Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Robust Truss Topology Design via Semidefinite Programming
SIAM Journal on Optimization
Global optimization of truss topology with discrete bar areas--Part I: theory of relaxed problems
Computational Optimization and Applications
Computational Optimization and Applications
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One of the classical problems in the structural optimization field is to find the stiffest truss, under a given load and with a bound on the total volume. This is a well-studied problem for continuous cross sectional areas. Generally, the optimal solutions obtained for this problem contain bars with many different cross sectional areas. However, in real life, only a finite set of possible values for those cross sectional areas can be considered. We propose a Semidefinite Programming with discrete variables for this problem. In order to solve the problem we derive and compare two exact algorithms. The first one is a branch and bound algorithm where the branching is done only on the bar-areas. The second algorithm has two stages. In the first stage a branch and bound on the nodes of the structure is performed. In the second stage, considering the nodes in the structure from the first stage, a branch and bound algorithm on the bar-areas is performed.