# American Institute of Mathematical Sciences

March  2018, 8(1): 47-62. doi: 10.3934/naco.2018003

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

 Lobachevsky State University of Nizhni Novgorod, 23, Gagarin Avenue, Nizhni Novgorod, Russia

* Corresponding author: Konstantin Barkalov

Received  December 2016 Revised  September 2017 Published  March 2018

Fund Project: The study was supported by the Russian Science Foundation, project No 16-11-10150.

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.

Citation: Victor Gergel, Konstantin Barkalov, Alexander Sysoyev. Globalizer: A novel supercomputer software system for solving time-consuming global optimization problems. Numerical Algebra, Control & Optimization, 2018, 8 (1) : 47-62. doi: 10.3934/naco.2018003
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##### References:
A Peano curve approximation for the third density level
The computational scheme for obtaining the value of the reduced one-dimensional function $\varphi(y(x))$
The architecture of the Globalizer system
Averaged number of executed iterations of the compared global optimization methods
 $N$ Problem class DIRECT DIRECTl MAGS 4 Simple $>$47282(4) 18983 11953 Hard $>$95708(7) 68754 25263 5 Simple $>$16057(1) 16758 15920 Hard $>$217215(16) $>$269064(4) $>$148342(4)
 $N$ Problem class DIRECT DIRECTl MAGS 4 Simple $>$47282(4) 18983 11953 Hard $>$95708(7) 68754 25263 5 Simple $>$16057(1) 16758 15920 Hard $>$217215(16) $>$269064(4) $>$148342(4)
Averaged numbers of iterations executed by GPMAGS for solving the test optimization problems
 p $N=4$ $N=5$ Simple Hard Simple Hard Ⅰ Serial trial computations 1 11953 25263 15920 $>$148342 (4) Ⅱ Parallel computations 2 4762 11178 13378 109075 on CPU 4 2372 5972 5203 51868 8 1393 2874 3773 51868 Ⅲ Parallel computations 60 171 393 382 3452 on Xeon Phi 120 85 182 249 1306 240 42 103 97 381
 p $N=4$ $N=5$ Simple Hard Simple Hard Ⅰ Serial trial computations 1 11953 25263 15920 $>$148342 (4) Ⅱ Parallel computations 2 4762 11178 13378 109075 on CPU 4 2372 5972 5203 51868 8 1393 2874 3773 51868 Ⅲ Parallel computations 60 171 393 382 3452 on Xeon Phi 120 85 182 249 1306 240 42 103 97 381
Speedup of parallel computations executed by GPMAGS
 p $N=4$ $N=5$ Simple Hard Simple Hard Ⅰ Serial trial computations. 1 11953 25263 15920 > 148342 (4) Average number of iterations Ⅱ 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 Ⅲ 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
 p $N=4$ $N=5$ Simple Hard Simple Hard Ⅰ Serial trial computations. 1 11953 25263 15920 > 148342 (4) Average number of iterations Ⅱ 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 Ⅲ 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
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