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      "source": [
        "# Bounded and constrained minimization problem, application to an energy absorber system"
      ]
    },
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      "source": [
        "This notebook aims at solving an optimization problem linked to the optimization of an energy absorber. The details about this bounded and constrained problem are given in the pdf Lecture_8_OPT.\n",
        "\n",
        "In this problem we want to minimize the mass of our energy absorber made of a foam-filled aluminium tube. This optimization problem contains bounds linked to the dimension of the tube as well as limits on the properties of the aluminium and the foam used as filling material. The performances of the absorber, its maximum force and the absorbed energy, are enforced through a system of constraints."
      ]
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      "source": [
        "# We import here the python modules we need for this example\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy import optimize"
      ]
    },
    {
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      "source": [
        "We define the plateau stress of the foam $\\sigma_f$ throught the function _get_foam_properties_, the stroke efficiency is defined in the function _get_SE_, the absorbed energy and the maximum force associated to the component are defined in the functions _get_E_ and _get_Fmax_ respectively."
      ]
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      "source": [
        "def get_foam_properties(rhof):\n",
        "    n       = 2.2\n",
        "    Cpow    = 61.0\n",
        "    return Cpow*(rhof)**n    "
      ]
    },
    {
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      "execution_count": 3,
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      "source": [
        "def get_SE(Favg,x):\n",
        "    [b,h,L,sigma0,rhof] = x\n",
        "    sigmaf = get_foam_properties(rhof)    \n",
        "    rhof0 = 2.79\n",
        "    epsD  = 1.0-1.5*(rhof/rhof0)\n",
        "    SEF   = 0.76*(1.0-1.7*(rhof/rhof0)**0.8)\n",
        "    A  = (b-h)*h\n",
        "    AF = (b-2.0*h)**2.0\n",
        "    F0avg = 13.06*sigma0*(b-h)**(1.0/3.0)*h**(5.0/3.0)\n",
        "    return ((F0avg+5.5*np.sqrt(sigmaf*sigma0)*A)*SEF+(sigmaf*AF)*epsD)/Favg"
      ]
    },
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      "execution_count": 4,
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      "source": [
        "def get_E(x):\n",
        "    [b,h,L,sigma0,rhof] = x\n",
        "    sigmaf = get_foam_properties(rhof)\n",
        "    A  = (b-h)*h\n",
        "    AF = (b-2.0*h)**2.0\n",
        "    F0avg = 13.06*sigma0*(b-h)**(1.0/3.0)*h**(5.0/3.0)\n",
        "    Favg  = (F0avg+sigmaf*AF+5.5*np.sqrt(sigma0*sigmaf)*A)\n",
        "    D = get_SE(Favg,x)*L\n",
        "    return Favg/1000.0*D/1000.0"
      ]
    },
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      "execution_count": 5,
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      "source": [
        "def get_Fmax(x):\n",
        "    [b,h,L,sigma0,rhof] = x\n",
        "    sigmaf = get_foam_properties(rhof)\n",
        "    A  = (b-h)*h\n",
        "    AF = (b-2.0*h)**2.0\n",
        "    AE0 = 0.48\n",
        "    AEF = 0.85    \n",
        "    F0avg = 13.06*sigma0*(b-h)**(1.0/3.0)*h**(5.0/3.0)\n",
        "    Fmax  = F0avg/AE0+(sigmaf*AF)/AEF+2.0*np.sqrt(sigma0*sigmaf)*A\n",
        "    return Fmax/1000.0"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "We define the mass of the component, our objective function, as _Mass_"
      ]
    },
    {
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      "source": [
        "def Mass(x):\n",
        "    [b,h,L,sigma0,rhof] = x\n",
        "    rho0 = 0.00000279\n",
        "    A  = (b-h)*h\n",
        "    AF = (b-2.0*h)**2.0    \n",
        "    return (4.0*rho0*A+(rhof*1e-6)*AF)*L"
      ]
    },
    {
      "cell_type": "markdown",
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      "source": [
        "The variables of our optimization problem are:\n",
        "\n",
        "1 the width of the component $b$\n",
        "\n",
        "2 the thickness of the aluminium tube $h$\n",
        "\n",
        "3 the length of the component $L$\n",
        "\n",
        "4 the strength of the aluminium alloy $\\sigma_0$\n",
        "\n",
        "5 the density of the aluminium foam $\\rho_f$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      },
      "source": [
        "We start by defining the bounds of these variables through a list in which we append the different minimum and maximum allowable values."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
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        "execution": {
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      "source": [
        "bounds = [] # Define bounds\n",
        "bounds.append((50.0,100.0))  #b\n",
        "bounds.append((1.0,3.0))     #h\n",
        "bounds.append((0.0,400.0))   #L\n",
        "#\n",
        "bounds.append((100.0,300.0)) #sigma0\n",
        "bounds.append((0.1,0.5))     #rhof"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nteract": {
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      },
      "source": [
        "We impose next the constraints on the performances of the components, the maximum allowable maximum force $F_{max}$, the minimum absorbed energy $E$,as well as the global stability limit $L/b$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
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      "source": [
        "constraints = [] # Define constraints\n",
        "constraints.append({'type': 'ineq', 'fun': lambda x: 70.0-get_Fmax(x)}) #Fmax <= 70 kN\n",
        "constraints.append({'type': 'ineq', 'fun': lambda x: get_E(x)-7.0})     #E    >=  7 kJ\n",
        "constraints.append({'type': 'ineq', 'fun': lambda x: 3.0-x[2]/x[0]})    #L/b  <=  3.0"
      ]
    },
    {
      "cell_type": "markdown",
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      },
      "source": [
        "Since we do not know if this problem is sensitive to local minima we define three starting points based on the bounds corresponding to:\n",
        "\n",
        "1 The minimum allowable parameters\n",
        "\n",
        "2 The average allowable parameters \n",
        "\n",
        "3 The maximum allowable parameters\n",
        "\n",
        "We store these starting points in a list to ease the comparison."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
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        "execution": {
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      "outputs": [],
      "source": [
        "x0s = []\n",
        "x0s.append([50.0,1.0,100.0,100.0,0.1])\n",
        "x0s.append([75.0,2.0,250.0,200.0,0.3])\n",
        "x0s.append([100.0,3.0,400.0,300.0,0.5])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nteract": {
          "transient": {
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      },
      "source": [
        "Next, we run three local optimizations and collect the resulting optimums."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
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        "execution": {
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      },
      "outputs": [],
      "source": [
        "x = []\n",
        "for x0 in x0s:\n",
        "    res = optimize.minimize(Mass, x0, method='SLSQP',bounds=bounds,options={'disp': False, 'maxiter':1000},constraints=constraints)\n",
        "    x.append(res.x)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
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        }
      },
      "source": [
        "From the three runs we can check if the optimizer violated or not our constraints. The cell below prints out the constraint functions for the three starting points. The local minimizer is able to fulfill the constraints equations and our components are therefore within the limit we specified."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
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        "execution": {
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      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Resulting constraints equations for the starting points corresponding to:\n",
            "          MIN   AVG   MAX\n",
            "  Fmax = 70.0  70.0  70.0\n",
            "  E    =  7.0   7.0   7.0\n",
            "  L/b  =  3.0   3.0   3.0\n"
          ]
        }
      ],
      "source": [
        "print('Resulting constraints equations for the starting points corresponding to:')\n",
        "print('          MIN   AVG   MAX')\n",
        "print('  Fmax = {:.1f}  {:.1f}  {:.1f}'.format(get_Fmax(x[0]),get_Fmax(x[1]),get_Fmax(x[2])))\n",
        "print('  E    =  {:.1f}   {:.1f}   {:.1f}'.format(get_E(x[0]), get_E(x[1]), get_E(x[2])))\n",
        "print('  L/b  =  {:.1f}   {:.1f}   {:.1f}'.format(x[0][2]/x[0][0], x[1][2]/x[1][0], x[2][2]/x[2][0]))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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            "deleting": false
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      },
      "source": [
        "Since our optimization are successful we can now look at the results we obtained. The next cell prints the resulting objective functions (i.e. the mass of the component) as well as the resulting variables (dimensions and material properties).\n",
        "\n",
        "Depending upon the starting point we obtain three different solutions which suggest that this problem is sensitive to local minima. The variation in mass is though rather small and probably negligible compared to the general accuracy of the analytical solution we employed."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
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      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "  Mass = 0.389  0.393  0.497\n",
            "################################\n",
            "     b = 58.70  61.55  83.93\n",
            "     h = 1.00  1.00  1.43\n",
            "     L = 176.10  184.65  251.80\n",
            "sigma0 = 165.45  267.32  300.00\n",
            "  rhof = 0.49  0.41  0.10\n"
          ]
        }
      ],
      "source": [
        "print('  Mass = {:.3f}  {:.3f}  {:.3f}'.format(Mass(x[0]), Mass(x[1]), Mass(x[2])))\n",
        "print('################################')\n",
        "vars = ['     b','     h','     L','sigma0','  rhof']\n",
        "for var, i in zip(vars,range(0,5)):\n",
        "    print('{} = {:.2f}  {:.2f}  {:.2f}'.format(var,x[0][i],x[1][i],x[2][i]))"
      ]
    },
    {
      "cell_type": "markdown",
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      },
      "source": [
        "In the next cell we try to investigate the reason for the local minima of our problem. We start by plotting the mass of the component for different values of the thickness $h$, the width $b$ and three different values of the foam's density $\\rho_f$. The thickness and the width are varied at the same time within the bounds of our problem. The abscissa yields 0 when the minimum thickness and width are used while it yields 1 for the maximum values.\n",
        "\n",
        "When looking at the resulting masses, we observe that the objective function is smooth and do not possess local mimina which should on principle give us a problem rather insensitive to the starting point."
      ]
    },
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        {
          "data": {
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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "bs = np.linspace(50.0,100.0,100)\n",
        "hs = np.linspace(1.0,3.0,100)\n",
        "xplot = np.linspace(0.0,1.0,100)\n",
        "Ls = 400.0\n",
        "#\n",
        "M = []\n",
        "for b,h in zip(bs,hs):\n",
        "    M.append(Mass([b,h,Ls,100.0,0.1]))\n",
        "plt.plot(xplot,M,'r',label='rhof = 0.1')\n",
        "M = []\n",
        "for b,h in zip(bs,hs):\n",
        "    M.append(Mass([b,h,Ls,100.0,0.25]))\n",
        "plt.plot(xplot,M,'b',label='rhof = 0.25')\n",
        "M = []\n",
        "for b,h in zip(bs,hs):\n",
        "    M.append(Mass([b,h,Ls,100.0,0.5]))\n",
        "plt.plot(xplot,M,'g',label='rhof = 0.5')\n",
        "plt.xlabel('Normalized variable (-)')\n",
        "plt.ylabel('Mass (kg)')\n",
        "plt.xlim([0.0,1.0])\n",
        "plt.ylim([0.0,3.0])\n",
        "plt.legend()\n",
        "plt.grid()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      },
      "source": [
        "If we now plot the maximum force and energy absorbed for the same components as in the previous cell, we see that these quantities are also smooth functions. The local minima problem appears because of the constraints which complexify the problem at hand.\n",
        "\n",
        "Even if constraints and bounds are common in optimization they can lead to the local minima we faced in this example. In our case the variation of mass in between the components is rather and could be neglected otherwise we will have to relax or tighten the constraints until we no longer have local minima. An alternative will be to employ a global optimizer."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "collapsed": true,
        "execution": {
          "iopub.execute_input": "2021-04-12T13:15:07.853Z",
          "iopub.status.busy": "2021-04-12T13:15:07.848Z",
          "iopub.status.idle": "2021-04-12T13:15:08.012Z",
          "shell.execute_reply": "2021-04-12T13:15:08.020Z"
        },
        "jupyter": {
          "outputs_hidden": false,
          "source_hidden": true
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "bs = np.linspace(50.0,100.0,100)\n",
        "hs = np.linspace(1.0,3.0,100)\n",
        "xplot = np.linspace(0.0,1.0,100)\n",
        "Ls = 400.0\n",
        "#\n",
        "fig,axs = plt.subplots(1,2)\n",
        "F = []\n",
        "E = []\n",
        "for b,h in zip(bs,hs):\n",
        "    F.append(get_Fmax([b,h,Ls,100.0,0.1]))\n",
        "    E.append(get_E([b,h,Ls,100.0,0.1]))    \n",
        "axs[0].plot(xplot,F,'r',label='rhof = 0.1')\n",
        "axs[1].plot(xplot,E,'r')\n",
        "F = []\n",
        "E = []\n",
        "for b,h in zip(bs,hs):\n",
        "    F.append(get_Fmax([b,h,Ls,100.0,0.25]))\n",
        "    E.append(get_E([b,h,Ls,100.0,0.25]))        \n",
        "axs[0].plot(xplot,F,'b',label='rhof = 0.25')\n",
        "axs[1].plot(xplot,E,'b')\n",
        "F = []\n",
        "E = []\n",
        "for b,h in zip(bs,hs):\n",
        "    F.append(get_Fmax([b,h,Ls,100.0,0.5]))\n",
        "    E.append(get_E([b,h,Ls,100.0,0.5]))        \n",
        "axs[0].plot(xplot,F,'g',label='rhof = 0.5')\n",
        "axs[1].plot(xplot,E,'g')\n",
        "axs[0].plot([0.0,1.0],[70.0,70.0],'k',label='Constraints')\n",
        "axs[1].plot([0.0,1.0],[7.0,7.0],'k')\n",
        "axs[0].set_xlabel('Normalized variable (-)')\n",
        "axs[1].set_xlabel('Normalized variable (-)')\n",
        "axs[1].set_ylabel('Energy (kJ)')\n",
        "axs[0].set_ylabel('Maximum force (kN)')\n",
        "#plt.xlim([0.0,1.0])\n",
        "#plt.ylim([0.0,3.0])\n",
        "plt.tight_layout()\n",
        "axs[0].legend()\n",
        "axs[0].grid()\n",
        "axs[1].grid()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "outputs_hidden": false,
          "source_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernel_info": {
      "name": "python3"
    },
    "kernelspec": {
      "argv": [
        "/Library/Frameworks/Python.framework/Versions/3.9/bin/python3.9",
        "-m",
        "ipykernel_launcher",
        "-f",
        "{connection_file}"
      ],
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.12.4"
    },
    "nteract": {
      "version": "0.28.0"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}