Abstract
The Chokuhotai-Bunkatsu-Zu, in Japanese, mean figures which represent how to partition a rectangular prism into some small rectangular prisms. So this is a dimensionless representation model of a building which forms of outside view and inside rooms are both rectangular prisms. It is possible to obtain the optimum outline plan of such building by means of dimension allocation for the C. B. Z. which is in match with initial planning conditions. But this dimensioning process is formulated for nonlinear nonconvex programing problem in terms of the minimization of a nonlinear nonconvex objective function which express construction costs or total floor area as function of dimensions of the C. B. Z. subject to such constraints as upper or lower limits of lengths, widths, heights, areas, of individual rooms and the outside view. At first, the multiplier method is shown applicable to such nonlinear nonconvex programing problem with R. T. Rockafellar's method. Next, dimensioning procedure for the C. B. Z. is encoded on the basis of it with FORTRAN IV. The program shown in Figure-2 has 426 statements. An example of the optimum outline plan which is generated under constraints as Figure-3 is shown in Figure-4. Executive c. p. u. time is 29.8min. with NEAC-ACOS system 900 computer. As shown in Figure-4, critical conditions which decide the optimum are found out at the same time from initial planning conditions. This program is so flexible that it is also applicable to produce the optimum outline plan as Figure-5 which has convex or concave parts by use of dummy rooms, walls or floors.
