Topology optimization with efficient rules of cellular automata

Bogdan Bochenek (Institute of Applied Mechanics, Cracow University of Technology, Kraków, Poland)
Katarzyna Tajs-Zielinska (Institute of Applied Mechanics, Cracow University of Technology, Kraków, Poland)

Engineering Computations

ISSN: 0264-4401

Publication date: 11 November 2013



Biologically inspired techniques like cellular automata (CA) are gaining nowadays attention of designers. This is because they are effective, do not require gradient information, and one can easily combine this type of algorithm with any finite element structural analysis code. The purpose of this paper is to develop a CA algorithm based on novel local rules oriented at solving compliance-based topology optimization problems.


The design domain is divided into lattice of cells, states of which are updated synchronously. The proposed rules include information coming from an individual cell and from its neighborhood, and by introducing weighting parameters allow to control and modify topology generation process.


The performance of the developed algorithm is very satisfactory, and a comparison with results of other authors, obtained with the use of various optimization techniques, shows efficiency of the present topology generation process. The results found within approach of this paper are in a good agreement with the ones already reported, both for optimal topologies and values of minimal compliance, which in some cases are found even improved.

Practical implications

The algorithm presented in the paper is quite general what allows its easy application to engineering design problems. Moreover, the local update rules are simple, so they can be easily implemented into professional FEM analysis codes, as an efficient add-on module for topology optimization.


The main advantage of the developed algorithm is that it is a fast convergent technique and usually requires far less iterations as to achieve the solution, when compared to other approaches. What is also important does not require any additional density filtering. It also overcomes some drawbacks of traditional approaches so that changing mesh density does not influence resulting topologies and solutions are free from checkerboard effect.



Bochenek, B. and Tajs-Zielinska, K. (2013), "Topology optimization with efficient rules of cellular automata", Engineering Computations, Vol. 30 No. 8, pp. 1086-1106.

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