TECHNICAL PAPERS
May 1, 1998

Optimized Design of Two-Dimensional Structures Using a Genetic Algorithm

Publication: Journal of Structural Engineering
Volume 124, Issue 5

Abstract

A design procedure incorporating a simple genetic algorithm (GA) is developed for discrete optimization of two-dimensional structures. The objective function considered is the total weight (or cost) of the structure. The objective function is minimized subjected to serviceability and strength requirements. The GA-based design procedure FEAPGEN is developed as a module in the Finite Element Analysis Program (FEAP). Special features of FEAPGEN include discrete design variables, an open format for prescribing constraints, design checking using the American Institute of Steel Construction Allowable Stress Design (AISC-ASD) specifications, multiple loading conditions, and a comprehensive AISC database of available structural steel members. Several strategies for reproduction and crossover are investigated. In particular, a group selection scheme for reproduction that does not require fitness scaling is applied. Various fitness and penalty functions are investigated for their appropriateness to the ASD design of two-dimensional structures. A comparison is presented between FEAPGEN genetic search design procedure and a classical continuous optimization method based on the optimality criterion.

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References

1.
Allwood, R. J., and Chung, Y. S.(1984). “Minimum-weight design of trusses by an optimality criteria method.”Int. J. Numer. Methods in Engrg., 20, 697–713.
2.
Arora, J. S.(1980). “Analysis of optimality criteria and gradient projection methods for optimal structural design.”Computer Methods Appl. Mech. Engrg., 23, 185–213.
3.
Arora, J. S., Haug, E. J. Jr., and Rim, K.(1975). “Optimal design of plane frames.”J. Struct. Div., ASCE, 101(10), 2063–2078.
4.
Barnett, R. L.(1961). “Minimum weight design of beams for deflection.”J. Engrg. Mech. Div., ASCE, 87(1), 75–109.
5.
Chang, K. J.(1992). “Optimality criteria methods using K-S functions.”Struct. Optimization, 4, 213–217.
6.
Cheng, F. Y., and Juang, D. S. (1985). “Optimum design of braced and unbraced frames for static, seismic, and wind forces with UBC, ATC-3, and TJ-11.”Struct. Ser. 85-10, Final Rep. for NSF, University of Missouri–Rolla.
7.
DeJong, K. A. (1975). “An analysis of the behavior of a class of genetic adaptive systems,” PhD dissertation, University of Michigan, Ann Arbor, Mich., Dissertation Abstract Int., 36(10), 5140B (University Microfilms No. 76-9381).
8.
Erbatur, F., and Al-Hussainy, M. M.(1992). “Optimum design of frames.”Comp. and Struct., 45(5/6), 887–891.
9.
Fleury, C.(1979). “Structural weight optimization by dual methods of convex programming.”Int. J. Numer. Methods in Engrg., 14, 1761–1783.
10.
Fleury, C., and Geradin, M.(1978). “Optimality criteria and mathematical programming in structural weight optimization.”Comp. and Struct., 8, 7–17.
11.
Gellaty, R. A., and Berke, L. (1971). “Optimal structural design.”Rep. No. AFFDL-TR-70-165, Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Ohio.
12.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning. Addison-Wesley Publishing Company, Inc., New York, N.Y.
13.
Goldberg, D. E., and Samtani, M. P. (1986). “Engineering optimization via genetic algorithm.”Proc., 9th Conf. Electronic Computation, ASCE, 471–482.
14.
Grierson, D. E., and Pak, W. H.(1993). “Optimal sizing, geometrical and topological design using genetic algorithms.”Struct. Optimization, 6, 151–159.
15.
Hall, S. K., Cameron, G. E., and Grierson, D. E.(1989). “Least weight design of steel frameworks accounting for P-Δ effects.”J. Struct. Engrg., ASCE, 115(6), 1463–1475.
16.
Holland, J. H. (1975). Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, Mich.
17.
How to use SODA: structural optimization design & analysis software for structural engineering. (1995). Acronym Software Incorporated, North Tonawanda, N.Y.
18.
Khan, M. R., Willmerrt, K. D., and Thornton, W. A.(1979). “An optimality criterion method for large scale structures.”AIAA J., 17(7), 753–761.
19.
Khot, N. S., Venkayya, V. B., and Berke, L. (1973). “Optimization of structures for strength and stability requirements.”Rep. No. AFFDL-TR-73-98, Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Ohio.
20.
Khot, N. S., Venkayya, V. B., and Berke, L.(1976). “Optimum structural design with stability constraints.”Int. J. Numer. Methods in Engrg., 10, 1097–1114.
21.
Kirsch, U.(1991). “Feasibility and optimality in structural design.”Comp. and Struct., 41(6), 1349–1356.
22.
Koza, J. R. (1992). Genetic programming: on the programming of computers by means of natural selection. MIT Press, Cambridge, Mass.
23.
Kuhn, H. W., and Tucker, A. W. (1951). “Nonlinear programming.”Proc., 2nd Berkeley Symp. on Mathematics, Statistics and Probability, University of California Press, Berkeley, Calif. 481–492.
24.
Lin, C. C., and Liu, I. W.(1989). “Optimal design based on optimality criterion for frame structures including buckling constraints.”Comp. and Struct., 31(4), 535–544.
25.
Lin, C. Y., and Hajela, P.(1992). “Genetic algorithms in optimization problems with discrete and integer design variables.”Engrg. Optimization, 19, 309–327.
26.
Manual of steel construction—allowable stress design. (1989). American Institute of Steel Construction, Chicago, Ill.
27.
Moses, F.(1964). “Optimum structural design using linear programming.”J. Struct. Div., ASCE, 90(6), 89–104.
28.
Pezeshk, S. (1989). “Optimal design of nonlinear framed structures under multiple loading based on a stability criterion.”Rep. No. SRS-547, University of Illinois at Urbana-Champaign, Urbana, Ill.
29.
Prager, W.(1968). “Optimality in structural design.”Proc., Nat. Academic of Sciences, University of California (San Diego), 61(3), 794–796.
30.
Qian, L. X., Zhang, W. X., Siu, Y. K., and Zhang, J. T.(1982). “Efficient optimum design of structures—program DDDU.”Comp. Methods in Appl. Mech. and Engrg., 30, 209–224.
31.
Rajan, S. D.(1995). “Sizing, shape, and topology design optimization of trusses using genetic algorithms.”J. Struct. Engrg., ASCE, 121(10), 1480–1487.
32.
Rajeev, S., and Krishnamoorthy, C. S.(1992). “Discrete optimization of structures using genetic algorithms.”J. Struct. Engrg., ASCE, 118(5), 1233–1250.
33.
Rashedi, R., and Moses, F.(1986). “Application of linear programming to structural system reliability.”Comp. and Struct., 24(3), 375–384.
34.
Rizzi, P. (1976). “Optimization of multi-constrained structures based on optimality criteria.”Proc., AIAA/ASME/SAE 17th Struct. Dyn. and Mat. Conf., King of Prussia, Pa.
35.
Rozvany, G. I. N., and Zhou, M.(1991). “The COC algorithms, part I: cross section optimization or sizing.”Comp. Methods in Appl. Mech. and Engrg., 89, 281–308.
36.
Rozvany, G. I. N., and Zhou, M. (1993). “Continuum-based optimality criteria (COC) methods: an introduction, in optimization of large structural systems.”Proc., NATO/DFG ASI, Berchtesgaden, 1991, Kluwer, Dordrecht, The Netherlands, 1–26.
37.
Rozvany, G. I. N., Zhou, M., and Gollub, W.(1990). “Continuum-type optimality criteria methods for large finite element systems with a displacement constraint-part II.”Struct. Optimization, 2, 77–104.
38.
Rozvany, G. I. N., Zhou, M., Rogghaus, M., Gollub, W., and Spengemann, F.(1989). “Continuum-type optimality criteria methods for large finite element systems with a displacement constraint—part I.”Struct. Optimization, 1, 47–72.
39.
Saka, M. P.(1991). “Optimum design of steel frames with stability constraints.”Comp. and Struct., 41(6), 1365–1377.
40.
Srividya, A., and Ranganathan, R.(1995). “Reliability based optimal design of reinforced concrete frames.”Comp. and Struct., 57(4), 651–661.
41.
Tabak, E. I., and Wright, P. M.(1981). “Optimality criteria method for building frames.”J. Struct. Div., ASCE, 107(7), 1327–1342.
42.
Takewaki, I., Conte, J. P., Mahin, S. A., and Pister, K. S.(1991). “Probabilistic multi-objective optimal design of seismic resistant braced steel frames using ARMA models.”Comp. and Struct., 41(4), 687–707.
43.
Turner, H. K., and Plaut, R. H.(1980). “Optimal design for stability under multiple loads.”J. Engrg. Mech. Div., ASCE, 106(6), 1365–1382.
44.
Uniform building code. (1994). International Conference of Building Officials, Whittier, Calif.
45.
Venkayya, V. B.(1971). “Design of optimum structures.”Int. J. Comp. and Struct., 1, 265–309.
46.
Venkayya, V. B., Khot, N. S., and Reddy, V. S. (1968). “Energy distribution in an optimum structural design.”AFFDL-TR-68-156, Flight Dynamics Laboratory, Wright Patterson AFB, Ohio.
47.
Zienkiewicz, O. C. (1982). The finite element method. McGraw-Hill Book Co., Inc., New York, N.Y.

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Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 124Issue 5May 1998
Pages: 551 - 559

History

Published online: May 1, 1998
Published in print: May 1998

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Authors

Affiliations

Charles Camp
Assoc. Prof., Dept. of Civ. Engrg., Campus Box 526570, The University of Memphis, Memphis, TN 38152.
Shahram Pezeshk
Assoc. Prof., Dept. of Civ. Engrg., Campus Box 526570, The University of Memphis, Memphis, TN.
Guozhong Cao
Struct. Engr., Friede & Goldman, New Orleans, LA 70112.

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