Keywords: size, shape, topology optimisation, evolution strategies, truss, structural optimisation.

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:

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.

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.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £85 +P&P)