Efficient Serial and Parallel Coordinate Descent Methods for Huge-Scale Truss Topology Design
In this work we propose solving huge-scale instances of the truss topology design problem with coordinate descent methods. We develop four efficient codes: serial and parallel implementations of randomized and greedy rules for the selection of the variable(s) (potential bar(s)) to be updated in the next iteration. Both serial methods enjoy an O(n/k) iteration complexity guarantee, where n is the number of potential bars and k the iteration counter. Our parallel implementations, written in CUDA and running on a graphical processing unit (GPU), are capable of speedups of up to two orders of magnitude when compared to their serial counterparts. Numerical experiments were performed on instances with up to 30 million potential bars.
KeywordsGraphical Processing Unit Graphical Processing Unit Implementation Coordinate Descent Method Graphical Processing Unit Device Ground Structure Approach
Unable to display preview. Download preview PDF.
- 2.GilbertM., Tyas A.: Layout optimization of large-scale pin-jointed frames, Engineering Computations 20 (8), 1044–1064 (2003)Google Scholar
- 3.Koˇcvara, M.: Truss topology design with integer variables made easy, Opt. Online (2010)Google Scholar
- 5.Nemirovski, A., Ben-Tal, A.: Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications. SIAM, Philadelphia, PA, USA (2001)Google Scholar
- 6.Nesterov, Yu.: Gradient methods for minimizing composite objective function. CORE Discussion Paper #2007/76 (2007)Google Scholar
- 7.Richt´arik, P.: Simultaneously solving seven optimization problems in relative scale. Optimization Online (2009)Google Scholar
- 8.Richt´arik, P., Tak´aˇc, M.: Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function. Technical Report ERGO 11-011 (2011)Google Scholar
- 10.Sokół, T.: Topology optimization of large-scale trusses using ground structure approach with selective subsets of active bars. Extended Abstract, Computer Methods in Mechanics (2011)Google Scholar