Nonlinear Integer and Discrete Programming for Topological Decision Making in Engineering Design

Abstract

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.