A general indirect representation for optimization of generative design systems by genetic algorithms: Application to a shape grammar-based design system

• Implementing genetic algorithms for optimization requires defining a representation.
• This paper presents a general indirect representation for generative design systems.
• The representation is applied to a shape grammar-based parametric design system.
• A standard uniform crossover, impossible with a direct representation, is performed.
• In an optimization example, convergence for a good solution is achieved fairly fast.

Generative design systems coupled with objective functions can be efficiently explored through the use of stochastic optimization algorithms, such as genetic algorithms. The first step in implementing genetic algorithms is to define a representation, that is, the data structure representative of the genotype space and its mathematical relation to the data of the phenotype space — the variables of the real problem. This can be a hard task, particularly if the design system contains dependency between variables. This paper presents a general representation, which enables the use of standard variation operators, allows defining both continuous and discrete variables from a single type of gene and is easily adaptable to different problems, with a larger or smaller number of variables. This representation was created to solve the representation problem in the design system for Frank Lloyd Wright's prairie houses, a shape grammar that was converted into a parametric design system.