{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": "true" }, "source": [ "# Table of Contents\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Simulated annealing in Python\n", "\n", "This small notebook implements, in [Python 3](https://docs.python.org/3/), the [simulated annealing](https://en.wikipedia.org/wiki/Simulated_annealing) algorithm for numerical optimization.\n", "\n", "## References\n", "- The Wikipedia page: [simulated annealing](https://en.wikipedia.org/wiki/Simulated_annealing).\n", "- It was implemented in `scipy.optimize` before version 0.14: [`scipy.optimize.anneal`](https://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.optimize.anneal.html).\n", "- [This blog post](http://apmonitor.com/me575/index.php/Main/SimulatedAnnealing).\n", "- These Stack Overflow questions: [15853513](https://stackoverflow.com/questions/15853513/) and [19757551](https://stackoverflow.com/questions/19757551/).\n", "\n", "## See also\n", "- For a real-world use of simulated annealing, this Python module seems useful: [perrygeo/simanneal on GitHub](https://github.com/perrygeo/simanneal).\n", "\n", "## About\n", "- *Date:* 20/07/2017.\n", "- *Author:* [Lilian Besson](https://GitHub.com/Naereen), (C) 2017.\n", "- *Licence:* [MIT Licence](http://lbesson.mit-license.org).\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> This notebook should be compatible with both Python versions, [2](https://docs.python.org/2/) and [3](https://docs.python.org/3/)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from __future__ import print_function, division # Python 2 compatibility if needed" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import numpy.random as rn\n", "import matplotlib.pyplot as plt # to plot\n", "import matplotlib as mpl\n", "\n", "from scipy import optimize # to compare\n", "\n", "import seaborn as sns\n", "sns.set(context=\"talk\", style=\"darkgrid\", palette=\"hls\", font=\"sans-serif\", font_scale=1.05)\n", "\n", "FIGSIZE = (19, 8) #: Figure size, in inches!\n", "mpl.rcParams['figure.figsize'] = FIGSIZE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "\n", "## Algorithm\n", "\n", "The following pseudocode presents the simulated annealing heuristic.\n", "\n", "- It starts from a state $s_0$ and continues to either a maximum of $k_{\\max}$ steps or until a state with an energy of $e_{\\min}$ or less is found.\n", "- In the process, the call $\\mathrm{neighbour}(s)$ should generate a randomly chosen neighbour of a given state $s$.\n", "- The annealing schedule is defined by the call $\\mathrm{temperature}(r)$, which should yield the temperature to use, given the fraction $r$ of the time budget that has been expended so far." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Simulated Annealing**:\n", "> \n", "> - Let $s$ = $s_0$\n", "> - For $k = 0$ through $k_{\\max}$ (exclusive):\n", "> + $T := \\mathrm{temperature}(k ∕ k_{\\max})$\n", "> + Pick a random neighbour, $s_{\\mathrm{new}} := \\mathrm{neighbour}(s)$\n", "> + If $P(E(s), E(s_{\\mathrm{new}}), T) \\geq \\mathrm{random}(0, 1)$:\n", "> * $s := s_{\\mathrm{new}}$\n", "> - Output: the final state $s$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "\n", "## Basic but generic Python code" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us start with a very generic implementation:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def annealing(random_start,\n", " cost_function,\n", " random_neighbour,\n", " acceptance,\n", " temperature,\n", " maxsteps=1000,\n", " debug=True):\n", " \"\"\" Optimize the black-box function 'cost_function' with the simulated annealing algorithm.\"\"\"\n", " state = random_start()\n", " cost = cost_function(state)\n", " states, costs = [state], [cost]\n", " for step in range(maxsteps):\n", " fraction = step / float(maxsteps)\n", " T = temperature(fraction)\n", " new_state = random_neighbour(state, fraction)\n", " new_cost = cost_function(new_state)\n", " if debug: print(\"Step #{:>2}/{:>2} : T = {:>4.3g}, state = {:>4.3g}, cost = {:>4.3g}, new_state = {:>4.3g}, new_cost = {:>4.3g} ...\".format(step, maxsteps, T, state, cost, new_state, new_cost))\n", " if acceptance_probability(cost, new_cost, T) > rn.random():\n", " state, cost = new_state, new_cost\n", " states.append(state)\n", " costs.append(cost)\n", " # print(\" ==> Accept it!\")\n", " # else:\n", " # print(\" ==> Reject it...\")\n", " return state, cost_function(state), states, costs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "\n", "## Basic example\n", "\n", "We will use this to find the global minimum of the function $x \\mapsto x^2$ on $[-10, 10]$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "interval = (-10, 10)\n", "\n", "def f(x):\n", " \"\"\" Function to minimize.\"\"\"\n", " return x ** 2\n", "\n", "def clip(x):\n", " \"\"\" Force x to be in the interval.\"\"\"\n", " a, b = interval\n", " return max(min(x, b), a)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def random_start():\n", " \"\"\" Random point in the interval.\"\"\"\n", " a, b = interval\n", " return a + (b - a) * rn.random_sample()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def cost_function(x):\n", " \"\"\" Cost of x = f(x).\"\"\"\n", " return f(x)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def random_neighbour(x, fraction=1):\n", " \"\"\"Move a little bit x, from the left or the right.\"\"\"\n", " amplitude = (max(interval) - min(interval)) * fraction / 10\n", " delta = (-amplitude/2.) + amplitude * rn.random_sample()\n", " return clip(x + delta)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def acceptance_probability(cost, new_cost, temperature):\n", " if new_cost < cost:\n", " # print(\" - Acceptance probabilty = 1 as new_cost = {} < cost = {}...\".format(new_cost, cost))\n", " return 1\n", " else:\n", " p = np.exp(- (new_cost - cost) / temperature)\n", " # print(\" - Acceptance probabilty = {:.3g}...\".format(p))\n", " return p" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def temperature(fraction):\n", " \"\"\" Example of temperature dicreasing as the process goes on.\"\"\"\n", " return max(0.01, min(1, 1 - fraction))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's try!" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Step # 0/30 : T = 1, state = -7.45, cost = 55.5, new_state = -7.45, new_cost = 55.5 ...\n", "Step # 1/30 : T = 0.967, state = -7.45, cost = 55.5, new_state = -7.44, new_cost = 55.4 ...\n", "Step # 2/30 : T = 0.933, state = -7.44, cost = 55.4, new_state = -7.5, new_cost = 56.2 ...\n", "Step # 3/30 : T = 0.9, state = -7.5, cost = 56.2, new_state = -7.59, new_cost = 57.6 ...\n", "Step # 4/30 : T = 0.867, state = -7.59, cost = 57.6, new_state = -7.64, new_cost = 58.3 ...\n", "Step # 5/30 : T = 0.833, state = -7.59, cost = 57.6, new_state = -7.51, new_cost = 56.4 ...\n", "Step # 6/30 : T = 0.8, state = -7.51, cost = 56.4, new_state = -7.53, new_cost = 56.6 ...\n", "Step # 7/30 : T = 0.767, state = -7.53, cost = 56.6, new_state = -7.58, new_cost = 57.5 ...\n", "Step # 8/30 : T = 0.733, state = -7.53, cost = 56.6, new_state = -7.6, new_cost = 57.8 ...\n", "Step # 9/30 : T = 0.7, state = -7.53, cost = 56.6, new_state = -7.51, new_cost = 56.4 ...\n", "Step #10/30 : T = 0.667, state = -7.51, cost = 56.4, new_state = -7.24, new_cost = 52.4 ...\n", "Step #11/30 : T = 0.633, state = -7.24, cost = 52.4, new_state = -6.98, new_cost = 48.7 ...\n", "Step #12/30 : T = 0.6, state = -6.98, cost = 48.7, new_state = -6.6, new_cost = 43.5 ...\n", "Step #13/30 : T = 0.567, state = -6.6, cost = 43.5, new_state = -6.69, new_cost = 44.8 ...\n", "Step #14/30 : T = 0.533, state = -6.6, cost = 43.5, new_state = -6.84, new_cost = 46.8 ...\n", "Step #15/30 : T = 0.5, state = -6.6, cost = 43.5, new_state = -6.45, new_cost = 41.6 ...\n", "Step #16/30 : T = 0.467, state = -6.45, cost = 41.6, new_state = -6.24, new_cost = 38.9 ...\n", "Step #17/30 : T = 0.433, state = -6.24, cost = 38.9, new_state = -6.52, new_cost = 42.5 ...\n", "Step #18/30 : T = 0.4, state = -6.24, cost = 38.9, new_state = -5.92, new_cost = 35.1 ...\n", "Step #19/30 : T = 0.367, state = -5.92, cost = 35.1, new_state = -6.35, new_cost = 40.4 ...\n", "Step #20/30 : T = 0.333, state = -5.92, cost = 35.1, new_state = -5.98, new_cost = 35.8 ...\n", "Step #21/30 : T = 0.3, state = -5.92, cost = 35.1, new_state = -5.35, new_cost = 28.6 ...\n", "Step #22/30 : T = 0.267, state = -5.35, cost = 28.6, new_state = -4.67, new_cost = 21.8 ...\n", "Step #23/30 : T = 0.233, state = -4.67, cost = 21.8, new_state = -4.44, new_cost = 19.7 ...\n", "Step #24/30 : T = 0.2, state = -4.44, cost = 19.7, new_state = -4.59, new_cost = 21.1 ...\n", "Step #25/30 : T = 0.167, state = -4.44, cost = 19.7, new_state = -4.04, new_cost = 16.3 ...\n", "Step #26/30 : T = 0.133, state = -4.04, cost = 16.3, new_state = -4.77, new_cost = 22.8 ...\n", "Step #27/30 : T = 0.1, state = -4.04, cost = 16.3, new_state = -4.7, new_cost = 22.1 ...\n", "Step #28/30 : T = 0.0667, state = -4.04, cost = 16.3, new_state = -3.44, new_cost = 11.8 ...\n", "Step #29/30 : T = 0.0333, state = -3.44, cost = 11.8, new_state = -2.6, new_cost = 6.78 ...\n" ] } ], "source": [ "annealing(random_start, cost_function, random_neighbour, acceptance_probability, temperature, maxsteps=30, debug=True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now with more steps:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "0.08501260465044064" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "0.007227142949452121" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "state, c, states, costs = annealing(random_start, cost_function, random_neighbour, acceptance_probability, temperature, maxsteps=1000, debug=False)\n", "\n", "state\n", "c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "\n", "## Visualizing the steps" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def see_annealing(states, costs):\n", " plt.figure()\n", " plt.suptitle(\"Evolution of states and costs of the simulated annealing\")\n", " plt.subplot(121)\n", " plt.plot(states, 'r')\n", " plt.title(\"States\")\n", " plt.subplot(122)\n", " plt.plot(costs, 'b')\n", " plt.title(\"Costs\")\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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7e2PTpk347bffinXZQadOnbB582YsX75c87zt7e0hk8l0bndbnNeasY6H4vRT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DothBDSVMJXTozB4sWLMXHiRPz2t78FAMybNw/FxcVYvXo1Jk2KXFSQ4zijkRCnjOc5zf8TFfWD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\n6557pD6SZ1LKyZH6bc+ewP44T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