Abstract
Although the genetic algorithm (GA) for structural optimization is very robust, it is very computationally intensive and hence slower than optimality criteria and mathematical programming methods. To speed up the design process, the authors present an adaptive reanalysis method for GA and its applications in the optimal design of trusses. This reanalysis technique is primarily derived from the Kirsch’s combined approximations method. An iteration scheme is adopted to adaptively determine the number of basis vectors at every generation. In order to illustrate this method, three classical examples of optimal truss design are used to validate the proposed reanalysis-based design procedure. The presented numerical results demonstrate that the adaptive reanalysis technique affects very slightly the accuracy of the optimal solutions and does accelerate the design process, especially for large-scale structures.
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References
Dorn W., Gomory R., Greenberg H.: Automatic design of optimal structures. J. Mech. 3(1), 25–52 (1964)
Guo X., Cheng G.D.: Epsilon-continuation approach for Truss topology optimization. Acta Mech. Sin. 20(5), 526–533 (2004)
Zhang W.H., Dai G.M., Wang F.W., Sun S.P., Bassir H.: Using strain energy-based prediction of effective elastic properties in topology optimization of material microstructures. Acta Mech. Sin. 2(1), 77–89 (2007)
Sui Y.K., Du J.Z., Guo Y.Q.: Independent continuous mapping for topological optimization of frame structures. Acta Mech. Sin. 22(6), 611–619 (2006)
Leu L.J.: A reduction method for boundary element reanalysis. Comput. Method. Appl. M. 178(13,14), 125–139 (1999)
Levy R., Kirsch U., Liu S.: Reanalysis of trusses using modied initial designs. Struct. Multidisc. Optim. 19(2), 105–112 (2000)
Kirsch U., Papalambros P.Y.: Exact and accurate reanalysis of structures for geometrical changes. Eng. Comp. 4(17), 363–372 (2001)
Kirsch U., Bogomolni M.: Error evaluation in approximate reanalysis of structures. Struct. Multidisc. Optim. 28(2,3), 77–86 (2004)
Chen S.H., Yang X.W., Wu B.S.: Static displacement reanalysis of structures using perturbation and Pade approximation. Commun. Numer. Meth. Eng. 16(2), 75–82 (2000)
Chen S.H., Yang X.W.: Extended Kirsch combined method for eigenvalue reanalysis. AIAA J. 38(5), 927–930 (2000)
Chen S.H., Yang X.W., Lian H.D.: Comparison of several eigenvalue reanalysis methods for modified structures. Struct. Optim. 20(4), 253–259 (2000)
Leu L.J., Chang W.H.: Reanalysis-based optimal design of trusses. Int. J. Numer. Meth. Eng. 49(8), 1007–1028 (2000)
Goldberg D.E.: Genetic Algorithms in Search, Optimization and Machine Learning, 1st edn. Addison-Wesley, Reading (1989)
Li S.J., Liu Y.X.: Identification of vibration loads on hydro generator by using hybrid genetic algorithm. Acta Mech. Sin. 22(6), 603–610 (2006)
Hadjigeorgiou E.P., Stavroulakis G.E., Massalas C.V.: Shape control and damage identification of beams using piezoelectric actuation and genetic optimization. Int. J. Eng. Sci. 44(7), 409–421 (2006)
Engelhardt M., Schanz M., Stavroulakis G.E., Antes H.: Defect identification in 3-D elastostatics using a genetic algorithm. Optim. Eng. 7(1), 63–79 (2006)
Gero M.B.P., García A.B., Díaz J.J.D.C.: Design optimization of 3D steel structures: genetic algorithms vs. classical techniques. J. Constr. Steel. Res. 62(12), 1303–1309 (2006)
Kirsch U.: Combined approximations—a general reanalysis approach for structural optimization. Struct. Optim. 20(2), 97–106 (2000)
Yang H.X., Zuo W.J., Wu D.F., Ren L.Q.: Inverse heat conduction analysis of quenching process based on finite element method and genetic algorithm. J. Comput. Theor. Nanos. 5(8), 1708–1712 (2008)
Schmit L.A., Farshi B.: Some approximation concepts for structural synthesis. AIAA J. 12(5), 692–699 (1974)
Rizzi, P.: Optimization of multiconstrained structures based on optimality criteria. AIAA/ASME/SAE 17th Structures, Structural Dynamics and Materials Conference, King of Prussia, PA (1976)
Leu L.J., Chang W.H.: Reanalysis-based optimal design of trusses. Int. J. Numer. Meth. Eng. 49(8), 1007–1028 (2000)
Zhou M., Rozvany G.I.N.: DCOC: an optimality criteria method for large systems, Part II: algorithm. Struct. Multidisc. Optim. 6(4), 250–262 (1993)
Lee K.S., Geem Z.W.: A new structural optimization method based on the harmony search algorithm. Comput. Struct. 82(9,10), 781–798 (2004)
Saka M.P.: Optimum design of pin-jointed steel structures with practical applications. J. Struct. Eng. ASCE 116(10), 2599–2620 (1990)
Thierauf G., Cai J.: Parallelization of evolution strategy for discrete structural optimization problems. Comput-Aided Civ. Inf. 13(1), 23–30 (1998)
Coello C.A., Christiansen A.D.: Multiobjective optimization of trusses using genetic algorithms. Comput. Struct. 75(6), 647–660 (2000)
Lamberti L., Pappalettere C.: Move limits definition in structural optimization with sequential linear programming, Part II: numerical examples. Comput. Struct. 81(4), 215–238 (2003)
Jenkins W.M.: A decimal-coded evolutionary algorithm for constrained optimization. Comput. Struct. 80(5,6), 471–480 (2002)
Toǧan V., Daloǧlu A.T.: An improved genetic algorithm with initial population strategy and self-adaptive member grouping. Comput. Struct. 86(11,12), 1204–1218 (2004)
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The project was supported by the National Natural Science Foundation of China (50975121) and the Project 2009-2007 of the Graduate Innovation Fund of Jilin University.
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Xu, T., Zuo, W., Xu, T. et al. An adaptive reanalysis method for genetic algorithm with application to fast truss optimization. Acta Mech Sin 26, 225–234 (2010). https://doi.org/10.1007/s10409-009-0323-x
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DOI: https://doi.org/10.1007/s10409-009-0323-x