# 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
##### References:

show all references

##### 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
 [1] Saeed Assani, Muhammad Salman Mansoor, Faisal Asghar, Yongjun Li, Feng Yang. Efficiency, RTS, and marginal returns from salary on the performance of the NBA players: A parallel DEA network with shared inputs. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021053 [2] Khosro Sayevand, Valeyollah Moradi. A robust computational framework for analyzing fractional dynamical systems. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021022 [3] Suzete Maria Afonso, Vanessa Ramos, Jaqueline Siqueira. Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021045 [4] Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1717-1746. doi: 10.3934/dcdss.2020451 [5] Longxiang Fang, Narayanaswamy Balakrishnan, Wenyu Huang. Stochastic comparisons of parallel systems with scale proportional hazards components equipped with starting devices. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021004 [6] Maoding Zhen, Binlin Zhang, Vicenţiu D. Rădulescu. Normalized solutions for nonlinear coupled fractional systems: Low and high perturbations in the attractive case. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2653-2676. doi: 10.3934/dcds.2020379 [7] John Leventides, Costas Poulios, Georgios Alkis Tsiatsios, Maria Livada, Stavros Tsipras, Konstantinos Lefcaditis, Panagiota Sargenti, Aleka Sargenti. Systems theory and analysis of the implementation of non pharmaceutical policies for the mitigation of the COVID-19 pandemic. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021004 [8] Juliang Zhang, Jian Chen. Information sharing in a make-to-stock supply chain. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1169-1189. doi: 10.3934/jimo.2014.10.1169 [9] Takeshi Saito, Kazuyuki Yagasaki. Chebyshev spectral methods for computing center manifolds. Journal of Computational Dynamics, 2021  doi: 10.3934/jcd.2021008 [10] Vandana Sharma. Global existence and uniform estimates of solutions to reaction diffusion systems with mass transport type boundary conditions. Communications on Pure & Applied Analysis, 2021, 20 (3) : 955-974. doi: 10.3934/cpaa.2021001 [11] Yuzhou Tian, Yulin Zhao. Global phase portraits and bifurcation diagrams for reversible equivariant Hamiltonian systems of linear plus quartic homogeneous polynomials. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2941-2956. doi: 10.3934/dcdsb.2020214 [12] Braxton Osting, Jérôme Darbon, Stanley Osher. Statistical ranking using the $l^{1}$-norm on graphs. Inverse Problems & Imaging, 2013, 7 (3) : 907-926. doi: 10.3934/ipi.2013.7.907 [13] Raghda A. M. Attia, Dumitru Baleanu, Dianchen Lu, Mostafa M. A. Khater, El-Sayed Ahmed. Computational and numerical simulations for the deoxyribonucleic acid (DNA) model. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021018 [14] Vieri Benci, Marco Cococcioni. The algorithmic numbers in non-archimedean numerical computing environments. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1673-1692. doi: 10.3934/dcdss.2020449 [15] Enkhbat Rentsen, N. Tungalag, J. Enkhbayar, O. Battogtokh, L. Enkhtuvshin. Application of survival theory in Mining industry. Numerical Algebra, Control & Optimization, 2021, 11 (3) : 443-448. doi: 10.3934/naco.2020036 [16] Mikhail Gilman, Semyon Tsynkov. Statistical characterization of scattering delay in synthetic aperture radar imaging. Inverse Problems & Imaging, 2020, 14 (3) : 511-533. doi: 10.3934/ipi.2020024 [17] Changjun Yu, Lei Yuan, Shuxuan Su. A new gradient computational formula for optimal control problems with time-delay. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021076 [18] Guillaume Bal, Wenjia Jing. Homogenization and corrector theory for linear transport in random media. Discrete & Continuous Dynamical Systems, 2010, 28 (4) : 1311-1343. doi: 10.3934/dcds.2010.28.1311 [19] Fioralba Cakoni, Shixu Meng, Jingni Xiao. A note on transmission eigenvalues in electromagnetic scattering theory. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021025 [20] Vassili Gelfreich, Carles Simó. High-precision computations of divergent asymptotic series and homoclinic phenomena. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 511-536. doi: 10.3934/dcdsb.2008.10.511

Impact Factor:

## Metrics

• HTML views (485)
• Cited by (5)

• on AIMS