The use of integer, discrete, and zero-one design variables to represent topological design decisions is presented. A general purpose algorithm for solving nonlinear problems involving material assembly and other topological decisions is described. The algorithm couples a branch and bound approach with an exterior penalty function and a quadratic programming method. Examples concerning the design of a support beam and a structural truss are presented with decisions involving material selection, assembly, and crossectional geometry included in the problem formulation.

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