{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulated annealing\n", "\n", "Simulated annealing is an optimization technique designed to approximate a globally optimal solution to a given problem. A simple example of such a problem is finding a global maximum or minimum of a function.\n", "\n", "The method is closely related to the Metropolis algorithm.\n", "Recall that for zero temperature $T = 0$ we would never move to a state with a higher energy in the Metropolis algorithm, but would eventually be stuck in a state which minimizes the energy.\n", "However, if our set of moves only allows us to move to neighboring microstates, we may end up being stuck in a local minimum as opposed to the global minimum.\n", "This issue is less relevant at finite temperature $T > 0$, since there is always a chance to get out of the local minimum by accepting occasionally a move to a state with higher energy.\n", "\n", "This logic can be applied to finding the minimum of a function.\n", "We probe different values of $x$. For $T = 0$ we would always only accept a state with a lower value of $f(x)$, thus ending up in at least a local minimum.\n", "For $T > 0$, however, we will have also the possibility to explore a broader range of $x$ values, and possibly moving away from a local minimum to the global one.\n", "\n", "We start out with a large value of $T$ which will allow us to cover initially a broad range of possibilities for finding the minimum.\n", "Eventually we will want to narrow down our search which can be achieved by lowering the temperature and thus prereferably accepting values which tend to minimize the function more.\n", "Eventually, the temperature can be set to zero to narrow down to a single minimum.\n", "\n", "The method is not guaranteed converge to the exact global minimum but can yield good approximate solution if the method of choosing candidates moves and the cooling schedule (the decrease of $T$ with time) are chosen appriately for the problem at hand.\n", "\n", "$$\\beta = \\frac{1}{T}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Function minimum\n", "\n", "Let us consider the following function as an example,\n", "$$\n", "f(x) = x^2 - \\cos(4\\pi x)\n", "$$\n", "which has several local minima" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "def f(x):\n", " return x**2 - np.cos(4*np.pi*x)\n", "flabel = \"${f(x) = x^2 - \\cos(4\\pi x)}$\"\n", "\n", "xplot = np.linspace(-2,2,400)\n", "yplot = f(xplot)\n", "\n", "plt.plot(xplot,yplot, label=flabel)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The global minimum is at $x = 0$, but also many local minima are present.\n", "Standard algorithms can thus end up in a local minimum instead of a global one.\n", "\n", "In the simulated annealing procedure we will randomly pick a new value of $x_{\\rm cand}$.\n", "We will consider $x_{\\rm cand}$ in the neighborhood of $x$, for instance, by sampling from Gaussian distribution with $\\sigma = 1$ (the value of sigma can be varied).\n", "The new value $x_{\\rm cand}$ will be accepted with a probability from the Metropolis method\n", "$$\n", "p_{a} = e^{-[f(x_{\\rm cand}) - f(x)]/T}~.\n", "$$\n", "\n", "The cooling schedule is chosen in the exponential form\n", "$$\n", "T_n = T_{\\rm max} e^{-n/\\tau}.\n", "$$\n", "The process proceeds until the temperature decreases below a certain threshold $T_{\\rm min}$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# A single step of the simulated annealing process at temperature T\n", "# for finding the minimum of a function f(x)\n", "# The candidate move xcand is sampled from a Gaussian distribution\n", "# around the present value of x, with a condition xmin <= xcand <= xmax\n", "# The move is accepted with the Metropolis based probability\n", "def simulated_annealing_step(f, T, x, sigma, xmin = -1e9, xmax = 1e9):\n", " fnow = f(x)\n", " xcand = np.random.normal(x,sigma)\n", " while (xcand < xmin or xcand > xmax):\n", " xcand = np.random.normal(x,sigma)\n", " fcand = f(xcand)\n", " if (fcand < fnow or (T>0 and np.random.rand() < np.exp(-(fcand-fnow)/T))):\n", " return xcand\n", " else:\n", " return x" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.display import clear_output\n", "import time\n", "\n", "# Let us take our function and try to find its minimum\n", "# with simulated annealing\n", "def f(x):\n", " return x**2 - np.cos(4*np.pi*x)\n", "flabel = \"${f(x) = x^2 - \\cos(4\\pi x)}$\"\n", "\n", "# We shall visualize the process\n", "x = 2\n", "sigma = 1.\n", "Tmin = 1.e-3\n", "Tmax = 10.\n", "T = Tmax\n", "t = 0\n", "tau = 100.\n", "\n", "fs = [f(x)]\n", "\n", "while (T > Tmin):\n", " T = Tmax * np.exp(-t/tau)\n", " x = simulated_annealing_step(f, T, x, sigma)\n", " t += 1\n", " fs.append(f(x))\n", " if (t%10 == 0):\n", " clear_output(wait=True)\n", " time.sleep(0.1)\n", " plt.title(\"Simulated annealing, T = \" + '{0:.3f}'.format(T) + \", f(x) = \" + '{0:.3f}'.format(f(x)))\n", " plt.plot(xplot,yplot, label=flabel)\n", " plt.xlim(-2,2)\n", " plt.xlabel(\"x\")\n", " plt.ylabel(\"y\")\n", " plt.axvline(x,color='r')\n", " plt.legend()\n", " plt.show()\n", " \n", "plt.title(\"Simulated annealing\")\n", "plt.plot(fs, label=flabel)\n", "plt.xlabel(\"Step\")\n", "plt.ylabel(\"f(x)\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another example\n", "$$\n", "f(x) = \\cos(x) + \\cos(\\sqrt{2}x) + \\cos(\\sqrt{3}x)\n", "$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f(x):\n", " return np.cos(x) + np.cos(np.sqrt(2)*x) + np.cos(np.sqrt(3)*x)\n", "\n", "flabel = \"${f(x) = \\cos(x) + \\cos(\\sqrt{2}x) + \\cos(\\sqrt{3}x)}$\"\n", "\n", "xplot = np.linspace(0,50,400)\n", "yplot = f(xplot)\n", "\n", "plt.plot(xplot,yplot, label=flabel)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us try to find the global one with simulated annealing in range $x \\in [0,50]$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = 50 * np.random.rand()\n", "sigma = 5.\n", "Tmin = 1.e-3\n", "Tmax = 10.\n", "T = Tmax\n", "t = 0\n", "tau = 100.\n", "\n", "while (T > Tmin):\n", " T = Tmax * np.exp(-t/tau)\n", " x = simulated_annealing_step(f, T, x, sigma, 0, 50)\n", " #print(T,\" \",x,\" \",f(x))\n", " # sigma *= np.exp(-1./tau)\n", " t += 1\n", " if (t%10 == 0):\n", " clear_output(wait=True)\n", " time.sleep(0.1)\n", " plt.title(\"Simulated annealing, T = \" + '{0:.3f}'.format(T) + \", f(x) = \" + '{0:.3f}'.format(f(x)))\n", " plt.plot(xplot,yplot, label=flabel)\n", " plt.xlim(0,50)\n", " plt.xlabel(\"x\")\n", " plt.ylabel(\"y\")\n", " plt.axvline(x,color='r')\n", " plt.legend()\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Percolation threshold\n", "\n", "Percolation theory studies the formation of long-range connectivity in random systems.\n", "Discrete percolation can be considered on a lattice, where each site can be either free or occuppied, and connected to neighboring sites. In continuum percolation one fills available space with overlapping object that can overlap and bond into clusters.\n", "\n", "Above a certain occupation threshold -- called percolation threshold $0 < p_c < 1$ there exists a giant connected component of order of system size, while below it it does not.\n", "In practice the connected component may correspond to fluid flow through a porous medium, or an electrically conductive admixture.\n", "\n", "Near $p = p_c$ the system can exhibit many interesting phenomena similar to critical phenomena near the critical point." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Square lattice percolation\n", "\n", "In square lattice percolation one has an $N$x$N$ grid where each site is occupied with a probability $p$ and the neighboring occupied sites can form a cluster.\n", "\n", "We can estimate the percolation threshold $p_c$ through Monte Carlo modeling.\n", "There are two strategies we can employ:\n", "- Consider different values of $p$. For every given $p$ label each site with probability $p$ to be occupied. Then use cluster-finding algorithm and see if a percolating cluster (for instance one that runs all the way from top to bottom of the grid) is formed. For large enough $N$ we expect that percolating cluster forms for $p > p_c$ and does not form for $p < p_c$.\n", "- Randomly pick unoccupied site and mark it as occupied. Check if a percolating cluster is found. If not, repeat the process by labeling a new unoccupied site as occupied until a percolating cluster is formed. We expect the percolating cluster to form when the ratio of occupied sites to the total number of sites is of order $p_c$.\n", "\n", "Let us implement the 2nd strategy. For efficient cluster finding we will use the [union-find data structure](https://en.wikipedia.org/wiki/Disjoint-set_data_structure)." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# Class implementing the union-find structure with a 2D (x,y) index\n", "# This will also store the minimum and maximum y (vertical) coordinate of each set\n", "class UnionFind:\n", " def __init__(self, N):\n", " self.N = N\n", " self.parent = list(range(N**2))\n", " self.rank = [0] * N**2\n", " self.maxy = [0] * N**2\n", " self.miny = [0] * N**2\n", " for x in range(N):\n", " for y in range (N):\n", " ind = self.index(x,y)\n", " self.maxy[ind] = y\n", " self.miny[ind] = y\n", "\n", " def index(self, x, y):\n", " return self.N * x + y\n", " \n", " def findxy(self, x, y):\n", " return self.find(self.index(x,y))\n", " \n", " def find(self, ind):\n", " if self.parent[ind] != ind:\n", " self.parent[ind] = self.find(self.parent[ind])\n", " return self.parent[ind]\n", " \n", " def unionxy(self, x1, y1, x2, y2):\n", " self.union(self.index(x1,y1), self.index(x2,y2))\n", "\n", " def union(self, ind1, ind2):\n", " root_1 = self.find(ind1)\n", " root_2 = self.find(ind2)\n", "\n", " if root_1 == root_2:\n", " return\n", "\n", " if self.rank[root_1] > self.rank[root_2]:\n", " self.maxy[root_1] = max(self.maxy[root_1], self.maxy[root_2])\n", " self.miny[root_1] = min(self.miny[root_1], self.miny[root_2])\n", " self.parent[root_2] = root_1\n", " else:\n", " self.maxy[root_2] = max(self.maxy[root_1], self.maxy[root_2])\n", " self.miny[root_2] = min(self.miny[root_1], self.miny[root_2])\n", " self.parent[root_1] = root_2\n", " if self.rank[root_1] == self.rank[root_2]:\n", " self.rank[root_2] += 1" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from IPython.display import clear_output\n", "import time\n", "import matplotlib.pyplot as plt\n", "from matplotlib.colors import ListedColormap\n", "\n", "plotSimulation = True\n", "\n", "## Simulate percolation threshold on a square in 2D\n", "## Return the fraction of occupied cells at percolation\n", "def simulateSquarePercolation(N):\n", " cells = np.zeros([N,N])\n", " occupied = 0\n", " uf = UnionFind(N)\n", " while True:\n", " # Choose unoccupied cell to occupy\n", " while True:\n", " ind = np.random.randint(N**2)\n", " x = ind // N\n", " y = ind % N\n", " if (cells[x][y] == 0):\n", " break\n", " cells[x][y] = 1\n", " occupied += 1\n", " \n", " # Add the new cell to existing clusters\n", " if (x > 0 and cells[x-1][y] == 1):\n", " uf.unionxy(x,y,x-1,y)\n", " if (x < N - 1 and cells[x+1][y] == 1):\n", " uf.unionxy(x,y,x+1,y)\n", " if (y > 0 and cells[x][y-1] == 1):\n", " uf.unionxy(x,y,x,y-1)\n", " if (y < N - 1 and cells[x][y+1] == 1):\n", " uf.unionxy(x,y,x,y+1)\n", " \n", " ymin = uf.miny[uf.find(ind)]\n", " ymax = uf.maxy[uf.find(ind)]\n", " \n", " # plot the data points\n", " if plotSimulation:\n", " toPlot = False\n", " # Percolating cluster found\n", " if (ymin == 0 and ymax == N-1):\n", " indperc = uf.find(ind)\n", " for x in range(N):\n", " for y in range(N):\n", " if (uf.findxy(x,y) == indperc):\n", " cells[x][y] = 2\n", " toPlot = True\n", " \n", " if (occupied%400 == 0):\n", " toPlot = True\n", " \n", " if (toPlot):\n", " clear_output(wait=True)\n", " # time.sleep(0.01)\n", " plt.title(\"Square percolation, ${p = }$\" + '{0:.3f}'.format(occupied / N**2))\n", " plt.xlabel(\"x\")\n", " plt.ylabel(\"y\")\n", " cmap = ListedColormap(['w', 'black', 'red'])\n", " CS = plt.imshow(cells.T, vmax=2, vmin=0,origin=\"lower\",extent=[0,N,0,N], cmap=cmap, interpolation='nearest')\n", " # plt.colorbar(CS)\n", " plt.show()\n", " \n", " # Check if percolating cluster is found\n", " if (ymin == 0 and ymax == N-1): \n", " return occupied / N**2" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "0.60003125" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plotSimulation = True\n", "simulateSquarePercolation(400)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# Simulate square NxN percolation M times\n", "# Returns average and the error estimate for pc\n", "def simulateSquarePercolationAverage(N, M):\n", " total = 0\n", " totalsq = 0\n", " for i in range(M):\n", " p = simulateSquarePercolation(N)\n", " total += p\n", " totalsq += p**2\n", " \n", " p_av = total / M\n", " p2_av = totalsq / M\n", " \n", " return p_av, np.sqrt((p2_av - p_av**2)/N)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Simulating square percolation\n", "NxN = 10 x 10 with M = 10000 samples\n", "p_c = 0.5895430000000046 +- 0.0234648271909072\n", "CPU times: user 2.67 s, sys: 6.86 ms, total: 2.68 s\n", "Wall time: 2.69 s\n" ] } ], "source": [ "%%time\n", "\n", "N = 10\n", "M = 10000\n", "plotSimulation = False\n", "\n", "pc, pc_err = simulateSquarePercolationAverage(N,M)\n", "print(\"Simulating square percolation\")\n", "print(\"NxN = \",N,\"x\",N,\" with M =\",M, \"samples\")\n", "print(\"p_c = \", pc, \"+-\", pc_err)" ] } ], "metadata": { "kernelspec": { "display_name": "CompPhys", "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": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 4 }