Discrete Lagrangian method for optimal design of truss structures

This paper studies the discrete sizing optimization of truss structures employing the discrete Lagrangian method (DLM). Theory of the DLM is briefly review first. A revised searching algorithm is proposed for weight minimization of truss structures subject to stress, buckling stress, and displacement constraints. Parameters that influence convergent speed and solution quality of the method are investigated and discussed. The feasibility of the DLM is validated by three design examples. The results from comparative studies of the DLM against other discrete optimization algorithms for the representative structural design problems are reported to show the solution quality of the DLM. It is shown that the DLM often finds good quality solutions by using appropriate weighting for the objective function and the changing speed for the Lagrange multipliers.