Fuzzy Genetic Algorithm for Optimization of Steel Structures
Publication: Journal of Structural Engineering
Volume 126, Issue 5
Abstract
In the traditional optimization algorithms, constraints are satisfied within a tolerance defined by a crisp number. In actual engineering practice, constraint evaluation involves many sources of imprecision and approximation. When an optimization algorithm is forced to satisfy the design constraints exactly, it can miss the global optimum solution within the confine of commonly acceptable approximations. Extending the augmented Lagrangian genetic algorithm (GA) of Adeli and Cheng, a fuzzy augmented Lagrangian GA is presented for optimization of steel structures subjected to the constraints of the AISC allowable stress design specifications taking into account the fuzziness in the constraints. The membership function for the fuzzy domain is found by the intersection of the fuzzy membership function for the objective function and the constraints using the max-min procedure of Bellman and Zadeh. Nonlinear quadratic fuzzy membership functions are used for objective function and constraints. The algorithm is applied to two space axial-load structures including a large 37-story structure with 1,310 members. The features and advantages of the new fuzzy GA include acknowledging the imprecision and fuzziness in the code-based design constraints, increased likelihood of obtaining the global optimum solution, improved convergence, and reduced total computer processing time.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Adeli, H., ed. (1988). Expert systems in construction and structural engineering. Chapman & Hall, London.
2.
Adeli, H., ed. (1990). Knowledge engineering—Volume one—Fundamentals. McGraw-Hill, New York.
3.
Adeli, H., and Balasubramanyam, K. V. (1988). Expert systems for structural design: A new generation. Prentice-Hall, Englewood Cliffs, N.J.
4.
Adeli, H., and Cheng, N.-T. (1993). “Integrated genetic algorithm for optimization of space structures.”J. Aerosp. Engrg., ASCE, 6(4), 315–328.
5.
Adeli, H., and Cheng, N.-T. (1994). “Augmented Lagrangian genetic algorithm for structural optimization.”J. Aerosp. Engrg., ASCE, 7(1), 104–118.
6.
Adeli, H., and Kamal, O. (1986). “Efficient optimization of space trusses.” Comp. and Struct., 24(3), 501–511.
7.
Adeli, H., and Park, H. S. (1998). Neurocomputing for design automation. CRC, Boca Raton, Fla.
8.
Bellman, R. E., and Zadeh, L. A. (1970). “Decision-making in a fuzzy environment.” Mgmt. Sci., 17, 141–164.
9.
Dhingra, A. K., Rao, S. S., and Kumar, V. (1992). “Nonlinear membership functions in multiobjective fuzzy optimization of mechanical and structural systems.” AIAA J., 30(1), 251–260.
10.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading, Mass.
11.
Holland, J. H. (1975). Adaption in natural and artificial systems. University of Michigan Press, Ann Arbor, Mich.
12.
Kim, J.-H., and Myung, H. (1996). “A two-phase evolutionary programming for general constrained optimization problem.” Proc., 5th Annu. Conf., on Evolutionary Programming, L. J. Fogel, P. J. Angeline, and T. Back, eds., MIT Press, Cambridge, Mass. 295–304.
13.
Kim, J.-H., and Myung, H. (1997). “Evolutionary programming techniques for constrained optimization problems.” IEEE Trans. on Evolutionary Computation, 1(2), 129–140.
14.
Manual of steel construction—allowable stress design. (1995). 9th ed., 2nd revision, American Institute of Steel Construction, Chicago.
15.
Powell, D., and Skolnick, M. M. (1993). “Using genetic algorithms in engineering design optimization with nonlinear constraints.” Proc., 5th Int. Conf. on Genetic Algorithms, S. Forrest, ed., Morgan Kaufmann Publishers, Inc., Los Altos, Calif., 424–431.
16.
Rao, S. S. (1987a). “Description and optimum design of fuzzy mechanical systems.” J. Mechanisms, Transmissions and Automation in Des., 109, 126–132.
17.
Rao, S. S. (1987b). “Multi-objective optimization of fuzzy structural systems.” Int. J. Numer. Methods in Engrg., 24(6), 1157–1171.
18.
Schoenauer, M., and Xanthakis, S. (1993). “Constrained GA optimization.” Proc., 5th Int. Conf. on Genetic Algorithms, S. Forrest, ed., Morgan Kaufmann Publishers, Inc., Los Altos, Calif., 573–580.
19.
Smith, A. E., and Tate, D. M. (1993). “Genetic optimization using a penalty function.” Proc., 5th Int. Conf. on Genetic Algorithms, S. Forrest, ed., Morgan Kaufmann Publishers, Inc., Los Altos, Calif., 499–505.
20.
Soh, C. K., and Yang, J. (1996). “Fuzzy controlled genetic algorithm search for shape optimization.”J. Comp. in Civ. Engrg., ASCE, 10(2), 143–150.
21.
Uniform building code. (1997). Vol. 2, International Conference of Building Officials, Whittier, Calif.
22.
Wang, G., and Wang, W. (1985a). “Fuzzy optimum design of structures.” Engrg. Optimization, 8, 291–300.
23.
Wang, G., and Wang, W. (1985b). “Fuzzy optimum design of aseismic structures.” Earthquake Engrg. and Struct. Dyn., 13(6), 827–837.
24.
Yeh, Y., and Hsu, D. (1990). “Structural optimization with fuzzy parameters.” Comp. and Struct., 37(6), 917–924.
25.
Zadeh, L. A. (1965). “Fuzzy sets.” Information and Control, 8(3), 338–353.
26.
Zimmermann, H.-J. (1978). “Fuzzy programming and linear programming with several objective functions.” Fuzzy Sets and Sys., 1, 45–55.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 126 • Issue 5 • May 2000
Pages: 596 - 604
History
Received: Jun 28, 1999
Published online: May 1, 2000
Published in print: May 2000
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.