Designing with Machines: solving architectural layout planning problems by the use of a constraint programming language and scheduling algorithms
T. Lömker · Cumulative Index of Computer Aided Architectural Design · 2006
In 1845 Edgar Allan Poe wrote the poem “The Raven”, an act full of poetry, love, passion, mourning, melancholia and death. In his essay “The Theory of Composition” which was published in 1846 Poe proved that the poem is based on an accurate mathematical description. Not only in literature are structures present that are based on mathematics. In the work of famous musicians, artists or architects like Bach, Escher or Palladio it is evident that the beauty and clarity of their work as well as its traceability has often been reached through the use of intrinsic mathematic coherences. If suchlike structures could be described within architecture, their mathematical abstraction could supplement “The Theory of Composition” of a building. This research focuses on an approach to describe principles in architectural layout planning in the form of mathematical rules that will be executed by the use of a computer. Provided that “designi is in principle a combinatorial problem, i.e. a constraint-based search for an overall optimal solution of a design problem, an exemplary method will be described to solve problems in architectural layout planning. Two problem domains will be examined: the design of new buildings, as well as the revitalization of existing buildings. Mathematical and syntactical difficulties that arise from the attempt to extract rules that relate to the process of building design will be pointed out. To avoid conflicts relating to theoretical subtleness a customary approach has been chosen in this work which is adopted from Operations Research. In this approach design is a synonym for planning, which could be described as a systematic and methodical course of action for the analysis and solution of current or future problems. The planning task is defined as an analysis of a problem with the aim to prepare optimal decisions by the use of mathematical methods. The decision problem of a planning task is represented by an optimization model and the application of an efficient algorithm to aid finding one or more solutions to the problem. The basic principle underlying the approach presented herein is the understanding of design in terms of searching for solutions that fulfill specific criteria. This search will be executed by the use of a constraint programming language, which refers to mathematical as well as to integer and mixed integer programming. Examples of architectural layout problems will be presented that can be solved by the use of this programming paradigm. In addition to this, a second programming approach resulting from the domain of resource-allocation has been followed in this research. It will be demonstrated that it is as well possible, to aid architectural layout planning by the use of scheduling algorithms.