Comparison of Optimality Criteria Algorithms for Minimum Weight Design of Structures

This paper presents a comparison of frequently used optimization algorithms based on optimality criteria to design a minimum weight structure. After summarizing the different methods, the relationship between the various algorithms is shown. They differ only in the degree of approximations made in formulating the recurrence relations to modify the design variables and to evaluate the Lagrange multipliers. A new iterative scheme, similar to Newton-Raphson, is also presented, with the equations written in such a form that it is not necessary to select the initial design vector of the unknown Lagrange multipliers. It is shown that with this scheme a minimum weight design can be obtained with a smaller number of analyses of the structure than with previously proposed methods.