{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "format compact" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Optymalizacja\n", "\n", "Przykłady zaczerpnięte z książki \n", "\n", "*K.-H. Chang, Design Theory and Methods using CAD/CAE. Academic Press, 2014*\n", "\n", "## Puszka na piwo (funkcja jednej zmiennej)\n", "\n", "Przy założeniu, że model geometryczny puszki jest walcem o promieniu $r$ i wysokości $h$, poszukiwana jest maksymalna objętość $V(r,h)$ przy zadanej powierzchni $A_0$.\n", "\n", "Maksymalizacja: $V(r,h)=\\pi r^2 h$\n", "Przy ograniczeniach: $A(r,h)=\\pi r(r+2h)=A_0,~~r>0,~~h>0$\n", "\n", "Czyli poszukiwane jest maksimum funkcji $$V(h) = \\pi \\,h\\,{\\left(-h+\\sqrt{h^2+\\frac{A_0}{\\pi}}\\right)}^2$$\n", "\n", "Zakładając, że $A_0=4 \\pi$\n", "\n", "$$V(h) = \\pi \\,h\\,{\\left(-h+\\sqrt{h^2+4}\\right)}^2$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Rozwiązanie analityczne" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "clear all\n", "syms h r A_0\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "V =\n", "h*pi*(h - (h^2 + 4)^(1/2))^2\n", " 2 2\n", "h pi (h - sqrt(h + 4))\n", "\n", "\n" ] } ], "source": [ "A0=4*pi;\n", "V=pi*h.*(-h+(h.^2+(A0/pi)).^0.5).^2\n", "pretty(V)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fplot(V,[0 8]) % lub ezplot()\n", "title(['V(h) = ' texlabel(V)])\n", "xlabel('h'),ylabel('V(h)')\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gradV =\n", "pi*(h - (h^2 + 4)^(1/2))^2 - 2*h*pi*(h - (h^2 + 4)^(1/2))*(h/(h^2 + 4)^(1/2) - 1)\n", "\n" ] } ], "source": [ "gradV=gradient(V,h) %dla jednego wymiaru równoważny z \"diff()\"" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "h_ext =\n", "(2*3^(1/2))/3\n", "\n" ] } ], "source": [ "h_ext=solve(gradV==0)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Rozwiazanie =\n", " 1.1547\n", "\n" ] } ], "source": [ "Rozwiazanie=double(h_ext)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "H =\n", "2*h*pi*(h/(h^2 + 4)^(1/2) - 1)^2 - 4*pi*(h - (h^2 + 4)^(1/2))*(h/(h^2 + 4)^(1/2) - 1) - 2*h*pi*(1/(h^2 + 4)^(1/2) - h^2/(h^2 + 4)^(3/2))*(h - (h^2 + 4)^(1/2))\n", "\n" ] } ], "source": [ "H=diff(gradV) %druga pochodna" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ans =\n", "-(pi*3^(1/2))/2\n", "\n" ] } ], "source": [ "subs(H,h_ext) %podstawienie " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ans =\n", " -2.7207\n", "\n" ] } ], "source": [ "double(ans)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Jeżeli pierwsza pochodna funkcji w punkcie $h_{ext}$ jest równa 0 a druga pochodna funkcji ujemna to jest to maksimum" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Rozwiązanie numeryczne" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "clear all\n", "h=0:0.1:8;\n", "A0=pi;\n", "V=pi*h.*(-h+(h.^2+4*A0/pi).^0.5).^2;" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(h,V);\n", "xlabel('h: height'); ylabel('V: volume');" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "f =\n", " function_handle with value:\n", " @(h)-(pi*h.*(-h+(h.^2+4*A0/pi).^0.5).^2)\n", "\n" ] } ], "source": [ "f=@(h)-(pi*h.*(-h+(h.^2+4*A0/pi).^0.5).^2)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "h_max =\n", " 1.1547\n", "\n" ] } ], "source": [ "h_max=fminsearch(f,0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Funkcja dwu zmiennnych\n", "\n", "Poszukiwane są ekstrema funkcji \n", "$$\n", "f(x_1,x_2)=x_{2}\\,{\\mathrm{e}}^{-{x_{1}}^2-{x_{2}}^2}\n", "$$\n", "\n", "w przedziale $[-2, 2]$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Rozwiązanie analityczne" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2 2\n", "x_2 exp(- x_1 - x_2 )\n", "\n", "\n" ] } ], "source": [ "syms x_1 x_2\n", "f=x_2*exp(-x_1^2-x_2^2);\n", "pretty(f)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fsurf(f,[-2,2])\n", "title(['f(x,y,z) = ' texlabel(f)])\n", "xlabel('x_1'), ylabel('x_2'), zlabel('f(x_1,x_2)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Gradient $\\nabla f$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gradf =\n", " -2*x_1*x_2*exp(- x_1^2 - x_2^2)\n", " exp(- x_1^2 - x_2^2) - 2*x_2^2*exp(- x_1^2 - x_2^2)\n", "\n" ] } ], "source": [ "gradf=gradient(f)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "/ 2 2 \\\n", "| -2 x_1 x_2 exp(- x_1 - x_2 ) |\n", "| |\n", "| 2 2 2 2 2 |\n", "\\ exp(- x_1 - x_2 ) - 2 x_2 exp(- x_1 - x_2 ) /\n", "\n", "\n" ] } ], "source": [ "pretty(gradf)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "extrem = \n", " struct with fields:\n", "\n", " x_1: [2x1 sym]\n", " x_2: [2x1 sym]\n", "\n" ] } ], "source": [ "extrem=solve(gradf==0)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x =\n", " 0 -0.7071\n", "\n" ] } ], "source": [ "x=double([extrem.x_1(1) extrem.x_2(1)])" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x =\n", " 0 -0.7071\n", " 0 0.7071\n", "\n" ] } ], "source": [ "x=[x; double([extrem.x_1(2) extrem.x_2(2)])]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hessian $\\mathbf{H} = \\nabla^2 f$" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "H =\n", "[ 4*x_1^2*x_2*exp(- x_1^2 - x_2^2) - 2*x_2*exp(- x_1^2 - x_2^2), 4*x_1*x_2^2*exp(- x_1^2 - x_2^2) - 2*x_1*exp(- x_1^2 - x_2^2)]\n", "[ 4*x_1*x_2^2*exp(- x_1^2 - x_2^2) - 2*x_1*exp(- x_1^2 - x_2^2), 4*x_2^3*exp(- x_1^2 - x_2^2) - 6*x_2*exp(- x_1^2 - x_2^2)]\n", "\n" ] } ], "source": [ "H=jacobian(gradf, [x_1, x_2])" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "H =\n", "[ 4*x_1^2*x_2*exp(- x_1^2 - x_2^2) - 2*x_2*exp(- x_1^2 - x_2^2), 4*x_1*x_2^2*exp(- x_1^2 - x_2^2) - 2*x_1*exp(- x_1^2 - x_2^2)]\n", "[ 4*x_1*x_2^2*exp(- x_1^2 - x_2^2) - 2*x_1*exp(- x_1^2 - x_2^2), 4*x_2^3*exp(- x_1^2 - x_2^2) - 6*x_2*exp(- x_1^2 - x_2^2)]\n", "\n" ] } ], "source": [ "H=hessian(f,[x_1,x_2])\n" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "H_1 =\n", " 0.8578 0\n", " 0 1.7155\n", "H_2 =\n", " -0.8578 0\n", " 0 -1.7155\n", "\n" ] } ], "source": [ "H_1=double(subs(H, [x_1 x_2], [x(1,1), x(1,2)]))\n", "H_2=double(subs(H, [x_1 x_2], [x(2,1), x(2,2)]))" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "detH_1 =\n", " 1.4715\n", "detH_2 =\n", " 1.4715\n", "\n" ] } ], "source": [ "detH_1=det(H_1),detH_2=det(H_2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Funkcja $f$ ma ekstremum gdy $\\nabla f = 0$ oraz wyznacznik hessianu H jest dodatni. Gdy H > 0 jest to minimum, a gdy H < 0 to maksimum." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Rozwiązanie numeryczne" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "clear x\n", "clear f" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "f =\n", " function_handle with value:\n", " @(x)x(2)*exp(-x(1)^2-x(2)^2)\n", "\n" ] } ], "source": [ "f=@(x) x(2)*exp(-x(1)^2-x(2)^2)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x_min =\n", " 0.0000 -0.7071\n", "g =\n", " function_handle with value:\n", " @(x)-f(x)\n", "x_max =\n", " 0.0000 0.7071\n", "\n" ] } ], "source": [ "x_min=fminsearch(f,[0 0])\n", "g=@(x)-f(x)\n", "x_max=fminsearch(g,[0 0])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Matlab", "language": "matlab", "name": "matlab" }, "language_info": { "codemirror_mode": "octave", "file_extension": ".m", "help_links": [ { "text": "MetaKernel Magics", "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" } ], "mimetype": "text/x-octave", "name": "matlab", "version": "0.15.0" } }, "nbformat": 4, "nbformat_minor": 2 }