Abstract
This paper describes several massively parallel implementations for a global search algorithm DIRECT. Two parallel schemes take different approaches to address DIRECT’s design challenges imposed by memory requirements and data dependency. Three design aspects in topology, data structures, and task allocation are compared in detail. The goal is to analytically investigate the strengths and weaknesses of these parallel schemes, identify several key sources of inefficiency, and experimentally evaluate a number of improvements in the latest parallel DIRECT implementation. The performance studies demonstrate improved data structure efficiency and load balancing on a 2200 processor cluster.
Similar content being viewed by others
References
Atkinson, M.D., Sack, J.-R., Santoro, N., Strothotte, T.: Min-max heap and generalized priority queues. Commun. ACM 29(10), 996–1000 (1986)
Baker, C.A., Watson, L.T., Grossman, B., Haftka, R.T., Mason, W.H.: Parallel global aircraft configuration design space exploration. In: Tentner, A. (ed.) High Performance Computing Symposium 2000, Soc. for Computer Simulation Internat, San Diego, CA, pp. 101–106 (2000)
Bartholomew-Biggs, M.C., Parkhurst, S.C., Wilson, S.P.: Global optimization approaches to an aircraft routing problem. EUR J. Oper. Res. 146(2), 417–431 (2003)
Chandra, R., Dagum, L., Kohr, D., Maydan, D., McDonald, J., Menon, R.: Parallel Programming in OpenMP. Morgan Kaufmann, San Francisco (2001)
Cray Research, Inc.: SHMEM Technical Note for C, SG-2516 2.3 (October 1994)
Esposito, W.R., Floudas, C.A.: Global optimization in parameter estimation of nonlinear algebraic models via the Error-In-Variables approach. Ind. Eng. Chem. Res. 37, 1841–1858 (1998)
Gablonsky, J.M.: Modifications of the DIRECT algorithm. PhD thesis, Department of Mathematics, North Carolina State University, Raleigh, NC (2001)
Gau, C., Stadtherr, M.A.: Nonlinear parameter estimation using interval analysis. In: AIchE Symposium, vol. 94, no. 320, pp. 445–450 (1999)
Grama, A., Gupta, A., Karypis, G., Kumar, V.: Introduction to Parallel Computing, 2nd edn. Pearson Education, Upper Saddle River (2003)
Gropp, W., Lusk, E., Thakur, R.: Using MPI-2: Advanced Features of the Message-Passing Interface. MIT Press, Cambridge (1999)
He, J., Verstak, A., Watson, L.T., Rappaport, T.S., Anderson, C.R., Ramakrishnan, N., Shaffer, C.A., Tranter, W.H., Bae, K., Jiang, J.: Global optimization of transmitter placement in wireless communication systems. In: Tentner, A. (ed.) Proc. High Performance Computing Symposium 2002, Soc. for Modeling and Simulation International, San Diego, CA, pp. 328–333 (2002)
He, J., Watson, L.T., Ramakrishnan, N., Shaffer, C.A., Verstak, A., Jiang, J., Bae, K., Tranter, W.H.: Dynamic data structures for a direct search algorithm. Comput. Optim. Appl. 23(1), 5–25 (2002)
He, J., Sosonkina, M., Shaffer, C.A., Tyson, J.J., Watson, L.T., Zwolak, J.W.: A hierarchical parallel scheme for global parameter estimation in systems biology. In: Proc. 18th Internat. Parallel & Distributed Processing Symp., CD-ROM, IEEE Computer Soc., Los Alamitos, CA (2004)
He, J., Sosonkina, M., Watson, L.T., Verstak, A., Zwolak, J.W.: Data-distributed parallelism with dynamic task allocation for a global search algorithm. In: Parashar, M., Watson, L. (eds.) Proc. High Performance Computing Symposium 2005, Soc. for Modeling and Simulation Internat., San Diego, CA, pp. 164–172 (2005)
Jones, D.R.: The DIRECT global optimization algorithm. In: Encyclopedia of Optimization, vol. 1, pp. 431–440. Kluwer Academic, Boston (2001)
Jones, D.R., Perttunen, C.D., Stuckman, B.E.: Lipschitzian optimization without the Lipschitz constant. J. Optim. Theory Appl. 79(1), 157–181 (1993)
Moles, C.G., Mendes, P., Banga, J.R.: Parameter estimation in biochemical pathways: a comparison of global optimization methods. Genome Res. 13, 2467–2474 (2003)
Nieplocha, J., Carpenter, B.: ARMCI: a portable remote memory copy library for distributed array libraries and compiler run-time systems. In: 3rd Workshop on Runtime Systems for Parallel Programming (RTSPP) of International Parallel Processing Symposium, IPPS/SDP’99, CDROM (1999)
Nieplocha, J., Harrison, R.J., Littlefield, R.J.: Global arrays: a nonuniform memory access programming model for high-performance computers. J. Supercomput. 10(2), 169–189 (1996)
Panning, T.D., Watson, L.T., Allen, N.A., Chen, K.C., Shaffer, C.A., Tyson, J.J.: Deterministic global parameter estimation for a model of the budding yeast cell cycle, J. Glob. Optim. (to appear)
Parzyszek, K., Nieplocha, J., Kendall, R.A.: A generalized portable SHMEM library for high performance computing. In: 12th IASTED International Conference Parallel and Distributed Computing and Systems (PDCS), pp. 401–406 (2000)
Watson, L.T., Baker, C.A.: A fully-distributed parallel global search algorithm. Eng. Comput. 18(1/2), 155–169 (2001)
Zhou, J., Deng, X., Dymond, P.: A 2-D parallel convex hull algorithm with optimal communication phases. Parallel Comput. 27(3), 243–255 (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
He, J., Verstak, A., Watson, L.T. et al. Design and implementation of a massively parallel version of DIRECT. Comput Optim Appl 40, 217–245 (2008). https://doi.org/10.1007/s10589-007-9092-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10589-007-9092-2