On Methods of Controlling Optimization Software Packages with the Application of Parallel Computing
The paper is dedicated to the analysis of methods and algorithms of controlling computational process of solving complex problems with the use of multiprocessor and/or multicore computer systems. We have developed an automatic and dialogue systems of control of unconstrained optimization process, wh...
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Інститут кібернетики ім. В.М. Глушкова НАН України
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| Zitieren: | On Methods of Controlling Optimization Software Packages with the Application of Parallel Computing / K.R. Aidazade, S.Z. Guliyev // Математичне та комп'ютерне моделювання. Серія: Фізико-математичні науки: зб. наук. пр. — Кам’янець-Подільський: Кам'янець-Подільськ. нац. ун-т, 2017. — Вип. 15. — С. 5-9. — Бібліогр.: 5 назв. — англ. |
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irk-123456789-1339222018-06-11T03:03:00Z On Methods of Controlling Optimization Software Packages with the Application of Parallel Computing Aidazade, K.R. Guliyev, S.Z. The paper is dedicated to the analysis of methods and algorithms of controlling computational process of solving complex problems with the use of multiprocessor and/or multicore computer systems. We have developed an automatic and dialogue systems of control of unconstrained optimization process, which have a graphical user interface. Работа посвящена анализу методов, алгоритмов управления вычислительным процессом решения сложных задач с использованием многопроцессорных (многоядерных) компьютерных систем. Разработана автоматическая и диалоговая системы управления процессом безусловной оптимизации, имеющие графический пользовательский интерфейс. 2017 Article On Methods of Controlling Optimization Software Packages with the Application of Parallel Computing / K.R. Aidazade, S.Z. Guliyev // Математичне та комп'ютерне моделювання. Серія: Фізико-математичні науки: зб. наук. пр. — Кам’янець-Подільський: Кам'янець-Подільськ. нац. ун-т, 2017. — Вип. 15. — С. 5-9. — Бібліогр.: 5 назв. — англ. 2308-5878 http://dspace.nbuv.gov.ua/handle/123456789/133922 519.6 en Математичне та комп'ютерне моделювання. Серія: Фізико-математичні науки Інститут кібернетики ім. В.М. Глушкова НАН України |
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The paper is dedicated to the analysis of methods and algorithms of controlling computational process of solving complex problems with the use of multiprocessor and/or multicore computer systems. We have developed an automatic and dialogue systems of control of unconstrained optimization process, which have a graphical user interface. |
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Article |
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Aidazade, K.R. Guliyev, S.Z. |
| spellingShingle |
Aidazade, K.R. Guliyev, S.Z. On Methods of Controlling Optimization Software Packages with the Application of Parallel Computing Математичне та комп'ютерне моделювання. Серія: Фізико-математичні науки |
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Aidazade, K.R. Guliyev, S.Z. |
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Aidazade, K.R. |
| title |
On Methods of Controlling Optimization Software Packages with the Application of Parallel Computing |
| title_short |
On Methods of Controlling Optimization Software Packages with the Application of Parallel Computing |
| title_full |
On Methods of Controlling Optimization Software Packages with the Application of Parallel Computing |
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On Methods of Controlling Optimization Software Packages with the Application of Parallel Computing |
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On Methods of Controlling Optimization Software Packages with the Application of Parallel Computing |
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on methods of controlling optimization software packages with the application of parallel computing |
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Інститут кібернетики ім. В.М. Глушкова НАН України |
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2017 |
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http://dspace.nbuv.gov.ua/handle/123456789/133922 |
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On Methods of Controlling Optimization Software Packages with the Application of Parallel Computing / K.R. Aidazade, S.Z. Guliyev // Математичне та комп'ютерне моделювання. Серія: Фізико-математичні науки: зб. наук. пр. — Кам’янець-Подільський: Кам'янець-Подільськ. нац. ун-т, 2017. — Вип. 15. — С. 5-9. — Бібліогр.: 5 назв. — англ. |
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Математичне та комп'ютерне моделювання. Серія: Фізико-математичні науки |
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Серія: Фізико-математичні науки. Випуск 15
5
UDC 519.6
K. R. Aidazade*, **, Doctor of Phys. and Mathem. Sciences, Professor,
Corresponding member of the Azerbaijan National Academy of Sciences
(ANAS),
S. Z. Guliyev**, ***, Cand. of Phys. and Mathem. Sciences, Associate Professor
*Baku State University, Azerbaijan, Baku,
**Institute of Control Systems (ANAS), Azerbaijan, Baku,
***Azerbaijan State Oil and Industry University, Azerbaijan, Baku
ON METHODS OF CONTROLLING OPTIMIZATION
SOFTWARE PACKAGES WITH THE APPLICATION
OF PARALLEL COMPUTING
The paper is dedicated to the analysis of methods and algo-
rithms of controlling computational process of solving complex
problems with the use of multiprocessor and/or multicore computer
systems. We have developed an automatic and dialogue systems of
control of unconstrained optimization process, which have a graph-
ical user interface.
Key words: optimization methods, parallel computations, mul-
tiprocessor and multicore systems, dialog systems.
Introduction. It is known that in spite of a large number of methods
for numerical solution to various classes of problems, the choice of the
most efficient method for solving a particular problem under specific val-
ues of its parameters requires a large number of comparative experiments.
As a rule, the end users tend to have difficulty both in carrying out such
experiments, which requires the knowledge of domain of applicability of
various numerical methods, and in proper conducting of the comparative
analysis of the results, which is time consuming.
In the paper, for the class of problems of multivariate unconstrained
optimization, we propose two approaches for facilitating the use of availa-
ble applied software packages using modern multi-processor (multi-core)
computer systems. One of the approaches involves active work of the user
with the optimization program package in a dialogue mode. The other ap-
proach involves the packet control by means of a specially developed con-
trol program in automatic mode.
Problem statement. Let :iP р х i N be the class of optimi-
zation problems (tasks). Here N is a given set defining individual prob-
lems of the class; п
iх D R are the arguments of each individual prob-
lem, which can take on values from some given admissible set iD , defined
by each specific optimization problem individually. It is assumed that for
© K. R. Aidazade, S. Z. Guliyev, 2017
Математичне та комп’ютерне моделювання
6
every problem iр х there exists a goal subset of extrema i iD D such
that iD . The problem iр х consists in finding at least one point
iх D . The set iD is called a set of solutions to the problem iр х .
To solve all the problems of the class Р , there is usually a corres-
ponding family of methods :jМ М j J , each of which solves the
problems iр х of the given class, i.e. they find a point iх D . Moreo-
ver, each method ,jМ j J , has different efficiency (in terms of time
used, the accuracy of the solution, etc.) when solving the problem iр х .
As the optimization techniques we use methods of direct search (zero-
order methods), gradient-based methods (first-order methods), and Newton-
type methods (second-order methods). These methods have a large number of
options settings, thus providing the ability to adapt the system to any process
quickly. Furthermore, the combination of direct search methods, gradient-
based methods, and Newton-type methods allows us to find an optimal solu-
tion for a smaller number of steps and/or calculations of the objective function,
which is important in terms of the cost of optimization process.
The report sets out the possible principles of management of optimi-
zation software package when solving a particular applied problem
iр х Р , allowing us to increase the overall efficiency of solving the
problem by combining the optimization methods in the process of solving
the problem with the use of a multiprocessor (multicore) computer system.
The principle of sequential implementation on a single core
(SISD) architecture is of important significance in own right, and can be
considered as the basic unit for the implementation on multiprocessor or
multicore architectures. Let us describe one of the principles of the possi-
ble schemes of implementation of the algorithm for solving optimization
problems on such architectures.
Let 1 2, ,..., kM M M be a list of optimization methods, composed of
algorithms in the software package of unconstrained optimization. It is
reasonable to include in the list diverse methods, if the structure of the
objective function is, generally speaking, not known.
The process of solving the problem is carried on in stages, each of which
consists of training and working steps. The first of these steps is intended to
identify the locally efficient algorithm from the available list of algorithms.
After that, the working step is carried out, which consists in solving the prob-
lem using only the algorithm that has proven to be the most efficient in the
first step. Both the training and working steps are carried out within a certain
time slice. One can use two variants of the training step:
Серія: Фізико-математичні науки. Випуск 15
7
1. To determine the local efficiency of the methods, the optimization
process starts from the same point 0x . In this case there is somewhat
wasteful consumption of machine time, and the training step is only
used to identify a locally efficient algorithm;
2. The training step is used not only to find an efficient algorithm, but
also to advance to an extreme point, because instead of the original
point we use the current point to train each of the following algorithm.
At the training step all the algorithms of the initial list 1 2, ,..., kM M M
have the opportunity to work within the given initial time slice, with the ex-
ception of only those methods that have been the least efficient for two con-
secutive training steps. These methods are not allocated any time slice and are
temporarily excluded from the list.
To calculate the values of the local efficiencies of the methods, we
make use of the following formula:
1 1| ( ) ( ) | /(| ( ) | ) || || /(|| || )k k k k k k
iE f x f x f x x x x .
Here iE is the local efficiency of the i th algorithm; 1,k kx x are the final
and initial points obtained using the i th algorithm; 1( ), ( )k kf x f x are the
values of the objective function at these points; || . || is the Euclidean norm;
is a small positive number.
The cycle criterion of the proposed procedure is the fulfillment of the
exit criteria for all methods. In conclusion, the user receives the accumu-
lated information on the search process, which includes:
the optimal chain of methods that worked at the working steps;
the total time of search for solutions;
the values of the objective function, of the coordinates, and of local
efficiencies of the methods obtained during the training step.
The principle of parallel implementation on a multicore architec-
ture. The simplest implementation of a multi-threaded version of the solu-
tion to the given optimization problem seems to be an approach that in-
volves several threads independently performing operations of the sequen-
tial algorithm described above.
The solution to an unconstrained optimization problem is carried out
in stages. At each stage, the following steps are implemented:
1. At the initial step, from the list of all available algorithms
1 2, ,..., kM M M of unconstrained optimization, we randomly select
several algorithms
1 2
, ,...,
Ns s sM M M , the number N of which is cho-
sen equal to the number of cores present on the computer system.
Математичне та комп’ютерне моделювання
8
2. At the working step, we identify the most efficient algorithms. The
duration iT of the working step may increase if any method has proven
to be the most efficient for several consecutive stages.
3. The current values of the local efficiencies iE of the methods are cal-
culated. From the list of working algorithms, we exclude a half of
those who have exhibited the lowest efficiency.
4. To the list of working algorithms we then add as many other algorithms as
were excluded in the previous step, and repeat steps 2 through 4 again.
When working with the automatic and dialogue systems, the user, in
accordance with the standard requirements, formulates an optimization
problem in any programming language in the form of a module (dynamic
link library), and then enters it into the system by specifying the full path
to the created library file; using the directives (instructions), the user runs
the most appropriate (in his/her opinion) algorithms of the library of mod-
ules, and tunes their various settings. The control program will then
organize the interaction of the modules from the package;
manages the input of the initial and current information;
interpret the user's directives (instructions);
load optimization modules into the computer memory dynamically;
output the results of computations on the display (at the same time you
can get results on a printer) in a prescribed form.
Analyzing the results of the computations, the user decides on the further
calculations, thus obtaining the possibility to monitor the progress of solving
the problem, to intervene promptly in the computation process, to choose the
working methods, and to adjust, if necessary, their parameters. The user de-
termines how often and in what form the results should be displayed on the
screen, and then, using a predefined set of directives carries out calculations.
The report will contain the protocols and results of computer-based
experiments for the class of unconstrained optimization problems using
different principles of management of the developed software package.
Conclusion. In the paper, we proposed an approach to control of
computational process of solving complex applied problems by an exam-
ple of multivariate unconstrained optimization problems using appropriate
software packages on multi-processor (multi-core) computer systems. The
proposed approaches essentially facilitate the end-users’ work of using
existing standard software packages. They require a different level of us-
ers’ knowledge of methods implemented in the software packages.
References:
1. Vasilyev F. P. Optimization Methods. M.: MTsNMO, 2011. Vol. 1 and 2. (in
Russian).
2. Polyak B. T. Introduction to optimization. M.: Lenand, 2014. 392 p. (in Russian).
Серія: Фізико-математичні науки. Випуск 15
9
3. Adam Freeman. Pro .NET Parallel Programming in C#. New York: Apress,
2010. 328 p.
4. Joe Duffy. Concurrent Programming on Windows. Boston, MA: Addison-
Wesley Professional, 2008. 1008 p.
5. Aidazade K. R., Sidorenko N. S. An approach to the construction of combined opti-
mization algorithms. Technical Cybernetics. 1982. Issue 6. P. 87–93. (in Russian)
Работа посвящена анализу методов, алгоритмов управления вычисли-
тельным процессом решения сложных задач с использованием много-
процессорных (многоядерных) компьютерных систем. Разработана авто-
матическая и диалоговая системы управления процессом безусловной
оптимизации, имеющие графический пользовательский интерфейс.
Ключевые слова: методы оптимизации, параллельные вычис-
ления, многопроцессорные и многоядерные системы, диалоговые
системы.
Date received 21.02.2017
УДК 519.6:539.3
А. А. Аралова, канд. фіз.-мат. наук
Інститут кібернетики імені В. М. Глушкова НАН України, м. Київ
ІДЕНТИФІКАЦІЯ ТЕРМІЧНОГО ОПОРУ
ПРИ ВІДОМОМУ ЗМІЩЕННІ ДЛЯ ТЕРМОПРУЖНОГО
ДЕФОРМУВАННЯ СКЛАДЕНОГО ЦИЛІНДРА
Розглянуто алгоритм розв’язання за допомогою градієнт-
них методів задачі ідентифікації термічного опору при відо-
мому зміщенні для термопружного деформування довгої
складеної циліндричної оболонки.
Ключові слова: термопружний стан, градієнтні методи,
циліндричні тіла.
Вступ. У роботі [1] на основі результатів теорії оптимального
керування станами різних багатокомпонентних розподілених сис-
тем [2] запропонована методологія побудови явних виразів градієнтів
функціоналів-нев'язок для ідентифікації градієнтними методами [3]
різних параметрів багатокомпонентних розподілених систем. У робо-
тах [4–6] ця методологія використана для ідентифікації параметрів
задач пружного, теплового та термопружного деформування довгого
порожнього циліндра.
Постановка задачі. Розглянемо довгий ізотропний циліндр з
порожниною. Врахувавши симетрію, виходячи з [7, 8] його термоп-
ружний стан описується рівняннями
© А. А. Аралова, 2017
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/SUO <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>
/SVE <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>
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/UKR <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>
/RUS <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>
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AllowImageBreaks true
/AllowTableBreaks true
/ExpandPage false
/HonorBaseURL true
/HonorRolloverEffect false
/IgnoreHTMLPageBreaks false
/IncludeHeaderFooter false
/MarginOffset [
0
0
0
0
]
/MetadataAuthor ()
/MetadataKeywords ()
/MetadataSubject ()
/MetadataTitle ()
/MetricPageSize [
0
0
]
/MetricUnit /inch
/MobileCompatible 0
/Namespace [
(Adobe)
(GoLive)
(8.0)
]
/OpenZoomToHTMLFontSize false
/PageOrientation /Portrait
/RemoveBackground false
/ShrinkContent true
/TreatColorsAs /MainMonitorColors
/UseEmbeddedProfiles false
/UseHTMLTitleAsMetadata true
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/BleedOffset [
0
0
0
0
]
/ConvertColors /ConvertToRGB
/DestinationProfileName (sRGB IEC61966-2.1)
/DestinationProfileSelector /UseName
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements true
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles true
/MarksOffset 6
/MarksWeight 0.250000
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PageMarksFile /RomanDefault
/PreserveEditing true
/UntaggedCMYKHandling /UseDocumentProfile
/UntaggedRGBHandling /LeaveUntagged
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [600 600]
/PageSize [419.528 595.276]
>> setpagedevice
|