Novel local rules of cellular automata applied to topology and size optimization

This article is devoted to the application of the cellular automata mathematical apparatus to the problem of continuous optimization. The cellular automaton with an objective function is introduced as a new modification of the classic cellular automaton. The algorithm of continuous optimization, which is based on dynamics of the cellular automaton having the property of geometric symmetry, is obtained. The results of the simulation experiments with the obtained algorithm on standard test functions are provided, and a comparison between the analogs is shown.

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“…A similar direction is presented in papers [10][11][12]. The solution of structural optimization problems is also considered.…”

Section: Introductionmentioning

confidence: 88%

The Algorithm of Continuous Optimization Based on the Modified Cellular Automaton

et al. 2016

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“…Cellular Automata (CA) as described in the work of Tovar et al [20], Bochenek and Tajs-Zielinska [21], is the second of the optimization methods in which some similarity to the CCSA algorithm can be found. The main and fundamental difference between CA and the CCSA is in the local nature of the CA procedure and its 'one-way' model optimization.…”

Section: The Constant Criterion Surface Algorithmmentioning

confidence: 99%

Multi-constrained topology optimization using constant criterion surface algorithm

Mrzygłód¹

2012

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. This paper sets out to describe a multi-constrained approach to topology optimization of structures. In the optimization, a constant criterion surface algorithm and the multi-constraint procedure is used. The multi-constraint procedure consists of constraints normalization and equivalent design space assembling. The work is illustrated by an example of the L-shaped domain optimization with the horizontal line support and complex loads. The example takes into consideration stress, fatigue and compliance constraints. The separate and simultaneous application of constraints resulted in significant differences in structure topology layouts. The application of a fatigue constraint gave more conservative results when compared to static stress or compliance limitations. The multi-constrained approach allowed effectively lowering the mass of the structure while satisfying all constraints.

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“…The majority of papers dealing with that subject were published during the last decade and a discussion on the application of CA to structural optimization can be found, e.g. in research papers (Bochenek and Tajs-Zielińska, 2012;Kicinger, 2004;Tovar et al, 2006). The most common application of CA in structural optimal design is topology optimization.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization with efficient rules of cellular automata

Bochenek

Tajs-Zielińska

2013

Engineering Computations

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Purpose -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. Design/methodology/approach -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. Findings -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. Originality/value -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.

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Novel local rules of cellular automata applied to topology and size optimization

Cited by 25 publications

References 29 publications

The Algorithm of Continuous Optimization Based on the Modified Cellular Automaton

The Algorithm of Continuous Optimization Based on the Modified Cellular Automaton

Multi-constrained topology optimization using constant criterion surface algorithm

Topology optimization with efficient rules of cellular automata

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