optimization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from ecell4 import *\n",
    "import numpy\n",
    "import matplotlib.pylab as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def singlerun(x, kon, koff, solver='ode'):\n",
    "    with reaction_rules():\n",
    "        A + B == C | (abs(kon), abs(koff))\n",
    "    data = run_simulation(x, y0={'C': 120}, solver=solver, species_list=['A'], return_type='array')\n",
    "    return numpy.asarray(data).T[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x0 = numpy.linspace(0, 10, 21)\n",
    "y0 = singlerun(x0, 0.01, 0.3, 'gillespie')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x68ee170>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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M+i8k7ZH0adt7yq0qd+9I+kJE7JF0v6TP1eCYJekxSefLLqJA/yDpexHx+5I+qsSP3faI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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x681bd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x0, y0, 'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def evaluate(individual):\n",
    "    x = numpy.linspace(0, 10, 21)\n",
    "    y = singlerun(x, *individual)\n",
    "    return ((y - y0) ** 2).sum(),"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import scipy.optimize\n",
    "params1, cov = scipy.optimize.curve_fit(singlerun, x0, y0, p0=(1.0, 1.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-0.01068974, -0.3105444 ]), (147.52589412177068,))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params1, evaluate(params1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kbT/0/O0fcWdrJgz/gteliIgkhKS9Qq+sfp+mgeVg6rIoIgJJGujh+p1Mzw1x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\nIpIiFOgiIilCgS4ikiIU6CIiKeJ/ATVJtk1uRg0UAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x3ff0590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = numpy.linspace(0, 10, 101)\n",
    "plt.plot(x0, y0, 'o')\n",
    "plt.plot(x1, singlerun(x1, *params1), '-')\n",
    "plt.plot(x1, singlerun(x1, 0.01, 0.3), '--')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from deap import base, creator\n",
    "creator.create(\"FitnessMin\", base.Fitness, weights=(-1.0, ))\n",
    "creator.create(\"Individual\", list, fitness=creator.FitnessMin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random\n",
    "from deap import tools\n",
    "\n",
    "IND_SIZE = 2\n",
    "\n",
    "toolbox = base.Toolbox()\n",
    "toolbox.register(\"attribute\", random.random)\n",
    "toolbox.register(\"individual\", tools.initRepeat, creator.Individual,\n",
    "                 toolbox.attribute, n=IND_SIZE)\n",
    "toolbox.register(\"population\", tools.initRepeat, list, toolbox.individual)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "toolbox.register(\"mate\", tools.cxTwoPoint)\n",
    "toolbox.register(\"mutate\", tools.mutGaussian, mu=0, sigma=1, indpb=1.0/IND_SIZE)\n",
    "# toolbox.register(\"mate\", tools.cxSimulatedBinaryBounded, low=0, up=1, eta=20.0)\n",
    "# toolbox.register(\"mutate\", tools.mutPolynomialBounded, low=0, up=1, eta=20.0, indpb=1.0/IND_SIZE)\n",
    "\n",
    "toolbox.register(\"select\", tools.selTournament, tournsize=3)\n",
    "toolbox.register(\"evaluate\", evaluate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def main_ga():\n",
    "    pop = toolbox.population(n=50)\n",
    "    CXPB, MUTPB, NGEN = 0.5, 0.2, 100\n",
    "\n",
    "    # Evaluate the entire population\n",
    "    fitnesses = map(toolbox.evaluate, pop)\n",
    "    for ind, fit in zip(pop, fitnesses):\n",
    "        ind.fitness.values = fit\n",
    "\n",
    "    for g in range(NGEN):\n",
    "        print(g, *min([(ind, evaluate(ind)) for ind in pop], key=lambda p: p[1]))\n",
    "        # Select the next generation individuals\n",
    "        offspring = toolbox.select(pop, len(pop))\n",
    "        # Clone the selected individuals\n",
    "        offspring = list(map(toolbox.clone, offspring))\n",
    "\n",
    "        # Apply crossover and mutation on the offspring\n",
    "        for child1, child2 in zip(offspring[::2], offspring[1::2]):\n",
    "            if random.random() < CXPB:\n",
    "                toolbox.mate(child1, child2)\n",
    "                del child1.fitness.values\n",
    "                del child2.fitness.values\n",
    "\n",
    "        for mutant in offspring:\n",
    "            if random.random() < MUTPB:\n",
    "                toolbox.mutate(mutant)\n",
    "                del mutant.fitness.values\n",
    "\n",
    "        # Evaluate the individuals with an invalid fitness\n",
    "        invalid_ind = [ind for ind in offspring if not ind.fitness.valid]\n",
    "        fitnesses = map(toolbox.evaluate, invalid_ind)\n",
    "        for ind, fit in zip(invalid_ind, fitnesses):\n",
    "            ind.fitness.values = fit\n",
    "\n",
    "        # The population is entirely replaced by the offspring\n",
    "        pop[:] = offspring\n",
    "\n",
    "    return pop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 [0.018356354406677933, 0.8705348091096281] (3016.6100104387083,)\n",
      "1 [0.018356354406677933, 0.3526768677576647] (873.25063714495241,)\n",
      "2 [0.018356354406677933, 0.46017297073907015] (336.48983979711153,)\n",
      "3 [0.018356354406677933, 0.46017297073907015] (336.48983979711153,)\n",
      "4 [0.018356354406677933, 0.46017297073907015] (336.48983979711153,)\n",
      "5 [0.018356354406677933, 0.6304894716335571] (873.03590949772331,)\n",
      "6 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "7 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "8 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "9 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "10 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "11 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "12 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "13 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "14 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "15 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "16 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "17 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "18 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "19 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "20 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "21 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "22 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "23 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "24 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "25 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "26 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "27 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "28 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "29 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "30 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "31 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "32 [0.018356354406677933, 0.4857341559026765] (331.23473190067051,)\n",
      "33 [-0.010397271552709569, 0.31233523551285286] (153.13380645059979,)\n",
      "34 [-0.010397271552709569, 0.31233523551285286] (153.13380645059979,)\n",
      "35 [-0.010397271552709569, 0.31233523551285286] (153.13380645059979,)\n",
      "36 [-0.010397271552709569, 0.31233523551285286] (153.13380645059979,)\n",
      "37 [-0.010397271552709569, 0.31233523551285286] (153.13380645059979,)\n",
      "38 [-0.010397271552709569, 0.31233523551285286] (153.13380645059979,)\n",
      "39 [-0.010397271552709569, 0.31233523551285286] (153.13380645059979,)\n",
      "40 [-0.010397271552709569, 0.31233523551285286] (153.13380645059979,)\n",
      "41 [-0.010397271552709569, 0.31233523551285286] (153.13380645059979,)\n",
      "42 [-0.010397271552709569, 0.31233523551285286] (153.13380645059979,)\n",
      "43 [-0.010397271552709569, 0.31233523551285286] (153.13380645059979,)\n",
      "44 [-0.010397271552709569, 0.31233523551285286] (153.13380645059979,)\n",
      "45 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "46 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "47 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "48 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "49 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "50 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "51 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "52 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "53 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "54 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "55 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "56 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "57 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "58 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "59 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "60 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "61 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "62 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "63 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "64 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "65 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "66 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "67 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "68 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "69 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "70 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "71 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "72 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "73 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "74 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "75 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "76 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "77 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "78 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "79 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "80 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "81 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "82 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "83 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "84 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "85 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "86 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "87 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "88 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "89 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "90 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "91 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "92 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "93 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "94 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "95 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "96 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "97 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "98 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n",
      "99 [-0.010397271552709569, -0.301526457654592] (148.73748012959126,)\n"
     ]
    }
   ],
   "source": [
    "pop = main_ga()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-0.010397271552709569, -0.301526457654592], (148.73748012959126,))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params2 = min([(ind, evaluate(ind)) for ind in pop], key=lambda p: p[1])[0]\n",
    "params2, evaluate(params2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1FBGRpJCyR+jlm9+ivtdQyEuKjzMVEfFcShZ6JNzI5PAm7u3R1esoIiJJIyUL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\nTajQRUTShApdRCRN/C+OaCJNDmVKBAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6f33e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = numpy.linspace(0, 10, 101)\n",
    "plt.plot(x0, y0, 'o')\n",
    "plt.plot(x1, singlerun(x1, *params2), '-')\n",
    "plt.plot(x1, singlerun(x1, 0.01, 0.3), '--')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "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": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}