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The program of search minimum scalar function, dependent from several independent arguments

First of all, excuse me for bad English. In order to not practice in language constructions, by places, I specially has supposed inaccuracies, in the description of attributes of classes. Lets will forgive me the programmers. And nevertheless, I hope, that the main sense I has managed to transmit

• Assignment
• Algorithms
• The brief description of components:
  • The module ChkRSearcher.exe - user interface
  • Library MyFunction.dll, containing user's function for minimizing
  • General information
  • How to create own dll
  • The library RSearcher.dll - realizes search
  • The class CRArg - contains argument of function
  • The class CRPoint - contains a testing point
  • The class CRGradient - calculates a vector-gradient of function in a testing point
  • The class CRMinOnLine - searches value of argument, for which value of the function is minimum
  • The class CRFileLog - write datas in a disk file
  • The class CRSearcher - realizes algorithms of search
• Download source code

Assignment:
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The modules, offered to your attention, are intended for a solution of a problem of definition minimum of scalar function f(x₁,…,x_n) several independent scalar variables, which range is n-dimensional parallelogram (x_min <= x <= x_max)

Algorithms:
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• RANDOMONLY: the main idea of a method consists in casual scatter uniformly distributed of testing points in a range of definition of function and choice among them such, for which significance of function f(x) is minimum. An amount of such scatters (max steps), as well as amount of testing points (max points), are parameters of algorithm. Depending on a character of a behaviour the functions in a range of definition, in a number of cases are possible manage an exactitude of a received solution, for what two improvings of main idea are realized: RANDOMWITHDESCENDIG and RANDOMWITHLINE
• RANDOMWITHDESCENDIG: Executes too, as RANDOMONLY, but in addition makes the following: If current casual scatter it is not exist a testing point, in which the significance of function would be less before found, the area of a scatter decreases on some factor (DESCENDINGCOEF) (for constant amount of scattered testing points, it increases a "denseness" researches of area of arguments at around the found point), and on the contrary, if the testing point, significance of function in which is detected, it is less than all before overlooked, the area of a scatter is increased by some factor (INCREASINGCOEF), and the centre of a scatter moves in the given point.
• RANDOMWITHLINE: is executed too, as RANDOMWITHDESCENDIG, but in addition following is made: on a set of testing points the point with minimum significance of function is selected and concerning it the vector-gradient in the party of decrease of value of function is created. Further, through a point with minimum significance of function in a direction of an obtained vector the direct line is carried out and along this direct in a range of definition of function the search of a point with minimum significance of function is made. If the found thus point has significance of function smaller all before found, this point is remembered, and the centre of a scatter of testing points moves in it.

The brief description of components:

The module ChkRSearcher.exe - executes search minimum value of the user's function, loaded through dll (Win32 API Dynamic Link Library)
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It allows:

• Load dll, containing user's function intended for minimization.
• Select algorithm (Scenario) and to adjust parameters (Max steps, Max points) of process search minimum value of the loaded function.
• Change a range of definition for function (Arg #, Min, Max).
• Begin and stop process of search.
• Look through both resalts of search , and the events arisen during search (protocol of events is conducted, if the mode Log file is on).

Library MyFunction.dll – containing user's function for minimizing

General information:
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As it is visible from the description ChkRSearcher.exe, to take advantage of this module, it is necessary, that the user's function for minimizing was made as dynamic link library (Win32 API Dynamic Link Library), it is expected, that this library will contain only two functions: factor() and initargs():

• double factor(double args[], int nsize) – returns the calculated value of function depending on arguments, contained in the array args of the dimensionality nsize
• void initargs(CRSearcher* pRSearcher) – defines amount of arguments and range of their modification

Example of functions:

#ifdef PARABOLA_EXPORTS
#define PARABOLA_API __declspec(dllexport)
#else
#define PARABOLA_API __declspec(dllimport)
#endif

extern "C" PARABOLA_API double factor(double args[], int nsize)
{
   double f1, f2;
   f1 = args[0]-args[1];
   f2 = args[0]+args[1]-10.0;
   return f1*f1+f2*f2/9.0;
}

extern "C" PARABOLA_API void initargs(CRSearcher* pRSearcher)
{
   pRSearcher->AddArg(-10.0, 10.0);
   pRSearcher->AddArg(-9.0, 11.0);
   pRSearcher->m_lpszComment = _T("(x1-x2)**2+(x1+x2-10)**2/9");
}

Here lines

   pRSearcher->AddArg(-10.0, 10.0);
   pRSearcher->AddArg(-9.0, 11.0);

in function initargs() means, that the function depends on two independent arguments, and the allowable significances first are in an interval [-10.0, 10.0], the second in [-9.0, 11.0], and the average point of these intervals will be selected as an initial testing point.

The line:

   pRSearcher->m_lpszComment = _T("(x1-x2)**2+(x1+x2-10)**2/9");

defines the comment for your function, which is recorded in the file of resalts and will allow you to distinguish one functions from other.

How to create dll-library, containing the functions: factor() and initargs()
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For creation dll, containing you functions is necessary to do the following:

In Microsoft Visual C++ 6.0 create the new project (menu item File\New… on tab Projects enter name yours future dll (field Project name) type Win32 Dynamic-Link Library and locate it in the subdirectory (field Location) …\RandomSearcher\Functions\ (on step 1 from 1 check: A DLL that exports some symbols)

Being in the created project, select tab FileView and do the following:

In the stdafx.h file replace a line

// TODO: reference additional headers your program requires here

On

#include "..\..\RSearcher\Common.h"
#include "..\..\RSearcher\RFileLog.h"
#include "..\..\RSearcher\RArg.h"
#include "..\..\RSearcher\RPoint.h"
#include "..\..\RSearcher\RGradient.h"
#include "..\..\RSearcher\RMinOnLine.h"
#include "..\..\RSearcher\RSearcher.h"

In your MyDllName.h file delete the text after a line

// This class is exported from the MyDllName.dll

and insert there following:

extern "C" MYDLLNAME_API double factor(double args[], int nsize);
extern "C" MYDLLNAME_API void initargs(CRSearcher* pRSearcher);

here, certainly, the constant MYDLLNAME_API is necessary for replacing with your constant, determined in the beginning of your MyDllName.h file

In your MyDllName.cpp file delete the text after a line

// This is an example of an exported variable

and insert there following:

// This are an exported functions:

extern "C" MYDLLNAME_API double factor(double args[], int nsize)
{
   /*
     double f1, f2;
     f1 = args[0]-args[1];
     f2 = args[0]+args[1]-10.0;
     return f1*f1+f2*f2/9.0;
   */
}

extern "C" MYDLLNAME_API void initargs(CRSearcher* pRSearcher)
{
   /*
     pRSearcher->AddArg(-10.0, 10.0);
     pRSearcher->AddArg(-9.0, 11.0);
     pRSearcher->m_lpszComment = _T("(x1-x2)**2+(x1+x2-10)**2/9");
   */
}

here, the constant MYDLLNAME_API also is necessary for replacing with your constant, determined in the beginning of the MyDllName.h file

Further, delete the comment in body of functions factor(), initargs() and write instead of it their your definitions.

Attention: an amount of the pRSearcher->AddArg(MyMinArgValue, MyMaxArgValue); in function initargs() and it's order should correspond to an amount of arguments (array elements args[] in your function factor() and it's order in an array args[]).

By using menu item Project\Insert Project into WorkSpace... add in your project, project named RSearcher (..\..\Rsearcher\RSearcher.dsp) and further, by taking advantage the menu item Project\Dependence... is necessary set dependence of your project on the project RSearcher (mark it for your project)

Set the folder for yours DLL. For this purpose select in a tree objects your project, press the right mouse button and from the arisen menu select item Set as Active Project. Further, by using the menu item Project\Settings…, in the arisen dialogue be switched on your project, select a tab Link and for Category General in a field Output file name enter the following ..\..\Bin\MyDllName.dll, that will allow to receive created yours Dll directly in the folder …\RandomSearcher\Bin\

After removal of all syntactical errors, as I hope, you receive the dll-file containing yours function for minimizing, and capable dynamically load it from the program ChkRSearcher.exe

The library RSearcher.dll – contains the following classes:
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The class CRPoint – contains a testing point
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Download source code [458KB]
Download examples [442KB]

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