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Globalizer: A novel supercomputer software system for solving time-consuming global optimization problems

  • * Corresponding author: Konstantin Barkalov

    * Corresponding author: Konstantin Barkalov 
The study was supported by the Russian Science Foundation, project No 16-11-10150.
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  • In this paper, we describe the Globalizer software system for solving the global optimization problems. The system is designed to maximize the use of computational potential of the modern high-performance computational systems in order to solve the most time-consuming optimization problems. The highly parallel computations are facilitated using various distinctive computational schemes: processing several optimization iterations simultaneously, reducing multidimensional optimization problems using multiple Peano space-filling curves, and multi-stage computing based on the nested block reduction schemes. These novelties provide for the use of the supercomputer system capabilities with shared and distributed memory and with large numbers of processors to solve the global optimization problems efficiently.

    Mathematics Subject Classification: Primary: 90C26; Secondary: 65Y05.

    Citation:

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  • Figure 1.  A Peano curve approximation for the third density level

    Figure 2.  The computational scheme for obtaining the value of the reduced one-dimensional function $\varphi(y(x))$

    Figure 3.  The architecture of the Globalizer system

    Table 1.  Averaged number of executed iterations of the compared global optimization methods

    $N$Problem classDIRECTDIRECTlMAGS
    4 Simple$>$47282(4)1898311953
    Hard $>$95708(7)6875425263
    5 Simple $>$16057(1)1675815920
    Hard $>$217215(16) $>$269064(4) $>$148342(4)
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    Table 2.  Averaged numbers of iterations executed by GPMAGS for solving the test optimization problems

    p$N=4$$N=5$
    Simple Hard Simple Hard
    Serial trial computations1119532526315920 $>$148342 (4)
    Parallel computations247621117813378109075
    on CPU423725972520351868
    813932874377351868
    Parallel computations601713933823452
    on Xeon Phi120851822491306
    2404210397381
     | Show Table
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    Table 3.  Speedup of parallel computations executed by GPMAGS

    p $N=4$ $N=5$
    Simple Hard Simple Hard
    Serial trial computations. 1 11953 25263 15920 > 148342 (4)
    Average number of iterations
    Parallel computations 2 2.52 2.32 1.21 1.41
    of CPU. 4 5.05 4.24 3.13 2.92
    Speedup 8 8.68 8.88 4.24 6.66
    Parallel computations 60 8.18 7.37 9.99 6.66
    of Xeon Phi. 120 16.316 15.815 15.215 17.317
    Speedup 240 33.133 27.827 38.838 59.359
     | Show Table
    DownLoad: CSV
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