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

Victor Gergel; Konstantin Barkalov; Alexander Sysoyev

doi:10.3934/naco.2018003

Article Contents

2018, Volume 8, Issue 1: 47-62. Doi: 10.3934/naco.2018003

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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
* Corresponding author: Konstantin Barkalov

Received: December 2016

Revised: September 2017

Published: March 2018

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

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Abstract

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.

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

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

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

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Figure 3. The architecture of the Globalizer system

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Table 1. 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)

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Table 2. Averaged numbers of iterations executed by GPMAGS for solving the test optimization problems

		p	$N=4$		$N=5$
		p	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

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Table 3. Speedup of parallel computations executed by GPMAGS

		p	$N=4$		$N=5$
		p	Simple	Hard	Simple	Hard
Ⅰ	Serial trial computations.	1	11953	25263	15920	> 148342 (4)
Ⅰ	Average number of iterations	1	11953	25263	15920	> 148342 (4)
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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