Optimum seismic zoning for multiple types of structures

We consider zoning for the design criterion that minimizes the expected present value of the total cost, including the initial cost as well as losses due to damage and failure. The problem consists of the following: Given the number of zones, their boundaries and design coefficients must be such that they minimize the expected present value of all structures built in the region. We will refer to solutions in one or more dimensions, depending on the number of the types of structures built in the region to be zoned. Two methods are proposed to solve the problems. The first method is based on the different combinations performed in order to attain optimum zoning. The second method uses an analogy to the evolution of biological systems. The work ends by applying the methods developed to a region of known seismicity.