Abstract
The problem of optimal structural design having linked discrete variables is addressed. For such applications, when a discrete value for a variable is selected, values for other variables linked to it must also be selected from a table. The design of steel structures using available sections is a major application area of such problems. Three strategies that combine a continuous variable optimization method with a genetic algorithm, simulated annealing, and branch and bound method are presented and implemented into a computer program for their numerical evaluation. Three structural design problems are solved to study the performance of the proposed methods. CPU times for solution of the problems with discrete variables are large. Strategies are suggested to reduce these times.
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Al-Saadoun, S.S.; Arora, J.S. 1989: Interactive design optimization of framed structures.J. Comp. Civil Eng., ASCE 3, 60–74
Amir, H.M.; Hasegawa, T. 1989: Nonlinear mixed-discrete structural optimization.J. Struct. Eng., ASCE 115, 626–646
Arora, J.S. 1989:Introduction to optimum design. New York: McGraw Hill
Arora, J.S.; Huang, M.W. 1996: Discrete structural optimization with commercially available sections: a review.J. Struct. Earthquake Eng., JSCE 13, 93–110
Arora, J.S.; Huang, M.W.; Hsieh, C.C. 1994: Methods for optimization of nonlinear problems with discrete variables: a review.Struct. Optim. 8, 69–85.
Balling, R.J. 1991: Optimal steel frame design by simulated annealing.J. Struct. Eng., ASCE 117, 1780–1795
Balling, R.J.; Fonseca, F. 1989: Discrete optimization of 3D steel frames. In:Computer Utilization in Structural Engineering, pp. 458–467. New York: ASCE
Barthelemy, J.-F.M.; Haftka, R.T. 1993: Approximation concepts for optimum structural design: a review.Struct. Optim. 5, 129–144
Cameron, G.E.; Xu, L.; Grierson, D.E. 1991: Discrete optimal design of 3D frameworks. In: Ural, O.; Wang, T-L. (eds.)Proc. 10th Electronic Computation Conf., pp. 181–188. New York: ASCE
Cella, A.; Logher, R.D. 1971: Automated optimum design from discrete components.J. Struct. Eng., ASCE 97, 175–189
Chan, C.-M. 1992: An optimality criteria algorithm for tall steel building design using commercial standard sections.Struct. Optim. 5, 26–29
Chan, C.-M.; Grierson, D.E.; Sherbourne, A.N. 1995: Automatic optimal design of tall steel building frameworks.J. Struct. Eng., ASCE. 121, 838–847
Elwakeil, O.; Arora, J.S. 1995: Methods for finding feasible points in constrained optimizationAIAA J. 33, 1715–1719
Geoffrion, A.M. 1967: Integer programming by implicit enumeration and Balas' method.Soc. Indus. & Appl. Math. Rev. 9, 178–190
Glankwahmdee, A.; Liebman, J.S.; Hogg, G.L. 1979: Unconstrained discrete nonlinear programming.Eng. Optim. 4, 95–107
Gomory, R.E. 1960: An algorithm for the mixed integer problem.Report No. P-1885. Santa Monica: The Rand Corporation
Grierson, D.E.; Cameron, G.E. 1989: Microcomputer-based optimization of steel structures in professional practice.Microcomputers in Civil Engineering 4, 289–296
Grierson, D.E.; Lee, W.H. 1984: Optimal synthesis of steel frameworks using standard sections.J. Struct. Mech. 12, 335–370
Grierson, D.E.; Lee, W.H. 1986: Optimal synthesis of frameworks under elastic and plastic performance constraints using discrete sections.J. Struct. Mech. 14, 401–420
Hager, K.; Balling, R.J. 1988: New approach for discrete structural optimization.J. Struct. Eng., ASCE 114, 1120–1134
Haug, E.J.; Arora, J.S. 1979:Applied Optimal Design, New York: Wiley-Interscience, John Wiley and Sons
Hua, H.M. 1983: Optimization of structures of discrete-sized elements.Comp. Struct. 17, 327–333
Huang, M.W. 1995:Algorithms for mixed continuous-discrete variable problems in structural optimization. Ph.D. Dissertation, Civil and Environmental Engineering, The University of Iowa
Huang, M.W.; Arora, J.S. 1995: Engineering optimization with discrete variables. In:Proc. 36th AIAA SDM Conf. (held in New Orleans, LA), pp. 1475–1485 Washington D.C.: AIAA
Huang, M.W.; Arora, J.S. 1996: A self-scaling implicit SQP method for large scale structural optimization.Int. J. Num. Meth. Eng. 39, 1933–1953
Huang, M.W.; Arora, J.S. 1997: Optimal design with discrete variables: some numerical experiments.Int. J. Num. Meth. Eng. 40, 165–188
Lai, Y-S.; Achenbach, J.D. 1973: Direct search optimization method.J. Struct. Eng., ASCE 98, 19–31
Liebman, J.S.; Khachaturian, N.; Chanaratna, V. 1981: Discrete structural optimization.J. Struct. Eng., ASCE 107, 2177–2197
May, S.A.; Balling, R.J. 1991: Strategies which permit multiple discrete section properties per member in 3D frameworks. In: Ural, O.; Wang, T-L. (eds.)Proc. 10th Electronic Computation Conf., pp. 189–196. New York: ASCE
May, S.A.; Balling, R.J. 1992: A filtered simulated annealing strategy for discrete optimization of 3D steel frameworks.Struct. Optim. 4, 142–148.
Reinschmidt, K.F. 1971: Discrete structural optimization.J. Struct. Eng., ASCE 97, 133–156
Toakley, R. 1968: Optimum design using available sections.J. Struct. Eng., ASCE 94, 1219–1241.
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Huang, M.W., Arora, J.S. Optimal design of steel structures using standard sections. Structural Optimization 14, 24–35 (1997). https://doi.org/10.1007/BF01197555
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DOI: https://doi.org/10.1007/BF01197555