Integer and combinatorial optimization
Integer and combinatorial optimization
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
Robust Truss Topology Design via Semidefinite Programming
SIAM Journal on Optimization
Optimal Design of Truss Structures by Logic-Based Branch and Cut
Operations Research
Design of planar articulated mechanisms using branch and bound
Mathematical Programming: Series A and B
Global optimization of truss topology with discrete bar areas--Part I: theory of relaxed problems
Computational Optimization and Applications
Global optimization of truss topology with discrete bar areas--Part I: theory of relaxed problems
Computational Optimization and Applications
New branch and bound approaches for truss topology design with discrete areas
AMERICAN-MATH'10 Proceedings of the 2010 American conference on Applied mathematics
A hybrid cooperative search algorithm for constrained optimization
Structural and Multidisciplinary Optimization
Global optima for the Zhou---Rozvany problem
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
A new Branch and Bound method for a discrete truss topology design problem
Computational Optimization and Applications
Design and optimization of roof trusses using morphological indicators
Advances in Engineering Software
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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 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.