Building Problem

A hypothetic building design problem in optimization with constraints proposed by Bhatti (2000, pp. 3-5). To save energy costs for heating and cooling, an architect wishes to design a cuboidal building that is partially underground. Let n be the number of stories (which therefore must be a positive integer), d the depth of the building below ground, h the height of the building above ground, l the length of the building, and w<l the width of the building. The floor space needed is at least 20000 m^2, the lot size requires that w,l<50 m, the building shape is specified so that l/w=phi (the golden ratio, approximately 1.618), each story is 3.5 m high, heating and cooling costs are estimated at $100/m^2 for exposed surface of the building, and it has been specified that annual climate control costs should not exceed $225000. The problem then asks to minimize the volume that must be excavated to build the building.

This is equivalent to minimizing the function


subject to the constraints


There is a fairly large region of parameter spacing giving near-optimal solution (and all well within the specified precision of the problem), with f minimized near d=81.028397 m, h=13.471603 m, w=21.396330 m, (corresponding to n=27 and l=34.619990), giving f=60021.0 m^3.

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Bhatti, M. A. Practical Optimization Methods with Mathematica Applications. New York: Springer-Verlag, 2000.

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Building Problem

Cite this as:

Weisstein, Eric W. "Building Problem." From MathWorld--A Wolfram Web Resource.

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