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Civil-Comp Proceedings ISSN 1759-3433
CCP: 76 PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
Edited by: B.H.V. Topping and Z. Bittnar
Paper 64 Discrete and Continuous Structural Optimisation Using Evolution Strategies
A.F. Ulusoy and F. Erbatur Department of Civil Engineering, Middle East Technical University, Ankara, Turkey
Full Bibliographic Reference for this paper
A.F. Ulusoy, F. Erbatur, "Discrete and Continuous Structural Optimisation Using Evolution Strategies", in B.H.V. Topping, Z. Bittnar, (Editors), "Proceedings of the Third International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 64, 2002. doi:10.4203/ccp.76.64
Keywords: size, shape, topology optimisation, evolution strategies, truss, structural optimisation.
Summary
Evolutionary optimisation methods, namely, Genetic Algorithms (GAs),
Evolutionary Programming (EP) and Evolution Strategies (ESs) have received
significant interest amongst researchers in the optimisation area. This paper deals
with optimum design (minimum weight) of structures using ESs. After a brief
review of structural optimisation and ES fundamentals, size and/or shape and/or
topology optimum design of plane and space trusses subjected to stress,
displacement and stability constraints is considered and illustrated with numerical
examples including comparisons with previously published works.
Although, particularly, the use of GA in optimum structural design is widely
covered, the application of ES is very limited in the literature [1,2]. Evolution
Strategies was developed by Rechenberg and Schwefel in 1960s [3,4]. In this study
the multi-membered
-ES, where best individuals are selected out of
individuals, is used. Classical ES is a continuous optimization technique and can be
used in continuous parameter optimization problems as:
 |
(64.1) |
where is the objective function, is the vector of continuous design variables,
is the set of feasible points and finally is the number of continuous design
variables. However most of the engineering application problems involve
simultaneous use of discrete and continuous design variables. An improved
technique; Generalized Evolution Strategy [5], is developed to overcome this
drawback which also allows handling of discrete variables. Since both discrete and
continuous design variables are used in simultaneous structural optimisation (size
and shape; size, shape and topology), this improved technique is adapted in this
study.
Layout optimisation of trusses is a challenging and complex problem. Size
optimisation involves cross-sectional areas (continuous or discrete) of structural
members. The design variables in the shape optimisation problem are the
coordinates (continuous) of the nodal points. Topology optimisation is concerned
with the existence or non-existence of members (discrete) in the initial configuration
of a truss. Thus, the simultaneous optimisation problem involves a large number of
design variables of different characteristics and results in quite a complex design
space. Traditional techniques are not capable of handling such a problem adequately
due to the complexity in the design space. Furthermore, the discontinuity and
singularity introduced by the topologic variables make the problem even impossible
to be solved by classical methods. Evolutionary algorithms have certain advantages
over the traditional techniques and have been proved to be quite effective in dealing
with complex problems of structural optimisation.
In the paper the computational procedure for truss optimisation using ES is
explained in detail and also summarised in a flowchart. Three numerical examples
are presented. As compared to results obtained by other techniques better solutions
are obtained which reveal the effectiveness of the use of ES in optimum structural
design problems.
References
- 1
- Thierauf, G. and Cai, J., "Parallel Evolution Strategy for Solving Structural Optimisation", Engineering Structures, 19, 318-324, 1997. doi:10.1016/S0141-0296(96)00076-4
- 2
- Lagaros, N.D., Papadrakakis, M. and Kokossalakis, G., "Structural Optimization Using Evolutionary Algorithms", Computers & Structures, 80, 571-589, 2002. doi:10.1016/S0045-7949(02)00027-5
- 3
- Rechenberg, I., "Cybernetic Solution Path of an Experimental Problem", Royal Aircraft Establishment, Library translation No. 1122, Farnborough, Hants., UK, 1965.
- 4
- Schwefel, H.-P., "Kybernetische Evolution als Strategie der experimentellen Forschung in der Strömungstechnik", Diplomarbeit, Technische Universität Berlin, 1965.
- 5
- Bäck, T., and Schütz, M., "Evolutionary Strategies for Mixed-integer Optimization of Optical Multilayer Systems", In: Proc. 4th Annual Conference on Evolutionary Computation (McDonnell, J.R., Reynolds, R.G., and Fogel, D.B., eds.), MIT Press, Cambridge, MA, 33?51, 1995.
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