Economics of Engineering Design under Interval (and Fuzzy) Uncertainty: Case Study of Building Design

One of the main objectives of engineering design is to flnd a design that is the cheapest among all designs that satisfy given con- straints. Most of the constraints must be satisfled under all possible val- ues within certain ranges. Checking all possible combinations of values is often very time-consuming. In this paper, we propose a faster algorithm for checking such constraints. 1 Formulation of the Problem General problem of engineering design. In engineering design, e.g., when de- signing a building, the problem is usually to flnd the cheapest design among all designs that satisfy given constraints. This is a problem behind the usual bidding process when the constraints (requirements) are announced beforehand, and the contract goes to the lowest bidder among those whose design satisfles the constraints. Checking constraints is often di-cult. Most design constraints require that some condition is satisfled for all possible values of parameters within given ranges. For example, a levee must withstand all Category 4 hurricanes, i.e., all the winds within a certain range. A building must remain stable under all possible distribution of loads in difierent rooms on difierent ∞oors. There are many possible distributions, so checking all of them is not practi- cally possible. It is therefore desirable to come up with e-cient algorithms for checking such constraints. General mathematical description of the problem. Let us denote the number of parameters by n, the i-th parameter by xi, and the range of possible values of the i-th parameter by xi = (xi;xi). For example, for the building stability, xi is the load in the i-th room. The desired constraint can be described as a restriction on some character- istics depending on these parameters xi: e.g., that at every point, the strain does not exceed the critical value. Each constraint of this type can be described as f(x1;:::;xn) • f0, where the (known) function f(x1;:::;xn) describes the