A general indirect representation for optimization of generative design systems by genetic algorithms: Application to a shape grammar-based design system Vasco Granadeiro a,d, ⁎, Luis Pina b , José P. Duarte c,d , João R. Correia d , Vítor M.S. Leal e a IN+, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal b Pina Robotic Solutions, Rua Eduardo Coelho 43-3 Esq., 1200-165 Lisboa, Portugal c CIAUD, Faculty of Architecture, Technical University of Lisbon, Rua Sá Nogueira, 1349-055 Lisboa, Portugal d Instituto Superior Técnico/ICIST, Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal e Institute of Mechanical Engineering, Faculty of Engineering of the University of Porto (IDMEC-FEUP), Rua Dr. Roberto Frias, 4200-465 Porto, Portugal abstract article info Article history: Accepted 18 May 2013 Available online xxxx Keywords: Generative design system Shape grammars Parametric design Optimization Genetic algorithm Representation 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 pre- sents 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. © 2013 Elsevier B.V. All rights reserved. 1. Introduction A generative design system is a model composed of a set of com- putational rules that are applied to generate alternative designs [1–3]. In addition to enabling the desired design variety, rules encode constraints to create only the intended output. Therefore, through a well-designed system of rules, generative design systems have the ca- pability of maintaining stylistic coherence and design identity while generating diverse designs. The advantage of having alternative designs is to allow choosing the one that better fits a certain context or achieves a defined objec- tive. Frequently, this can be translated into an objective function, linked to the design system. Within the flexibility of the design system, variables (in the form of rule applications and/or parameters) can be edited to improve the value of the objective function, looking for the best performing design. However, for a large number of variables, search algorithms are a much more efficient method to explore the solution space. Of course, this requires design systems to be programmed in numerical computing languages. Exhaustive search is the ideal method for small solution spaces. Exact optimization algorithms, such as linear programming, branch- and-bound and dynamic programming, are very proficient in finding the best solution in convex solution spaces. However, in general, gen- erative design systems involve very large and non-convex solution spaces. Therefore, stochastic optimization algorithms are the most appropriate search method, even though they do not guarantee find- ing the global optimal solution. Among them, genetic algorithms have been proven to find high quality solutions in large solution spaces and in reasonable time periods [4]. The first step in solving an optimization problem with genetic algo- rithms is to define an adequate representation and a corresponding geno- type–phenotype mapping. The real-world problem involves variables. Genetic algorithms work with genes, the corresponding entities for the variables. The representation is the definition of the genes and the geno- type–phenotype mapping is the mathematical relation between genes and variables. The informal term “genetification” is sometimes used as a mnemonic for the task of creating the representation and the genotype– phenotype mapping. The two main requirements for a representation are encoding all the possible solutions of the problem and enabling the application of the variation operators to them (crossover and mutation). Automation in Construction xxx (2013) xxx–xxx ⁎ Corresponding author at: IN+, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal. Tel.: +351 918506061. E-mail addresses: vascogranadeiro@ist.utl.pt, vgrana@media.mit.edu (V. Granadeiro), luismppina@gmail.com (L. Pina), jduarte@fa.utl.pt (J.P. Duarte), jcorreia@civil.ist.utl.pt (J.R. Correia), vleal@fe.up.pt (V.M.S. Leal). AUTCON-01585; No of Pages 9 0926-5805/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.autcon.2013.05.012 Contents lists available at SciVerse ScienceDirect Automation in Construction journal homepage: www.elsevier.com/locate/autcon Please cite this article as: V. Granadeiro, et al., A general indirect representation for optimization of generative design systems by genetic algorithms: Application to a shape..., Automation in Construction (2013), http://dx.doi.org/10.1016/j.autcon.2013.05.012