A Sequential Optimization Algorithm Using Logarithmic Barriers: Applications to Structural Optimization

Abstract

A sequential approximation algorithm is presented here that is particularly suited for problems in engineering design and structural optimization, where the number of variables is very large and function and sensitivity evaluations are computationally expensive. A sequence of sub-problems are generated using a linear approximation for the objective function and setting move limits on the variables using a barrier method. These sub-problems are strictly convex and computation per iteration is significantly reduced by not solving the sub-problems exactly. Instead a few Newton-steps are taken for each sub-problem generated. A criterion, for setting the move limit, is described that reduces or eliminates step size reduction during line search. The method was found to perform well for unconstrained and linearly constrained optimization problems. It is particularly suitable for application to design of optimal shape and topology of structures by minimizing their compliance since it requires very few function evaluations, does not require the hessian of the objective function and evaluates its gradient only once for every sub-problem generated. [S1050-0472(00)01603-2]