer, An augmented lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design,, Transactions of the ASME, 116 (1994), 405.  doi: 10.1115/1.2919393.  Google Scholar

[26]

D. Karaboga, An Idea Based on Honey Bee Swarm for Numerical Optimization,, Technical report, (2005).   Google Scholar

[27]

D. Karaboga and B. Akay, A comparative study of artificial bee colony algorithm,, Applied Mathematics and Computation, 214 (2009), 108.  doi: 10.1016/j.amc.2009.03.090.  Google Scholar

[28]

D. Karaboga, B. Gorkemli, C. Ozturk and N. Karaboga, A comprehensive survey: Artificial bee colony (abc) algorithm and applications,, Artificial Intelligence Review, (2012), 1.  doi: 10.1007/s10462-012-9328-0.  Google Scholar

[29]

D. Karaboga and C. Ozturk, A novel clustering approach: Artificial bee colony (ABC) algorithm,, Applied Soft Computing, 11 (2011), 652.  doi: 10.1016/j.asoc.2009.12.025.  Google Scholar

[30]

A. Kaveh and S. Talatahari, Engineering optimization with hybrid particle swarm and ant colony optimization,, Asian journal of civil engineering (building and housing), 10 (2009), 611.   Google Scholar

[31]

A. Kaveh and S. Talatahari, An improved ant colony optimization for constrained engineering design problems,, Engineering Computations, 27 (2010), 155.  doi: 10.1108/02644401011008577.  Google Scholar

[32]

K. S. Lee and Z. W. Geem, A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice,, Computer Methods in Applied Mechanics and Engineering, 194 (2005), 3902.  doi: 10.1016/j.cma.2004.09.007.  Google Scholar

[33]

M. Mahdavi, M. Fesanghary and E. Damangir, An improved harmony search algorithm for solving optimization problems,, Applied Mathematics and Computation, 188 (2007), 1567.  doi: 10.1016/j.amc.2006.11.033.  Google Scholar

[34]

V. K. Mehta and B. Dasgupta, A constrained optimization algorithm based on the simplex search method,, Engineering Optimization, 44 (2012), 537.  doi: 10.1080/0305215X.2011.598520.  Google Scholar

[35]

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs,, Springer - Verlag, (1994).   Google Scholar

[36]

E. M. Montes and C. A. C. Coello, An empirical study about the usefulness of evolution strategies to solve constrained optimization problems,, International Journal of General Systems, 37 (2008), 443.  doi: 10.1080/03081070701303470.  Google Scholar

[37]

E. M. Montes, C. A. C. Coello, J. V. Reyes and L. M. Davila, Multiple trial vectors in differential evolution for engineering design,, Engineering Optimization, 39 (2007), 567.  doi: 10.1080/03052150701364022.  Google Scholar

[38]

M. G. H. Omran and A. Salman, Constrained optimization using CODEQ,, Chaos, 42 (2009), 662.   Google Scholar

[39]

K. M. Ragsdell and D. T. Phillips, Optimal design of a class of welded structures using geometric programming,, ASME Journal of Engineering for Industries, 98 (1976), 1021.  doi: 10.1115/1.3438995.  Google Scholar

[40]

K. H. Raj, R. S. Sharma, G. S. Mishra, A. Dua and C. Patvardhan, An evolutionary computational technique for constrained optimisation in engineering design,, Journal of the Institution of Engineers India Part Me Mechanical Engineering Division, 86 (2005), 121.   Google Scholar

[41]

S. S. Rao, Engineering Optimization: Theory and Practice,, 3rd edition, (1996).   Google Scholar

[42]

T. Ray and K. M. Liew, Society and civilization : An optimization algorithm based on the simulation of social behavior,, IEEE Transactions on Evolutionary Computation, 7 (2003), 386.  doi: 10.1109/TEVC.2003.814902.  Google Scholar

[43]

T. Ray and P. Saini, Engineering design optimization using a swarm with an intelligent information sharing among individuals,, Engineering Optimization, 33 (2001), 735.  doi: 10.1080/03052150108940941.  Google Scholar

[44]

E. Sandgren, Nonlinear integer and discrete programming in mechanical design,, Proceedings of the ASME Design Technology Conference, (1988), 95.   Google Scholar

[45]

Y. Shi and R. C. Eberhart, A modified particle swarm optimizer,, IEEE International Conference on Evolutionary Computation, (1998), 69.   Google Scholar

[46]

J. Tsai, Global optimization of nonlinear fractional programming problems in engineering design,, Engineering Optimization, 37 (2005), 399.  doi: 10.1080/03052150500066737.  Google Scholar

[47]

C. Zhang and H. P. Wang, Mixed-discrete nonlinear optimization with simulated annealing,, Engineering Optimization, 21 (1993), 277.  doi: 10.1080/03052159308940980.  Google Scholar

[48]

M. Zhang, W. Luo and X. Wang, Differential evolution with dynamic stochastic selection for constrained optimization,, Information Sciences, 178 (2008), 3043.  doi: 10.1016/j.ins.2008.02.014.  Google Scholar

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