机械优化设计鲍威尔法编程.docx

1、机械优化设计鲍威尔法编程鲍威尔法求解二维函数极小值的程序说明一 题目利用鲍威尔法求函数的极小值点。二 鲍威尔法基本思想:1) 给定初始点，选取初始方向组，它由n各线性无关的向量所组成。2) 从出发，顺次沿作一维搜索得。接着以为起点，沿方向移动一个的距离，得到分别称为一轮迭代的始点，终点和反射点。始点，终点，反射点所对应的函数值分别表示为同时计算各中间点处的函数值，并记为因此有计算n个函数值之差，记作其中最大者记作3) 根据是否满足判别条件和来确定是否要对原方向组进行替换。若不满足判别条件，则下轮迭代应对原方向组进行替换，将补充到原方向组的最后位置，而除掉。即新方向组为，作为下轮迭代的搜索方向。

2、下轮迭代的始点取方向进行一维搜索得极小点。4) 判断是否满足收敛准则。若满足则取为极小点，否则应置，返回2，继续 进行下一轮迭代。改进后的鲍威尔法程序框图如下：三 用鲍威尔法求函数程序如下：/鲍威尔法Dlg.cpp : implementation file/#include stdafx.h#include 鲍威尔法.h#include 鲍威尔法Dlg.h#ifdef _DEBUG#define new DEBUG_NEW#undef THIS_FILEstatic char THIS_FILE = _FILE_;#endif/ CAboutDlg dialog used for App A

3、boutclass CAboutDlg : public CDialogpublic: CAboutDlg();/ Dialog Data /AFX_DATA(CAboutDlg) enum IDD = IDD_ABOUTBOX ; /AFX_DATA / ClassWizard generated virtual function overrides /AFX_VIRTUAL(CAboutDlg) protected: virtual void DoDataExchange(CDataExchange* pDX); / DDX/DDV support /AFX_VIRTUAL/ Implem

4、entationprotected: /AFX_MSG(CAboutDlg) /AFX_MSG DECLARE_MESSAGE_MAP();CAboutDlg:CAboutDlg() : CDialog(CAboutDlg:IDD) /AFX_DATA_INIT(CAboutDlg) /AFX_DATA_INITvoid CAboutDlg:DoDataExchange(CDataExchange* pDX) CDialog:DoDataExchange(pDX); /AFX_DATA_MAP(CAboutDlg) /AFX_DATA_MAPBEGIN_MESSAGE_MAP(CAboutDl

5、g, CDialog) /AFX_MSG_MAP(CAboutDlg) / No message handlers /AFX_MSG_MAPEND_MESSAGE_MAP()/ CMyDlg dialogCMyDlg:CMyDlg(CWnd* pParent /*=NULL*/) : CDialog(CMyDlg:IDD, pParent) /AFX_DATA_INIT(CMyDlg) m_x01 = 0.0f; m_x02 = 0.0f; m_x1 = 0.0f; m_x2 = 0.0f; /AFX_DATA_INIT / Note that LoadIcon does not requir

6、e a subsequent DestroyIcon in Win32 m_hIcon = AfxGetApp()-LoadIcon(IDR_MAINFRAME);void CMyDlg:DoDataExchange(CDataExchange* pDX) CDialog:DoDataExchange(pDX); /AFX_DATA_MAP(CMyDlg) DDX_Text(pDX, IDC_x01, m_x01); DDX_Text(pDX, IDC_x02, m_x02); DDX_Text(pDX, IDC_x1, m_x1); DDX_Text(pDX, IDC_x2, m_x2);

7、/AFX_DATA_MAPBEGIN_MESSAGE_MAP(CMyDlg, CDialog) /AFX_MSG_MAP(CMyDlg) ON_WM_SYSCOMMAND() ON_WM_PAINT() ON_WM_QUERYDRAGICON() /AFX_MSG_MAPEND_MESSAGE_MAP()/ CMyDlg message handlersBOOL CMyDlg:OnInitDialog() CDialog:OnInitDialog(); / Add About. menu item to system menu. / IDM_ABOUTBOX must be in the sy

8、stem command range. ASSERT(IDM_ABOUTBOX & 0xFFF0) = IDM_ABOUTBOX); ASSERT(IDM_ABOUTBOX AppendMenu(MF_SEPARATOR); pSysMenu-AppendMenu(MF_STRING, IDM_ABOUTBOX, strAboutMenu); / Set the icon for this dialog. The framework does this automatically / when the applications main window is not a dialog SetIc

9、on(m_hIcon, TRUE); / Set big icon SetIcon(m_hIcon, FALSE); / Set small icon / TODO: Add extra initialization here return TRUE; / return TRUE unless you set the focus to a controlvoid CMyDlg:OnSysCommand(UINT nID, LPARAM lParam) if (nID & 0xFFF0) = IDM_ABOUTBOX) CAboutDlg dlgAbout; dlgAbout.DoModal()

10、; else CDialog:OnSysCommand(nID, lParam); / If you add a minimize button to your dialog, you will need the code below/ to draw the icon. For MFC applications using the document/view model,/ this is automatically done for you by the framework.void CMyDlg:OnPaint() if (IsIconic() CPaintDC dc(this); /

11、device context for painting SendMessage(WM_ICONERASEBKGND, (WPARAM) dc.GetSafeHdc(), 0); / Center icon in client rectangle int cxIcon = GetSystemMetrics(SM_CXICON); int cyIcon = GetSystemMetrics(SM_CYICON); CRect rect; GetClientRect(&rect); int x = (rect.Width() - cxIcon + 1) / 2; int y = (rect.Heig

12、ht() - cyIcon + 1) / 2; / Draw the icon dc.DrawIcon(x, y, m_hIcon); else CDialog:OnPaint(); / The system calls this to obtain the cursor to display while the user drags/ the minimized window.HCURSOR CMyDlg:OnQueryDragIcon() return (HCURSOR) m_hIcon;void CMyDlg:OnOK() / TODO: Add extra validation her

13、e /CDialog:OnOK(); UpdateData(true); int i,n; double h1,h2,h3,m,flag,X0021,d0121,d0221,d0321; /确定键的执行程序 double X0121,X0221,X0321; double F0,F1,F2,F3,e1,e2,em; double X21; double f0,f1,f2,f3; X0000=m_x01; /对初始搜索点进行赋值 X0010=m_x02; d0100=1,d0110=0; /初始索索方向的确定 d0200=0,d0210=1; i=1; do F0=(X0000*X0000+2*

14、X0010*X0010-4*X0000-2*X0000*X0010),f0=F0; /初始点函数值 h1=(4*d0100+2*d0100*X0010+2*d0110*X0000)/(2*d0100*d0100+ /确定搜索方向 4*d0110*d0110-4*d0110*d0100); X0100=X0000+h1*d0100,X0110=X0010+h1*d0110; F1=(X0100*X0100+2*X0110*X0110-4*X0100-2*X0100*X0110),f1=F1; /确定F的函数值 h2=(4*d0200+2*d0200*X0110+2*d0210*X0100)/(2

15、*d0200*d0200+ /确定搜索步长 4*d0210*d0210-4*d0210*d0200); X0200=X0100+h2*d0200 ;X0210=X0110+h2*d0210; F2=(X0200*X0200+2*X0210*X0210-4*X0200-2*X0200*X0210),f2=F2;/确定F2的函数值 e1=f0-f1; /进行判定 e2=f1-f2; if(e1e2) em=e1,m=1; else em=e2,m=2; / d0300=X0200-X0000; d0310=X0210-X0010; X0300=2*X0200-X0000; X0310=2*X021

16、0-X0010; F3=(X0300*X0300+2*X0310*X0310-4*X0300-2*X0300*X0310),f3=F3; /确定F3的函数值 while (F3=F0 & (F0-2*F2+F3)*(F0-F2-em)*(F0-F2-em)=0.5*(F0-F3)*(F0-F3) /不满足判别条件 i+; if (F2e2) em=e1,m=1; /进行判断 else em=e2,m=2; d0300=X0200-X0000; /确定新的搜索方向 d0310=X0210-X0010; X0300=2*X0200-X0000; X0310=2*X0210-X0010; F3=(X

17、0300*X0300+2*X0310*X0310-4*X0300-2*X0300*X0310),f3=F3;/确定函数值 else X0000=X0300,X0010=X0310; F0=(X0000*X0000+2*X0010*X0010-4*X0000-2*X0000*X0010),f0=F0; h1=(4*d0100+2*d0100*X0010+2*d0110*X0000)/(2*d0100*d0100+ 4*d0110*d0110-4*d0110*d0100); X0100=X0000+h1*d0100,X0110=X0010+h1*d0110; F1=(X0100*X0100+2*X

18、0110*X0110-4*X0100-2*X0100*X0110),f1=F1; h2=(4*d0200+2*d0200*X0110+2*d0210*X0100)/(2*d0200*d0200+ 4*d0210*d0210-4*d0210*d0200); X0200=X0100+h2*d0200 ;X0210=X0110+h2*d0210; F2=(X0200*X0200+2*X0210*X0210-4*X0200-2*X0200*X0210),f2=F2; e1=f0-f1; e2=f1-f2; if(e1e2) em=e1,m=1; else em=e2,m=2; d0300=X0200-

19、X0000; d0310=X0210-X0010; X0300=2*X0200-X0000; X0310=2*X0210-X0010; F3=(X0300*X0300+2*X0310*X0310-4*X0300-2*X0300*X0310),f3=F3; if(m=1) d0100=d0300,d0110=d0310; else if(m=2) d0200=d0300,d0210=d0310; h3=(4*d0300+2*d0300*X0210+2*d0310*X0200)/(2*d0300*d0300+ 4*d0310*d0310-4*d0310*d0300); X0000=X0200+h3*d0300; X0010=X0210+h3*d0310; if(i=2) break; while (abs(X0200-X0000)0.001&abs(X0210-X0010)0.001);/输出极小值点X00=X0000,X10=X0010; m_x1=X00;m_x2=X10;UpdateData(false); 程序运行结果：四 结论由该程序的运行结果可知，要求函数的极小值的在（10,5）处。该程序利用VC+6.0下的MFC插件，创建对话框，将运算结果很形象的表现出来。经验证，运算结果完全正确。验证了该程序的可行性。