Optimization with Variable Sets of Constraints and anApplication to Truss Design
Computational Optimization and Applications
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
Optimal Design of Truss Structures by Logic-Based Branch and Cut
Operations Research
Global optimization of truss topology with discrete bar areas--Part I: theory of relaxed problems
Computational Optimization and Applications
Free Material Optimization with Fundamental Eigenfrequency Constraints
SIAM Journal on Optimization
Computational Optimization and Applications
Optimization Methods & Software - The International Conference on Engineering Optimization (EngOpt 2008)
Operations Research Letters
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Our paper considers a classic problem in the field of Truss Topology Design, the goal of which is to determine the stiffest truss, under a given load, with a bound on the total volume and discrete requirements in the cross-sectional areas of the bars. To solve this problem we propose a new two-stage Branch and Bound algorithm.In the first stage we perform a Branch and Bound algorithm on the nodes of the structure. This is based on the following dichotomy study: either a node is in the final structure or not. In the second stage, a Branch and Bound on the bar areas is conducted. The existence or otherwise of a node in this structure is ensured by adding constraints on the cross-sectional areas of its incident bars. In practice, for reasons of stability, free bars linked at free nodes should be avoided. Therefore, if a node exists in the structure, then there must be at least two incident bars on it, unless it is a supported node. Thus, a new constraint is added, which lower bounds the sum of the cross-sectional areas of bars incident to the node. Otherwise, if a free node does not belong to the final structure, then all the bar area variables corresponding to bars incident to this node may be set to zero. These constraints are added during the first stage and lead to a tight model. We report the computational experiments conducted to test the effectiveness of this two-stage approach, enhanced by the rule to prevent free bars, as compared to a classical Branch and Bound algorithm, where branching is only performed on the bar areas.