A SIMPLEX-BASED APPROACH TO A CLASS OF PROBLEMS ASSOCIATED WITH TRUSS DESIGN

Abstract

Determination of the cross-sectional areas of the members of a structural truss in order to minimize structural weight, subject to performance constraints, gives rise to a discrete non-linear mathematical programming problem. A Lagrangian scheme for the solution of this type of problem is described and an effective simplex-based method developed for solving the Lagrangian dual subproblems that thus arise. Structure inherent in the problem permits the use of simplex tableaux which are very much reduced in size, thereby enabling subproblems to be solved quickly. Moreover, the ideas developed here have potential for more general application.

Keywords:

• Discrete variables
• duality
• Lagrangian relaxation
• structural optimization
• simplex