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Efficient Serial and Parallel Coordinate Descent Methods for Huge-Scale Truss Topology Design

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Operations Research Proceedings 2011

Part of the book series: Operations Research Proceedings ((ORP))


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.

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  1. Ben-Tal, A., Nemirovski, A.: Robust truss topology design via semidefinite programming, SIAM Journal on Optimization 7, 991–1016 (1997)

    Article  Google Scholar 

  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 

  4. Li, Y., Osher, S.: Coordinate descent optimization for l1 minimization with application to compressed sensing; a greedy algorithm, Inverse Problems and Imaging 3, 487–503 (2009)

    Article  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 

  9. Rozvany, G., Bendsøe, M.P., Kirsch, U.: Layout optimization of structures. Applied Mechanics Reviews, 48 (2), 41–119 (1995)

    Article  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 

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Correspondence to Peter Richtárik .

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Richtárik, P., Takáč, M. (2012). Efficient Serial and Parallel Coordinate Descent Methods for Huge-Scale Truss Topology Design. In: Klatte, D., Lüthi, HJ., Schmedders, K. (eds) Operations Research Proceedings 2011. Operations Research Proceedings. Springer, Berlin, Heidelberg.

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