An automated shape grammar approach to structural design description and optimisation

Abstract

The main objective of this research is to develop and evaluate an automated design description and optimisation framework based on the Shape Grammar (SG) syntax. In particular, an algorithmic methodology to automate the SG syntax using evolutionary intelligence is proposed. The proposed automation of SG is achieved by mapping the genetic information provided by a Genetic Algorithm (GA) to context-free grammar rules by a means of Backus-Naur Form (BNF) syntax known as Grammatical Evolution (GE). GE is an efficient optimisation tool, which can be used in a variety of optimisation problems. First, its use in single and multi-objective optimisation of mathematical functions is demonstrated. Several techniques for synthesis of variables using specific BNF syntaxes are proposed. The results obtained from numerical experiments are compared with those obtained using a standard GA. Interestingly, the results show a notable improvement in the convergence speed over the standard GA for the functions tested. This observation surpassed expectations, since the GE is based on the GA. The use of GE is then extended to automate the SG syntax by deriving a grammar based design shape description and optimisation framework. To evaluate its efficacy and to demonstrate the concept, this framework is applied to two distinctive classes of problems frequently encountered in engineering practice. The first class of problems is related to shape descriptions and optimisation aspects of structural design. A specific BNF syntax is developed for planar shapes which makes use of four SG rules with arc primitives of variable size given by a radius and an angle of rotation. These SG rules are then used in the synthesis of piecewise parametric curves for the shape description and optimisation of a planar crane hook. The experimental results show superiority in convergence speed when compared to shape optimisation of the same problem based on Non-Uniform Rational B-Spline (NURBS) combined with a GA search strategy. The second class of problems considered here relates to the topology description and optimisation of planar trusses. Several BNF syntaxes are developed to achieve simultaneous topology, size and configuration optimisation. The experimental results thus obtained show good agreement with the results reported in the literature using an alternative truss optimisation method based on GA. Furthermore, by using the proposed truss description and optimisation method the computational expense is significantly reduced. The proposed design description and optimisation framework based on the SG syntax is a fast and efficient design exploration tool. The successful application of this proposed framework combining SG with design exploration in a range of structural problems validates the proposed idea.

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