Floor plan design using block algebra and constraint satisfaction Francisco Regateiro ⇑ , João Bento, Joaquim Dias Department of Civil Engineering and Architecture, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal article info Article history: Received 16 November 2010 Received in revised form 3 January 2012 Accepted 6 January 2012 Available online 13 February 2012 Keywords: Computer-aided architectural design Floor plan layout Relational algebras Constraint satisfaction Qualitative and quantitative reasoning abstract Architectural floor plan layout design is what architects and designers do when they conceptually com- bine design units, such as rooms or compartments. At the end of this activity, they deliver precise geo- metric schemas as solutions to particular problems. More research on this topic is needed to develop productive tools. The authors propose orthogonal compartment placement (OCP) as a new approach to this activity. OCP includes a problem formulation and a solution method in which qualitative and quan- titative knowledge are combined. Topological knowledge underlies human spatial reasoning. Computers can adequately perform repetitive topological reasoning. We believe that OCP is the first approach in CAAD to incorporate a full relational algebra to generate floor plan layouts. Based on block algebra (BA) and constraint satisfaction (CS), OCP can generate candidate solutions that correspond to distinct topological options. The analysis of a case study using a prototype tool is included. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Computer-aided architectural design (CAAD) is a broad research field in which new computer-based approaches are proposed to facilitate the work of the architect [1,2]. Lawson considered CAAD to be in an embryonic stage [3]. For that reason, he encouraged the development of tools capable of supporting distinct activities, which could also be combined into larger support systems. Architectural floor plan layout design is a fundamental activity in building architecture in which the designer/architect has to ar- range compartments in a building floor plan layout (dimensioned geometric schema) such that it satisfies specific requirements. This activity has an exploratory and iterative nature and entails a con- sistency maintenance effort to ensure that the requirements are satisfied. Since it typically occurs in the course of preliminary de- sign phase, this activity is particularly important because it affects the subsequent phases of the building lifecycle. In this paper, we present orthogonal compartment placement (OCP). OCP is a problem-solving perspective on the arrangement of compartments based on topological reasoning. OCP concerns the sizing and positioning of compartments. It is a computational approach that receives specifications of particular problems (in- stances) with metric and topological requirements, and it gener- ates feasible layouts that are topologically distinct. OCP is related to other existing perspectives on the arrangement of design units, such as space planning [4–7], space allocation [8,9], floor plan de- sign [10], spatial synthesis [11], sketch design [12], and automated building design [13]. As its main contribution, OCP is the only ap- proach, to the best of the authors’ knowledge, to address the design of floor plan layouts based on a topological complete formalism, such as a relational algebra. We believe that architects can benefit from tools that help them to explore possible ways to specify and solve problems. We seek to (1) model the specification of required characteristics of compart- ments and topological relations and (2) combine quantitative (metric) and qualitative (topological) knowledge to (3) generate solutions. Our work culminates in a prototype tool capable of receiving specifications and generating precise drawings. We present in section two a review of related work, including an introduction to the techniques that are applied in OCP. Afterwards, in section three, we formulate the problem. In section four, we introduce the solving algorithms that were implemented in the prototype. In section five, we analyse a case study from the literature. Finally, section six contains the conclusions and final remarks. 2. Context We begin this section with an overview of related work on the role of artificial intelligence (AI), problem-solving perspective, floor plan design, types of constraints, and other related topics. Next, we introduce the topological relations and provide details about the algebras that support those relations in our work. Finally, we end with some background on constraint satisfaction (CS). 1474-0346/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.aei.2012.01.002 ⇑ Corresponding author. E-mail addresses: fasr@civil.ist.utl.pt, francisco.regateiro@gmail.com (F. Regateiro), joao@civil.ist.utl.pt (J. Bento), jdias@civil.ist.utl.pt (J. Dias). Advanced Engineering Informatics 26 (2012) 361–382 Contents lists available at SciVerse ScienceDirect Advanced Engineering Informatics journal homepage: www.elsevier.com/locate/aei