Solution of mixed-discrete structural optimization problems with a new sequential linearization algorithm

Abstract

In practical structural optimization problems it is often desirable to obtain solutions where all or some of the design variables take their values from a given set of discrete values. As structural optimization problems typically include large models that are expensive to compute, one of the major demands for optimization algorithms is that the number of structural evaluations (i.e. calculations of deformations and stresses) that are needed during the iterative optimization process is as small as possible. In this article an algorithm is developed that meets this requirement, while finding global solutions for the mixed-discrete problem. The method is based on a combination of the well established branch and bound method with a sequential linearization procedure. Branch and bound is applied within a subproblem that is based on a linearization of the original problem. After a brief literature survey the method is described, followed by some comments on its algorithmic implementation. The algorithm is then applied to several structural optimization problems of different type and size to demonstrate its efficiency. All results are compared with solutions obtained by branch and bound.