ORIGINAL PAPER Multidisciplinary grammars supporting design optimization of buildings Philipp Geyer Received: 24 June 2007 / Accepted: 21 September 2007 / Published online: 11 January 2008 Ó Springer-Verlag London Limited 2008 Abstract Optimization often focuses only on the varia- tion of parameters while neglecting the consideration of alternative systems. However, the rearrangement of the components of a design offers important scope for improvement. To deal with such variations concerning the system structure of models for multidisciplinary design optimization (MDO), this paper proposes a framework for generating models dynamically using a design grammar with an underlying component-oriented analysis. Decom- position and modification rules support the derivation of alternative optimization model and the formalization of system changes. By linking qualitative characteristics with quantitative analyses, the components serve to assign architectural qualities to economic and environmental resources such as costs and energy consumption and thus to include non-numerical, qualitative characteristics within numerical optimization. The approach is developed with the help of a frame-based hall design and demonstrates system modifications of the optimization model by a spe- cific rule set. The rule set focuses on the structural design but considers the effects for the other essential disciplines involved in the design case. The setup and the prototypical implementation of an optimization model for this design illustrate a way of including grammar-based system vari- ations in MDO. Keywords Design grammar  Multidisciplinary design optimization  Shape grammar  Performance-oriented building design 1 Introduction The emerging technology of Multidisciplinary Design Optimization (MDO) supports the design process in vari- ous fields of engineering. The objective-driven improvement helps the designer to generate better artifacts and also to gather information about the nature of the design space, which may be even more valuable for the design process. The formal method of optimization uses an objective function and constraints to describe the problem. The usual form of the design problem statement is minimize or maximize JðxÞ ð1Þ subject to gðxÞ 0; and hðxÞ¼ 0: ð2Þ Thus, the start of the conventional optimization process requires a complete description of the objective function J and the constraints g and h. The problem is then solved by selecting the best parameter vector, usually carried out by a heuristic or a deterministic, gradient-based search algorithm. This parameter-focused formalism restricts the process of design optimization since the objective function and the constraints are static. The complete description of the design including all possible variations is required from the beginning. This contradicts the dynamic development of the design process. Design optimization, understood in a broader sense as a method for improving a design by systemically changing it and observing the outcome with respect to certain objec- tive aspects, seems to overlap with essential activities of P. Geyer (&) Institut fu ¨r Architektur, Fachgebiet fu ¨r Tragwerksentwurf und – konstruktion, Technische Universita ¨t Berlin, Straße des 17. Juni 152 - A16, 10623 Berlin, Germany e-mail: Philipp.Geyer@TU-Berlin.de; p.geyer@tu-berlin.de 123 Res Eng Design (2008) 18:197–216 DOI 10.1007/s00163-007-0038-6