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Optimum Design of Geodesic Steel Domes Under Code Provisions Using Metaheuristic Techniques

Year 2010, Volume: 2 Issue: 2, 88 - 103, 01.06.2010

Abstract

Metaheuristic search techniques strongly employ randomized decisions while searching for solutions to structural optimization problems. These techniques play an increasingly important role for practically solving hard combinatorial problems from various domains. Over the past few years there has been considerable success in developing metaheuristic search algorithms as well as randomized systematic search methods for obtaining solutions to discrete programming problems. This paper examines minimum weight design of pinjointed geodesic steel domes using seven metaheuristic search techniques; namely, simulated annealing, genetic algorithms, evolution strategies, particle swarm optimizer, tabu search, ant colony optimization and harmony search methods. The optimum design problem of geodesic steel domes is formulated according to design limitations stipulated by ASD-AISC (Allowable Stress Design Code of American Institute of Steel Institution). The minimum design loads and combined load effects are established as specified by ASCE 7-98 (Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers). A numerical example is presented, where seven metaheuristic methods are implemented to achieve minimum weight design of a 130member geodesic steel dome subjected to a total of eight combined load cases of dead, live, snow and temperature loads

References

  • 1. Atrek, E., “New Directions in Optimum Structural Design”, John Wiley & Sons, 1984.
  • 2. Dorigo, M. ”Optimization, Learning and Natural Algorithms”,(in Italian), Phd thesis, Dipartimento di Elettronica e Informazione, Politecnico di Milano, IT, 1992
  • 3. Xie, Y.M. and Steven, G.P. “Evolutionary Structural Optimization”, Springer-Verlag, Berlin, Germany, 1997
  • 4. Reeves, C.R. “Modern Heuristic Techniques for Combinatorial Problems”, Blackwell Scientific Publications, 1993
  • 5. Horst, R. and Tuy, H.,“Global Optimization; Deterministic Approaches”, Springer, 1995.
  • 6. Paton,, R., “Computing with Biological Metaphors”, Chapman & Hall, USA, 1994.
  • 7. Adami, C., “An introduction to Artificial Life”, Springer-Verlag/Telos, 1998
  • 8. Matheck, C., “Design in Nature: Learning from Trees”, Springer-Verlag, Berlin, 1998.
  • 9. Mitchell, M., “An Introduction to Genetic Algorithms”, The MIT Press, 1998
  • 10. Kennedy, J., Eberhart, R. and Shi, Y., “Swarm Intelligence”, Morgan Kaufmann Publishers, 2001
  • 11. Kochenberger, G. A. and Glover, F., “Handbook of Metaheuristics”, Kluwer Academic Publishers, 2003
  • 12. De Castro, L. N. and Von Zuben, F. , J., “Recent Developments in Biologically Inspired Computing”, Idea Group Publishing, USA, 2005.
  • 13. Dreo, J., Petrowski, A., Siarry, P. and Taillard, E., “Metaheuristics for Hard Optimization”, Springer-Verlag, Berlin, Heidelberg, 2006.
  • 14. Saka, M. P., “Optimum Design of Steel Frames using Metaheuristic Search Techniques Based on Natural Phenomena: A Review”, Civil Engineering Computations: Tools and Techniques, Ed. B. H. V. Topping, Saxe-Coburgh Publications, pp: 105-147, 2007.
  • 15. Kirkpatrick, S., Gerlatt, C. D. and Vecchi, M. P.,“Optimization by Simulated Annealing“, Science, 220, 671-680, 1983.
  • 16. Rechenberg, I., “Cybernetic Solution Path of An Experimental Problem”, Royal Aircraft Establishment, Library translation No. 1122, Farnborough, Hants., UK, 1965.
  • 17. Kennedy, J. and Eberhart, R. “Particle Swarm Optimization”, IEEE International Conference on Neural Networks, IEEE Press, Vol. 4, 1942-1948, 1995.
  • 18. Glover, F., “Tabu Search-Part I”, ORSA Journal on Computing, 1(3), 190-206, 1989.
  • 19. Dorigo, M. and Stützle, T., “Ant Colony Optimization”, A Bradford Book, Massachusetts Institute of Technology, U.S.A., 2004.
  • 20. Lee, K. S. and Geem, Z. W.,“A New Structural Optimization Method Based on the Harmony Search Algorithm”, Computers and Structures, 82, 781-798, 2004.
  • 21. Goldberg, D. E., “Genetic Algorithms in Search, Optimization and Machine Learning”, Addison Wesley, 1989.
  • 22. Manual of Steel Construction, Allowable Stress Design, 9th edition, AISC, American Institutes of Steel Construction, Inc, Chicago, Illinois, USA, 1989.
  • 23. Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers, 1998.
  • 24. Cerny, V., “Thermodynamical Approach to the Traveling Salesman Problem: An efficient Simulation Algorithm”, Journal of Optimization Theory and Applications, 45, 41-51, 1985.
  • 25. Balling, R. J., “Optimal Steel Frame Design by Simulated Annealing”, Journal of Structural Engineering , 117 (6), 1780-1795, 1991.
  • 26. Bennage, W. A., and Dhingra, A. K., “Single and Multi-Objective Structural Optimization in Discrete-Continuous Variables Using Simulated Annealing”, International Journal in Numerical Methods in Engineering, 38, 2753-2773, 1995.
  • 27. Shim, P. Y., and Manoochehri, S., “Generating Optimal Configurations in Structural Design using Simulated Annealing”, International Journal for Numerical Methods in Engineering, 40, 1053-1069, 1997.
  • 28. Lamberti, L., “An Efficient Simulated Annealing Algorithm for Design Optimization of Truss Structures”, Computers and Structures, 86, 1936-1953, 2008.
  • 29. Hasançebi, O., Çarbaş, S., and Saka, M.P., “Improving the Performance of Simulated Annealing in Structural Optimization”, Structural and Multidisciplinary Optimization, DOI: 10.1007/s00158-009-0418-9, 2009.
  • 30. Holland, J. H., “Adaptation in Natural and Artificial Systems”, University of Michigan Press, Ann Arbor, 1975.
  • 31. Goldberg, D., and Samtani M., “Engineering optimization via genetic algorithm”, in Will K.M. (Eds), In: Proceeding of the 9th Conference on Electronic Computation, ASCE, 1986, 471-482.
  • 32. Pezeshk S., Camp CV, Chen D., “Design of nonlinear structures using genetic optimization.”, Journal of Structural Engineering, ASCE 126(3):382-388, 2000.
  • 33. Erbatur F., Hasançebi O., Tütüncü, I., Kılıç H., “Optimal design of planar and structures with genetic algorithms” , Computers and Structures, 75:209-224, 2000.
  • 34. Coello C.A., Christiansen A.D., “Multiobjective optimization of trusses using genetic algorithms.”, Computers and Structures, 75(6):647-660, 2000.
  • 35. Kameshki E.S., Saka M.P., “Genetic algorithm based optimum bracing design of nonswaying tall frames.”, Journal of Constructional Steel Research 57:1081-1097, 2001.
  • 36. Kaveh A., and Kalatjari V., “Topology optimization of trusses using genetic algorithm, force method, and grapg theory.”, International Journal of Numerical Methods in Engineering, 58(5):771-791, 2003.
  • 37. Schwefel, H. -P. “Numerical Optimization of Computer Models”, Wiley, Chichester, 1981.
  • 38. Cai, J. and Thierauf, G., “Evolution Strategies for Solving Discrete Optimization Problems”, Advances in Engineering Software, 2, 177-183, 1996.
  • 39. Bäck, T. and Schütz, M., “Evolutionary strategies for mixed-integer optimization of optical multilayer systems”, Proc. of the 4th Annual Conference on Evolutionary Programming, McDonnel, J.R., Reynolds, R.G. and Fogel, D.B. (eds.), MIT Press, Cambridge, MA, 33-51, 1995.
  • 40. Hasançebi, O., “Discrete Approaches in Evolution Strategies Based Optimum Design of Steel Frames”, Structural Engineering and Mechanics, 26(2), 191-210, 2007.
  • 41. Lagaros, N.D., Papadrakakis, M. and Kokossalakis, G., “Structural optimization using evolutionary algorithms”, Computers and Structures, 80, 571-589, 2002.
  • 42. Hasançebi, O., “Optimization of truss bridges within a specified design domain using evolution strategies”, Engineering Optimization, 39(6), 737-756, 2007.
  • 43. Venter, G. and Sobieszczanski-Sobieski, J., “Multidisciplinary Optimization of a Transport Aircraft Wing Using Particle Swarm Optimization”, Structural and Multidisciplinary Optimization, 26, 121-131, 2004.
  • 44. Perez, R. E. and Behdinan, K., “Particle Swarm Approach for Structural Design Optimization”, Computers and Structures, 85 (19-20), 1579-1588, 2007.
  • 45. S. He, E. Prempain and Q.H. Wu, “Improved Particle Swarm Optimizer for Mechanical Design Optimization Problems”, Engineering Optimization, 36, 5, 585-605, 2004
  • 46. Fourie, P. and Groenwold, A., “The Particle Swarm Optimization Algorithm in Size and Shape Optimization”, Structural and Multidisciplinary Optimization, 23 (4), 259-267, 2002.
  • 47. Bland, J. A., “Discrete-Variable Optimal Structural Design using Tabu Search”, Structural Optimization, 10, 87-93, 1995.
  • 48. Kargahi, M., Anderson, J. C., and Dessouky, M. M., “Structural Weight Optimization using Tabu Search I: Optimization Procedure”, Journal of Structural Engineering ASCE, 132 (12), 1858-1868, 2006.
  • 49. Colorni, A., Dorigo, M. and Maniezzo, V., “Distributed Optimization by Ant Colony”, Proceedings of the First European Conference on Artificial Life, USA, 134-142, 1991.
  • 50. Dorigo, M., “Optimization, Learning and Natural Algorithms”, PhD Thesis, Dipartimento Elettronica e Informazione, Politecnico di Milano, Italy, 1992.
  • 51. Camp, C. V., Bichon, J. B. and Stovall S. P., “Design of Steel Frames Using Ant Colony Optimization”, Journal of Structural Engineering, ASCE, 131 (3), 369-379, 2004.
  • 52. Aydoğdu, İ. and Saka, M. P., “Ant colony optimization of irregular steel frames including effect of warping”, Civil-Comp 09, The Twelfth International Conference on Civil Structural and Environmental Engineering Computing, Paper No: 69, 1-4 September, 2009, Madeira, Portugal
  • 53. M. P. Saka, “Optimum geometry design of geodesic domes using harmony search method”, Advances in Structural Engineering, 10, 6, 595-606, 2007.
  • 54. M. P. Saka, “Optimum design of steel frames to BS5950 using harmony search algorithm”, Journal of Constructional Steel Research, Vol. 65, 36-43, 2009
  • 55. Erdal F., and Saka M.P., “Effect of beam spacing in the harmony search based optimum design of grillages”, Asian Journal of Civil Engineering, Vol. 9, No.3, 215-228, 2008
  • 56. Erdal F., and Saka M.P., “Optimum Design of Grillage Systems Using Harmony Search Algorithm”, Journal of Structural and Multidisciplinary Optimization, Vol. 38, No.1, 25- 41, 2009.
  • 57. Hasançebi, O., Erdal, F., and Saka, M. P., “An Adaptive Harmony Search Method for Structural Optimization”, Journal of Structural Engineering, ASCE, (Accepted for publication), 2009.
  • 58. Hasançebi, O., Çarbaş, S., Doğan, E., Erdal, F. and Saka, M. P., “Performance evaluation of metaheuristic search techniques in the optimum design of real size pin jointed structures”, Computers and Structures, 87 (5-6), 284-302, 2009.
Year 2010, Volume: 2 Issue: 2, 88 - 103, 01.06.2010

Abstract

References

  • 1. Atrek, E., “New Directions in Optimum Structural Design”, John Wiley & Sons, 1984.
  • 2. Dorigo, M. ”Optimization, Learning and Natural Algorithms”,(in Italian), Phd thesis, Dipartimento di Elettronica e Informazione, Politecnico di Milano, IT, 1992
  • 3. Xie, Y.M. and Steven, G.P. “Evolutionary Structural Optimization”, Springer-Verlag, Berlin, Germany, 1997
  • 4. Reeves, C.R. “Modern Heuristic Techniques for Combinatorial Problems”, Blackwell Scientific Publications, 1993
  • 5. Horst, R. and Tuy, H.,“Global Optimization; Deterministic Approaches”, Springer, 1995.
  • 6. Paton,, R., “Computing with Biological Metaphors”, Chapman & Hall, USA, 1994.
  • 7. Adami, C., “An introduction to Artificial Life”, Springer-Verlag/Telos, 1998
  • 8. Matheck, C., “Design in Nature: Learning from Trees”, Springer-Verlag, Berlin, 1998.
  • 9. Mitchell, M., “An Introduction to Genetic Algorithms”, The MIT Press, 1998
  • 10. Kennedy, J., Eberhart, R. and Shi, Y., “Swarm Intelligence”, Morgan Kaufmann Publishers, 2001
  • 11. Kochenberger, G. A. and Glover, F., “Handbook of Metaheuristics”, Kluwer Academic Publishers, 2003
  • 12. De Castro, L. N. and Von Zuben, F. , J., “Recent Developments in Biologically Inspired Computing”, Idea Group Publishing, USA, 2005.
  • 13. Dreo, J., Petrowski, A., Siarry, P. and Taillard, E., “Metaheuristics for Hard Optimization”, Springer-Verlag, Berlin, Heidelberg, 2006.
  • 14. Saka, M. P., “Optimum Design of Steel Frames using Metaheuristic Search Techniques Based on Natural Phenomena: A Review”, Civil Engineering Computations: Tools and Techniques, Ed. B. H. V. Topping, Saxe-Coburgh Publications, pp: 105-147, 2007.
  • 15. Kirkpatrick, S., Gerlatt, C. D. and Vecchi, M. P.,“Optimization by Simulated Annealing“, Science, 220, 671-680, 1983.
  • 16. Rechenberg, I., “Cybernetic Solution Path of An Experimental Problem”, Royal Aircraft Establishment, Library translation No. 1122, Farnborough, Hants., UK, 1965.
  • 17. Kennedy, J. and Eberhart, R. “Particle Swarm Optimization”, IEEE International Conference on Neural Networks, IEEE Press, Vol. 4, 1942-1948, 1995.
  • 18. Glover, F., “Tabu Search-Part I”, ORSA Journal on Computing, 1(3), 190-206, 1989.
  • 19. Dorigo, M. and Stützle, T., “Ant Colony Optimization”, A Bradford Book, Massachusetts Institute of Technology, U.S.A., 2004.
  • 20. Lee, K. S. and Geem, Z. W.,“A New Structural Optimization Method Based on the Harmony Search Algorithm”, Computers and Structures, 82, 781-798, 2004.
  • 21. Goldberg, D. E., “Genetic Algorithms in Search, Optimization and Machine Learning”, Addison Wesley, 1989.
  • 22. Manual of Steel Construction, Allowable Stress Design, 9th edition, AISC, American Institutes of Steel Construction, Inc, Chicago, Illinois, USA, 1989.
  • 23. Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers, 1998.
  • 24. Cerny, V., “Thermodynamical Approach to the Traveling Salesman Problem: An efficient Simulation Algorithm”, Journal of Optimization Theory and Applications, 45, 41-51, 1985.
  • 25. Balling, R. J., “Optimal Steel Frame Design by Simulated Annealing”, Journal of Structural Engineering , 117 (6), 1780-1795, 1991.
  • 26. Bennage, W. A., and Dhingra, A. K., “Single and Multi-Objective Structural Optimization in Discrete-Continuous Variables Using Simulated Annealing”, International Journal in Numerical Methods in Engineering, 38, 2753-2773, 1995.
  • 27. Shim, P. Y., and Manoochehri, S., “Generating Optimal Configurations in Structural Design using Simulated Annealing”, International Journal for Numerical Methods in Engineering, 40, 1053-1069, 1997.
  • 28. Lamberti, L., “An Efficient Simulated Annealing Algorithm for Design Optimization of Truss Structures”, Computers and Structures, 86, 1936-1953, 2008.
  • 29. Hasançebi, O., Çarbaş, S., and Saka, M.P., “Improving the Performance of Simulated Annealing in Structural Optimization”, Structural and Multidisciplinary Optimization, DOI: 10.1007/s00158-009-0418-9, 2009.
  • 30. Holland, J. H., “Adaptation in Natural and Artificial Systems”, University of Michigan Press, Ann Arbor, 1975.
  • 31. Goldberg, D., and Samtani M., “Engineering optimization via genetic algorithm”, in Will K.M. (Eds), In: Proceeding of the 9th Conference on Electronic Computation, ASCE, 1986, 471-482.
  • 32. Pezeshk S., Camp CV, Chen D., “Design of nonlinear structures using genetic optimization.”, Journal of Structural Engineering, ASCE 126(3):382-388, 2000.
  • 33. Erbatur F., Hasançebi O., Tütüncü, I., Kılıç H., “Optimal design of planar and structures with genetic algorithms” , Computers and Structures, 75:209-224, 2000.
  • 34. Coello C.A., Christiansen A.D., “Multiobjective optimization of trusses using genetic algorithms.”, Computers and Structures, 75(6):647-660, 2000.
  • 35. Kameshki E.S., Saka M.P., “Genetic algorithm based optimum bracing design of nonswaying tall frames.”, Journal of Constructional Steel Research 57:1081-1097, 2001.
  • 36. Kaveh A., and Kalatjari V., “Topology optimization of trusses using genetic algorithm, force method, and grapg theory.”, International Journal of Numerical Methods in Engineering, 58(5):771-791, 2003.
  • 37. Schwefel, H. -P. “Numerical Optimization of Computer Models”, Wiley, Chichester, 1981.
  • 38. Cai, J. and Thierauf, G., “Evolution Strategies for Solving Discrete Optimization Problems”, Advances in Engineering Software, 2, 177-183, 1996.
  • 39. Bäck, T. and Schütz, M., “Evolutionary strategies for mixed-integer optimization of optical multilayer systems”, Proc. of the 4th Annual Conference on Evolutionary Programming, McDonnel, J.R., Reynolds, R.G. and Fogel, D.B. (eds.), MIT Press, Cambridge, MA, 33-51, 1995.
  • 40. Hasançebi, O., “Discrete Approaches in Evolution Strategies Based Optimum Design of Steel Frames”, Structural Engineering and Mechanics, 26(2), 191-210, 2007.
  • 41. Lagaros, N.D., Papadrakakis, M. and Kokossalakis, G., “Structural optimization using evolutionary algorithms”, Computers and Structures, 80, 571-589, 2002.
  • 42. Hasançebi, O., “Optimization of truss bridges within a specified design domain using evolution strategies”, Engineering Optimization, 39(6), 737-756, 2007.
  • 43. Venter, G. and Sobieszczanski-Sobieski, J., “Multidisciplinary Optimization of a Transport Aircraft Wing Using Particle Swarm Optimization”, Structural and Multidisciplinary Optimization, 26, 121-131, 2004.
  • 44. Perez, R. E. and Behdinan, K., “Particle Swarm Approach for Structural Design Optimization”, Computers and Structures, 85 (19-20), 1579-1588, 2007.
  • 45. S. He, E. Prempain and Q.H. Wu, “Improved Particle Swarm Optimizer for Mechanical Design Optimization Problems”, Engineering Optimization, 36, 5, 585-605, 2004
  • 46. Fourie, P. and Groenwold, A., “The Particle Swarm Optimization Algorithm in Size and Shape Optimization”, Structural and Multidisciplinary Optimization, 23 (4), 259-267, 2002.
  • 47. Bland, J. A., “Discrete-Variable Optimal Structural Design using Tabu Search”, Structural Optimization, 10, 87-93, 1995.
  • 48. Kargahi, M., Anderson, J. C., and Dessouky, M. M., “Structural Weight Optimization using Tabu Search I: Optimization Procedure”, Journal of Structural Engineering ASCE, 132 (12), 1858-1868, 2006.
  • 49. Colorni, A., Dorigo, M. and Maniezzo, V., “Distributed Optimization by Ant Colony”, Proceedings of the First European Conference on Artificial Life, USA, 134-142, 1991.
  • 50. Dorigo, M., “Optimization, Learning and Natural Algorithms”, PhD Thesis, Dipartimento Elettronica e Informazione, Politecnico di Milano, Italy, 1992.
  • 51. Camp, C. V., Bichon, J. B. and Stovall S. P., “Design of Steel Frames Using Ant Colony Optimization”, Journal of Structural Engineering, ASCE, 131 (3), 369-379, 2004.
  • 52. Aydoğdu, İ. and Saka, M. P., “Ant colony optimization of irregular steel frames including effect of warping”, Civil-Comp 09, The Twelfth International Conference on Civil Structural and Environmental Engineering Computing, Paper No: 69, 1-4 September, 2009, Madeira, Portugal
  • 53. M. P. Saka, “Optimum geometry design of geodesic domes using harmony search method”, Advances in Structural Engineering, 10, 6, 595-606, 2007.
  • 54. M. P. Saka, “Optimum design of steel frames to BS5950 using harmony search algorithm”, Journal of Constructional Steel Research, Vol. 65, 36-43, 2009
  • 55. Erdal F., and Saka M.P., “Effect of beam spacing in the harmony search based optimum design of grillages”, Asian Journal of Civil Engineering, Vol. 9, No.3, 215-228, 2008
  • 56. Erdal F., and Saka M.P., “Optimum Design of Grillage Systems Using Harmony Search Algorithm”, Journal of Structural and Multidisciplinary Optimization, Vol. 38, No.1, 25- 41, 2009.
  • 57. Hasançebi, O., Erdal, F., and Saka, M. P., “An Adaptive Harmony Search Method for Structural Optimization”, Journal of Structural Engineering, ASCE, (Accepted for publication), 2009.
  • 58. Hasançebi, O., Çarbaş, S., Doğan, E., Erdal, F. and Saka, M. P., “Performance evaluation of metaheuristic search techniques in the optimum design of real size pin jointed structures”, Computers and Structures, 87 (5-6), 284-302, 2009.
There are 58 citations in total.

Details

Other ID JA65JA25ZM
Journal Section Articles
Authors

O. Hasançebi This is me

F. Erdal This is me

M. P. Saka This is me

Publication Date June 1, 2010
Published in Issue Year 2010 Volume: 2 Issue: 2

Cite

APA Hasançebi, O., Erdal, F., & Saka, M. P. (2010). Optimum Design of Geodesic Steel Domes Under Code Provisions Using Metaheuristic Techniques. International Journal of Engineering and Applied Sciences, 2(2), 88-103.
AMA Hasançebi O, Erdal F, Saka MP. Optimum Design of Geodesic Steel Domes Under Code Provisions Using Metaheuristic Techniques. IJEAS. June 2010;2(2):88-103.
Chicago Hasançebi, O., F. Erdal, and M. P. Saka. “Optimum Design of Geodesic Steel Domes Under Code Provisions Using Metaheuristic Techniques”. International Journal of Engineering and Applied Sciences 2, no. 2 (June 2010): 88-103.
EndNote Hasançebi O, Erdal F, Saka MP (June 1, 2010) Optimum Design of Geodesic Steel Domes Under Code Provisions Using Metaheuristic Techniques. International Journal of Engineering and Applied Sciences 2 2 88–103.
IEEE O. Hasançebi, F. Erdal, and M. P. Saka, “Optimum Design of Geodesic Steel Domes Under Code Provisions Using Metaheuristic Techniques”, IJEAS, vol. 2, no. 2, pp. 88–103, 2010.
ISNAD Hasançebi, O. et al. “Optimum Design of Geodesic Steel Domes Under Code Provisions Using Metaheuristic Techniques”. International Journal of Engineering and Applied Sciences 2/2 (June 2010), 88-103.
JAMA Hasançebi O, Erdal F, Saka MP. Optimum Design of Geodesic Steel Domes Under Code Provisions Using Metaheuristic Techniques. IJEAS. 2010;2:88–103.
MLA Hasançebi, O. et al. “Optimum Design of Geodesic Steel Domes Under Code Provisions Using Metaheuristic Techniques”. International Journal of Engineering and Applied Sciences, vol. 2, no. 2, 2010, pp. 88-103.
Vancouver Hasançebi O, Erdal F, Saka MP. Optimum Design of Geodesic Steel Domes Under Code Provisions Using Metaheuristic Techniques. IJEAS. 2010;2(2):88-103.

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