05674552

j

05674552 Achtziger, Wolfgang Stolpe, Mathias Global optimization of truss topology with discrete bar areas. II: Implementation and numerical results. Comput. Optim. Appl. 44, No. 2, 315-341 (2009). 2009 Springer, Norwell, MA EN truss topology optimization global optimization branch-and-bound Zbl 1181.90202

doi:10.1007/s10589-007-9152-7

Summary: A classical problem within the field of structural optimization is to find the stiffest truss design subject to a given external static load and a bound on the total volume. The design variables describe the cross sectional areas of the bars. This class of problems is well-studied for continuous bar areas. We consider here the difficult situation that the truss must be built from pre-produced bars with given areas. This paper together with Part I [ibid. 40, No.~2, 247--280 (2008; Zbl 1181.90202)] proposes an algorithmic framework for the calculation of a global optimizer of the underlying non-convex mixed integer design problem. In this paper we use the theory developed in Part I to design a convergent nonlinear branch-and-bound method tailored to solve large-scale instances of the original discrete problem. The problem formulation and the needed theoretical results from Part I are repeated such that this paper is self-contained. We focus on the implementation details but also establish finite convergence of the branch-and-bound method. The algorithm is based on solving a sequence of continuous non-convex relaxations which can be formulated as quadratic programs according to the theory in Part I. The quadratic programs to be treated within the branch-and-bound search all have the same feasible set and differ from each other only in the objective function. This is one reason for making the resulting branch-and-bound method very efficient. The paper closes with several large-scale numerical examples. These examples are, to the knowledge of the authors, by far the largest discrete topology design problems solved by means of global optimization.