Synthesis and Optimization of Small Rectangular Floor Plans

This paper describes a set of algorithms for the production of a certain class of architectural plans. Each plan is made up from rectangular rooms arranged within a simple rectangular overall plan shape. The effective upper limit on the number of component rectangles which may presently be treated is eight. Given certain specified requirements as to which rooms shall be adjacent, the algorithms produce exhaustively all topologically distinct arrangements of rooms in which those requirements are satisfied. Constraints on the dimensions and areas of each room may then be introduced. Several approaches for the dimensioning of the rectangular arrangements have been explored. In certain cases, appropriate dimensions may be found by solving simultaneous linear equations. Under special conditions linear programming may be used to find that assignment of dimensions to rooms which gives least cost—where cost is for example calculated as a function of the enclosing surfaces. A more general solution may be found with the use of nonlinear programming methods. One further possibility, where dimensions are allowed to vary only by modular increments, is for all feasible dimensional solutions to be enumerated exhaustively.