机械优化设计鲍威尔法编程

1、鲍威尔法求解二维函数极小值的程序说明题目224x1 2x1x2 的极小值点。利用鲍威尔法求函数 f (x1,x2) x12 2x22鲍威尔法基本思想 :1)给定初始点 x0 ，选取初始方向组，它由n 各线性无关的向量0 0 0di ,d2.dn所组成。2)k接着以 xn 为起点，沿方向dnkk kiXnX0移动一个 xnkkx0k 的距离，得到kc kXn i 2Xnkx0k k k k k k k从xo出发，顺次沿di ,d2 ,.dn作一维搜索得Xi,X2,.Xn 。kkk终点，反射点所对应x0k , xnk , xnk 1分别称为一轮迭代的始点，终点和反射点。始点，的函数值分别表示为k

2、k kF0f (xk),F2f (xnk), F3f(xnk 1)同时计算各中间点处的函数值，并记为i f ( xik )( i 0,1,2,.n)因此有 F0 f0,F2计算 n 个函数值之差，记作其中最大者记作m maX3)根据是否满足判别条件F3 F02F3)2(F0 2F2 F3)(F0 F2 m )2 0.5 m(F0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dn1补充到原方向组的最后位置，而除掉dm。即新方向组为dk dk . dm1 dm1 . d n d n i作为下轮迭代的搜索方向。下轮迭代的始点取d n 1方向进行一维搜索得极小

3、点k 1Xo k i、.4）判断是否满足收敛准则。若满足则取Xo为极小点，否则应置 k k 1 ,返回2,继续进行下一轮迭代。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 Aboutclass CAb

4、outDlg : public CDialogpublic:CAboutDlg();/ Dialog Data /AFX_DATA(CAboutDlg) enum IDD = IDD_ABOUTBOX ; /AFX_DATA/ ClassWizard generated virtual function overrides /AFX_VIRTUAL(CAboutDlg) protected:/ DDX/DDV supportvirtual void DoDataExchange(CDataExchange* pDX); /AFX_VIRTUAL/ Implementation protecte

5、d:/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(CAboutDlg, CDialog) /AFX_MSG

6、_MAP(CAboutDlg)/ No message handlers/AFX_MSG_MAP END_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 require a subsequent DestroyIcon in

7、 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);/AFX_DATA_MAPBEGIN_MESSAGE_MAP(CMy

8、Dlg, 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 system command range. ASSERT(IDM_ABOUTBOX

9、 & 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 SetIcon(m_hIcon, TRUE);/ Set big iconSetIcon(m

10、_hIcon, FALSE); / Set small icon/ TODO: Add extra initialization herereturn 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();elseCDialog:OnSysCommand(nID, lParam);/ If you

11、 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); / device context for paintingSendMessage(WM_ICONERASEB

12、KGND, (WPARAM) dc.GetSafeHdc(), 0);/ Center icon in client rectangleint cxIcon = GetSystemMetrics(SM_CXICON);int cyIcon = GetSystemMetrics(SM_CYICON);CRect rect;GetClientRect(&rect);int x = (rect.Width() - cxIcon + 1) / 2;int y = (rect.Height() - cyIcon + 1) / 2;/ Draw the icondc.DrawIcon(x, y, m_hI

13、con);elseCDialog: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 here/CDialog:OnOK();UpdateData(true);int i,n;double h1,h2,h3,m,flag,X0

14、021,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;doF0=(X0000*X0000+2*X0010*X0010-4*X0000-2*X0000*X0010),f0=F0;/ 初始点函数值h1=(4*d0100+2*d0100*X0010+2

15、*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*d0200*d0200+/ 确定搜索步长4*d0210*d0210-4*d0210*d0200);X0200=X0100+h2*d0200 ;X0210

16、=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*X0210-X0010;F3=(X0300*X0300+2*X0310*X0310-4*X0300-2*X0300*X0310),f3=F3;/确定F3的函数值while (F3=F0

17、& (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=(X0300*X0300+2*X0310*X0310-4*X0300-2*X0300*X0310),f3=F3; / 确定函数值elseX0000=X0300,X0010=X0310;F0=(X0000

18、*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*X0110*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=f