AEC.06 - Evolutionary Multi-Objective Optimization.ipynb

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      "## Demonstration Class 06\n",
      "# Evolutionary Multi-Objective Optimization\n",
      "\n",
      "### Luis Mart\u00ed, LIRA/[DEE](http://www.ele.puc-rio.br)/[PUC-Rio](http://www.puc-rio.br)\n",
      "\n",
      "[http://lmarti.com](http://lmarti.com); [lmarti@ele.puc-rio.br](mailto:lmarti@ele.puc-rio.br) \n",
      "\n",
      "[Advanced Evolutionary Computation: Theory and Practice](http://lmarti.com/aec-2014) "
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      "This notebook is better viewed rendered as slides. You can convert it to slides and view them by:\n",
      "- using [nbconvert](http://ipython.org/ipython-doc/1/interactive/nbconvert.html) with a command like:\n",
      "  ```bash\n",
      "  $ ipython nbconvert --to slides --post serve <this-notebook-name.ipynb>\n",
      "  ```\n",
      "- installing [Reveal.js - Jupyter/IPython Slideshow Extension](https://github.com/damianavila/live_reveal)\n",
      "- using the online [IPython notebook slide viewer](https://slideviewer.herokuapp.com/) (some slides of the notebook might not be properly rendered).\n",
      "\n",
      "This and other related IPython notebooks can be found at the course github repository:\n",
      "* [https://github.com/lmarti/evolutionary-computation-course](https://github.com/lmarti/evolutionary-computation-course)"
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     "source": [
      "# In this notebook\n",
      "\n",
      "* Present the basic concepts related to evolutionary multi-objective optimization algorithms.\n",
      "* The Non-dominated Sorting Genetic Algorithm II (NSGA-II).\n",
      "* Benchmark test problems.\n",
      "* Experiment design and results comparison."
     ]
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      "# How can we handle multiple conflicting objectives?\n",
      "\n",
      "Even choosing a fruit implies dealing with conflicting objectives.\n",
      "\n",
      "<div align='center'><img src='http://imgs.xkcd.com/comics/fuck_grapefruit.png' width='56%' align='center'/>\n",
      "taken from http://xkcd.com/388/</div>"
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      "# [Multi-objective optimization](http://en.wikipedia.org/wiki/Multi-objective_optimization)\n",
      "\n",
      "* Most -*if not all*- optimization problems involve more than one objective function to be optimized simultaneously.\n",
      "* For example, you must optimize a given feature of an object while keeping under control the resources needed to elaborate that object.\n",
      "* Sometimes those other objectives are converted to constraints or fixed to default values, but that does not means that they are there.\n",
      "* Multi-objective optimization is also known as *multi-objective programming*, *vector optimization*, *multicriteria optimization*, *multiattribute optimization* or *Pareto optimization* (and probably by other names, depending on the field).\n",
      "* Multi-objective optimization has been applied in [many fields of science](http://en.wikipedia.org/wiki/Multi-objective_optimization#Examples_of_multi-objective_optimization_applications), including engineering, economics and logistics (see the section on applications for detailed examples) where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives."
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      "## Formalization of a Multi-objective Optimization Problem (MOP)\n",
      "\n",
      "$$\n",
      "\\renewcommand{\\vec}[1]{\\mathbf{#1}}\n",
      "\\newcommand{\\set}[1]{\\mathcal{#1}}\n",
      "\\newcommand{\\dom}{\\preccurlyeq}\n",
      "\\left.\n",
      "\\begin{array}{rl}\n",
      "\\mathrm{minimize}             & \\vec{F}(\\vec{x})=\\langle f_1(\\vec{x}),\\ldots,f_M(\\vec{x})\\rangle\\,,\\\\ \n",
      "\\mathrm{subject}\\ \\mathrm{to} & c_1(\\vec{x}),\\ldots,c_C(\\vec{x})\\le 0\\,,\\\\\n",
      "\t\t\t\t\t\t\t  & d_1(\\vec{x}),\\ldots,d_D(\\vec{x})= 0\\,,\\\\\n",
      "& \\text{with}\\ \\vec{x}\\in\\set{D}\\,,\n",
      "\\end{array}\\right\\}\n",
      "$$\n",
      "\n",
      "* $\\mathcal{D}$ is known as the *decision set* or *search set*.\n",
      "* functions $f_1(\\mathbf{x}),\\ldots,f_M(\\mathbf{x})$ are the *objective functions*. If $M=1$ the problem reduces to a single-objective optimization problem. \n",
      "* Image set, $\\set{O}$, result of the projection of $\\set{D}$ via $f_1(\\vec{x}),\\ldots,f_M(\\vec{x})$ is called *objective set* ($\\vec{F}:\\set{D}\\rightarrow\\set{O}$).\n",
      "* $c_1(\\vec{x}),\\ldots,c_C(\\vec{x})\\le 0$ and $d_1(\\vec{x}),\\ldots,d_D(\\vec{x})= 0$  express the constraints imposed on the values of $\\vec{x}$.\n",
      "\n",
      "*Note:* In case you are -still- wondering, a maximization problem can be posed as the minimization one: $\\min\\ -\\vec{F}(\\vec{x})$."
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     "source": [
      "## Example: A two variables and two objectives MOP\n",
      "<img src='static/mop-2d.jpg' height='56%' align='center'/>"
     ]
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      "## MOP (optimal) solutions\n",
      "\n",
      "Usually, does not exists a unique solution that minimizes all objective functions simultaneously, but, instead, a set of equally good trade-off solutions.\n",
      "\n",
      "* *Optimality* can be defined in terms of the *Pareto dominance* relation. That is, having $\\vec{x},\\vec{y}\\in\\set{D}$, $\\vec{x}$ is said to dominate $\\vec{y}$ (expressed as $\\vec{x}\\dom\\vec{y}$) iff $\\forall f_j$, $f_j(\\vec{x})\\leq f_j(\\vec{y})$ and $\\exists f_i$ such that $f_i(\\vec{x})< f_i(\\vec{y})$.\n",
      "* Having the set $\\set{A}$. $\\set{A}^\\ast$, the *non-dominated subset* of $\\set{A}$, is defined as\n",
      "\n",
      "$$\n",
      "\\set{A}^\\ast=\\left\\{ \\vec{x}\\in\\set{A} \\left|\\not\\exists\\vec{y}\\in\\set{A}:\\vec{y}\\dom\\vec{x}\\right.\\right\\}.\n",
      "$$\n",
      "\n",
      "* The *Pareto-optimal set*, $\\set{D}^{\\ast}$, is the solution of the problem. It is the subset of non-dominated elements of $\\set{D}$. It is also known as the *efficient set*.\n",
      "* It consists of solutions that cannot be improved in any of the objectives without degrading at least one of the other objectives.\n",
      "* Its image in objective set is called the *Pareto-optimal front*, $\\set{O}^\\ast$.\n",
      "* Evolutionary algorithms generally yield a set of non-dominated solutions, $\\set{P}^\\ast$, that approximates $\\set{D}^{\\ast}$.\n"
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      "As usual, we need some initialization and configuration."
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     "input": [
      "import time, array, random, copy, math\n",
      "\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "\n",
      "import seaborn\n",
      "seaborn.set(style=\"whitegrid\")\n",
      "\n",
      "from deap import algorithms, base, benchmarks, tools, creator"
     ],
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      "<div class=\"alert alert-info\" role=\"alert\">\n",
      "<span class=\"sr-only\"><b>Important Notice:</b></span>\n",
      "  For this notebook I am using the development version of DEAP. If you want to try it on your own you might have to install DEAP manually from https://github.com/DEAP/deap. \n",
      "</div>"
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     "source": [
      "Planting a constant seed to always have the same results (and avoid surprises in class). -*you should not do this in a real-world case!*"
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      "# Visualizing the Pareto dominance relation\n",
      "\n",
      "* To start, lets have a visual example of the Pareto dominance relationship in action.\n",
      "* In this notebook we will deal with two-objective problems in order to simplify visualization. \n",
      "* Therefore, we can create:"
     ]
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     "input": [
      "creator.create(\"FitnessMin\", base.Fitness, weights=(-1.0,-1.0))\n",
      "creator.create(\"Individual\", array.array, typecode='d', \n",
      "               fitness=creator.FitnessMin)"
     ],
     "language": "python",
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      "## DTLZ2: One -of many- MOP benchmarks\n",
      "\n",
      "* We will use a common benchmark problem known as [DTLZ2](http://www.tik.ee.ethz.ch/sop/download/supplementary/testproblems/dtlz2/).\n",
      "* DTLZ problems can be configured to have as many objectives as desired, but as we want to visualize results we will stick to two objectives.\n",
      "* The Pareto-optimal front of DTLZ2 lies in the first [orthant](http://en.wikipedia.org/wiki/Orthant) of a unit (radius 1) hypersphere located at the coordinate origin ($\\vec{0}$).\n",
      "\n",
      "<div align='center'><img src='http://www.cs.cinvestav.mx/~emoobook/apendix-e/galeria4/dtlz2b.jpg' width=\"38%\" align='center'/>\n",
      "from Coello Coello, Lamont and Van Veldhuizen (2007) Evolutionary Algorithms for Solving Multi-Objective Problems, Second Edition. Springer [Appendix E](http://www.cs.cinvestav.mx/~emoobook/apendix-e/apendix-e.html).</div>"
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     "source": [
      "Preparing a DEAP `toolbox` with DTLZ2."
     ]
    },
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     "cell_type": "code",
     "collapsed": false,
     "input": [
      "toolbox = base.Toolbox()"
     ],
     "language": "python",
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      "BOUND_LOW, BOUND_UP = 0.0, 1.0\n",
      "NDIM = 2\n",
      "toolbox.register(\"evaluate\", lambda ind: benchmarks.dtlz2(ind, 2))"
     ],
     "language": "python",
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     "source": [
      "Defining components of the evolutionary algorithm."
     ]
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     "input": [
      "def uniform(low, up, size=None):\n",
      "    try:\n",
      "        return [random.uniform(a, b) for a, b in zip(low, up)]\n",
      "    except TypeError:\n",
      "        return [random.uniform(a, b) for a, b in zip([low] * size, [up] * size)]\n",
      "\n",
      "toolbox.register(\"attr_float\", uniform, BOUND_LOW, BOUND_UP, NDIM)\n",
      "toolbox.register(\"individual\", tools.initIterate, creator.Individual, toolbox.attr_float)\n",
      "toolbox.register(\"population\", tools.initRepeat, list, toolbox.individual)"
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     "source": [
      "Create an example random population and evaluate the individuals."
     ]
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     "input": [
      "num_samples = 50\n",
      "limits = [np.arange(BOUND_LOW, BOUND_UP, (BOUND_UP - BOUND_LOW)/num_samples)] * NDIM\n",
      "sample_x = np.meshgrid(*limits)"
     ],
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     "cell_type": "code",
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     "input": [
      "flat = []\n",
      "for i in range(len(sample_x)):\n",
      "    x_i = sample_x[i]\n",
      "    flat.append(x_i.reshape(num_samples ** NDIM))"
     ],
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      "example_pop = toolbox.population(n=num_samples ** NDIM)"
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      "for i, ind in enumerate(example_pop):\n",
      "    for j in range(len(flat)):\n",
      "        ind[j] = flat[j][i]"
     ],
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     "input": [
      "fitnesses = toolbox.map(toolbox.evaluate, example_pop)\n",
      "for ind, fit in zip(example_pop, fitnesses):\n",
      "    ind.fitness.values = fit"
     ],
     "language": "python",
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     "source": [
      "We also need `a_given_individual`."
     ]
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     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a_given_individual = toolbox.population(n=1)[0]\n",
      "a_given_individual[0] = 0.3\n",
      "a_given_individual[1] = 0.2"
     ],
     "language": "python",
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     "input": [
      "a_given_individual.fitness.values = toolbox.evaluate(a_given_individual)"
     ],
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     "source": [
      "DEAP comes with a Pareto dominance relation that we can use."
     ]
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     "input": [
      "def dominates(x,y):\n",
      "    return tools.emo.isDominated(x.fitness.values, y.fitness.values)"
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     "source": [
      "Lets compute the set of individuals that are `dominated` by `a_given_individual`, the ones that dominate it (its `dominators`) and the remaining ones."
     ]
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     "input": [
      "dominated = [ind for ind in example_pop if dominates(a_given_individual, ind)]\n",
      "dominators = [ind for ind in example_pop if dominates(ind, a_given_individual)]\n",
      "others = [ind for ind in example_pop if not ind in dominated and not ind in dominators]"
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      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "For `a_given_individual` (blue dot) we can now plot those that are dominated by it (in green), those that dominate it (in red) and those that are uncomparable."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(5,5))\n",
      "for ind in dominators:\n",
      "    plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'r.', alpha=0.5)\n",
      "for ind in dominated:\n",
      "    plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'g.', alpha=0.5)\n",
      "for ind in others:\n",
      "    plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'k.', ms=4)\n",
      "plt.plot(a_given_individual.fitness.values[0], a_given_individual.fitness.values[1], 'bo', ms=11);"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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MeeAkcDC/psowCPuSx9kfMKuR3zjnZr3CQyPAxRYaftbaFvD+rpd/6jv+KeBTObRLRozL\njtEuwZdXUEVRkI0eTXKW3K1atYpmswkk2zG613lh50A+a3pdxLnuQ99/CIA7fueOzD5f3GlLK+mr\npOuC/fcK+1l9ZT3P0PPQ9x/i9NnTnD57eikEpb9U+UnuwpbGuUyE9mT95LYsqVs8fBR+MjD+pXFp\nH3Lk0h1uNptL02PC5Dl5eebwDAAHdx9Ut3fAFH4yEFFb5YP7Cg9w7w4P6v4etIPv1Aunln4+uPtg\nZm2R+BR+MlBh8/1cdoOBeM/wcDlPXddyUPjJQIQtq3TtDrtWhVlK0iX2v8ff7e1FXeH+UfhJofgn\nJ7sEX5xBkKAVHv2s+MK6uod/eZhVL23vmP3Q9x9SAOZM4SeF4b8PGFQZxukOZyluQGrHl+JT+Enh\npLkP6DcsW9l7XeF9m/fxROUJQN3eflD4SWF4j8zstT44y+Vvea77jXu+fwT4njP38PU7vu7cNklH\n4SeFEbQpgssACMQfBBlkxedVezI4Cj8pNNf5gJ6sNkZIum1W3Pl+WzZuYcvGLQDsu25f5HslOwo/\nKaysBkC881xXePSbNwLcazRaU1/yo/CTwsty5Devis9FnPl+sLz5gfezAjBbCj8prLQTof2idnLO\nY3pMmLDQ84KxvrkeeI6kp/CToeMyEdp/XpyBjaz3AUxzPxCWA1BVX/YUfjJUXO4DQvEfe9lt5vAM\nvzrzKyaumrjsdYVefhR+MpSitq/KehVIP0Z/Xzz3IhNXTSyN/mrXl3wp/GSouFR74L4pgms3Nw9B\nc/2iQk8jwNko3ri/SAKuweeJux2+SxUXZ8t7r9rzz/fbtH6TU/Bp+/tsqPKToec68luv1yMfhO7J\na1v8sGovaDTaZVqMxKfwk6HmsgIE2iG1sLDgPACShGu1B5ev7Iia9tK9+7O6vdlQ+MlIcLkXODY2\nNpDJ0EFc5vr1otDLhsJPhlqcAZCjR49GXi+vKS9eWN76pVsB92rPtUKU+BR+MpJ6DYBksZNz2oov\nLMDueeIeJk5PrHhdoZcPhZ+MlDijvkn29YvbFnAbKZ45PMMz555hbtVc7GpP9wCTUfjJSPGCD9yf\n9RsnIONUhy6SzvXzaPOD5BR+MpJcl765dl+TdHPjjv5uWr+JiY0TkcGnqS/ZUPjJSAkLvXq9zsLC\nApDdpqe9zndd0vb4Lx/n2iuvXXpt/xv3MzU1Ffk+TX3JhsJPRp7/PiBkux1+knuBXoBde+W1PHX2\nKXZt3hU6ydl7TxCFXjIKPxlp/knQY2NjnDt3LvDcONvhd0s6+usFXxhNfclHaPgZY6rAAeANwAXg\nPdbaJ33Hfxe4F6gA/wT8mbX2N/k1VySZqHl+ce8DJpnyEncn57SDIRIuqvLbDVxhrd1hjJmmHXS7\nAYwxFeAB4B3W2p8bY94LXA/YPBssEof3zI6oeX557fISFJJBAeYPvKTVnu4BuokKv53AEQBr7XFj\nzI2+Y5PAGeCDxpjXAX9jrVXwSaEsLi4GHkszJzCP0d97nriHuVXtc546+9RlgyGa+pK9StjomDHm\nQeAr1tojnd9/AVxvrW0aY3YC/wf4N8CTwNeB/2at/WbQ9RqNRvCHifSJf9QX2vcCZ2dnI8+POq/7\nPYDT+fc8cc/Sz8+cewaATes3Lb22/437nd6//437OfzLwzy78CwA14xdw+7Nu53aOwqmpqYq0Wct\ni6r8zgIbfL9XrbXNzs9ngJNetWeMOQLcCASGX6eBcdrXV41GQ+1LYRjad+ONy50X12qvWq3Gvhfo\ndbddpq541V5tscbrr3s9EF3p+bvH3vvvO30fB2/JZ+rLMPzdxhUVfseAm4FHjDFvAn7gO/ZzoGaM\nuaEzCFIHPhe7BSIDEGe6S5JVHUnn+rl0b/2jv93dY9C9PldR4fc14CZjzLHO73uNMbcBNWvtg8aY\nO4CHO4Mfx6y1f5dnY0XS8g+A9JJmukvYdT3dAxr+uX77rtvn/F7Prs27ln7WKHA8oeFnrW0B7+96\n+ae+498EpnNol0guXAZA4oRenCkvQRWb6yRnzfXLliY5ixD/IehpH2zkWrFlsfEBqCvci8JPSs2/\nAgTcd3B2Pb/7fa6bmXqSVHve++ub65r2EkLhJ6XlDz7XCc5pV4HEWcqWZK6f//0/O/Mzbrrhpsj3\nlJXCT0ovbK4rxB8E6dUldhkI+dWZXzFx1fJOznG7xt3nvPqqV3PdldcB6vb2ovCT0nIJvTjPAk47\n3eXFcy8ycdVErMGMXltcab8/Nwo/kS5JtsDyi/MM31MvnGLuN3P85Fc/4VVrXwW4h14QhZ4bhZ+I\nT9z7gH5JH1y+bWIbT519ik3rN+U6ECKXU/iJdPiDL859QIhf7cHlwfWtmW85z/NLuukBaOqLn8JP\npIvrvUCXnZ6733fh0gV2fnbn0mtx1vB64qzq8N//044vl1P4iXRkPerb631rV6916qZ2r/tN0r3t\nHgypb647va8sFH4iEeKO+vrf55d0IGTbxDYgXuj1csfv3KFur4/CTyREkgGQ7tB74IE5vvAFeNWr\n4Omn26+98pXw2tfC3r3wrne1X7vniXuYOL08z88bCNmycUuiaq9XtajQW6bwE+mhe9lbVJcYeld6\nDz8Mt9++8tynn27/eewx+PQ3v8Rr/vgxnjn3DHOr5lYMhLjQ8z7iU/iJhEg7ufkLX4j+jBOH/gPP\nbv6fXLVx+bU4Axna8SUZhZ9ID6GV3sxM+38PHoxc7/vjH0d/VvPiWtb/v/1s2v0ZJjZOxFr/26vi\n044vbqqDboDI0JiZgQ0b4MgROHWK2po1kRsdePf4ojz7nX/P/jfuDw2uWq3Wc93wwd0Hlyq+uA86\nOn329FIIlo0qPxEXGzbA3BxUKnDhAvzkJ0Cy3Z7T6rV+1yX0kjxreJQp/ESirFoFzc5zu1otWFyE\nWo25f/7n4PfMzMDjj/PKK77L0795eeRH/OmfBh9LsjVWFE17UfiJhLv66uXg81x/PZw82fv8Tuhx\n7bUwN8dr+TFP8/uhH7FuHfzFX1zeRc6qSvNfp/taZQ09j+75iURZu3b55z17egef/37g3Fy7W7xt\nG3s3Ho68/Cc+AZs2tZ/1G7QXYJwQDLo3KJdT+ImEee45uPJKePnL213egwcvPz4zA1u3tkPv/Hn4\nl39pv16rwZYtvOvZT/GZz7Sru27r1sFnPgN3370yrOIGXpCsrjOKFH4iUZ57rv3Hb+tWWLNmudJ7\n4QUYH4dqtR18J08uBeW+ffDzn8Ndd8HLXtb+c9ddUKncwN13L4fe7OxsoqDqrvQUeG4UfiJxXH11\ne8T3ySfh0qXlULz2WpiYgHe+s2e3eNMm+B8vzHDm5hkuXKjxuc/VqFafBZKFVdZd2+npaaany/UU\nWg14iLi6+mp4/vnLX6tUliu9IP5BEGhPlVm7NnGV101VXjKq/ESSqlTac1TCRn63boVTp5YHQYC5\n229PPYCRtmvbfc3jx49z/PjxxNcbRqr8RFw991y7+jtzJni6i7f07fHH24EHSyO/PPUUbNmyctAk\nhrSBl/Yao0ThJxJH98CHZ2YGvvKV9qAHtAdA1q1r/+mM/PKtbzl/TNj8vCTX6KYAVPiJpLN1K/zi\nF+1VIIuL7ft51Sps7GzREnU/sEvaQQwFnjuFn0hS/j3/Ll1qT32pVtsDG7s6z9mI6OL6w67ZbFKt\ntm/DZzXHT4Ip/ESS6J61XK22V4K84x3hgde5J1h79NGeh9OMAGc1v8+b8jLqAyAKP5GkKpX2qg9o\nj/oGhZ431QVCp7uEPbqymwYv0gsNP2NMFTgAvAG4ALzHWvtkj/MeAM5Ya+/OpZUiRXP+/HL1d/58\n73O80Juba59z/nz7523bmLv99kSjvnnM8+sO0lGv+DxR8/x2A1dYa3cAHwbu7T7BGPM+4HVA9EMO\nREaJF2jdujc5eOGF9usbNy6P/MYIvn7M8yujqG7vTuAIgLX2uDHmRv9BY8wOYDtwP7AtlxaKDIOt\nW+HZ9nI1Ll5cHvl92cuWu7q7dsUOvW6a9pKdqPC7Ejjr+33RGFO11jaNMZuAjwK3AP8xrwaKFN66\nde2g81QqsHr15ZscOOoVUgq8fFTCHtRijLkX+J619pHO76ettdd1ft4H7AFeBF4BrAc+Yq39YtD1\nGo2GusYyUib37mX8hz/E/6DL5hVX0Fq1ihf+8A/5xf79oe+v1+s9X5+dnU3UHu96s7Ozl/1cBlNT\nU5Xos5ZFVX7HgJuBR4wxbwJ+4B2w1t4H3AdgjNkDbAsLPl8D47SvrxqNhtqXQinbt2FDe1XH/Hz7\n91qNVZ3pLhPARMDbvKrMm9cH7Xl+586dS9Uc73pTU1Opr+U3DH+3cUWF39eAm4wxxzq/7zXG3AbU\nrLUPdp2rqk7K59gx2LkTfvYzeOtbo6e77NpF7dFHez71LckXGLKf5+cZ9fl+oeFnrW0B7+96+ac9\nzjuUZaNEhsqxYytf88/tg+XpLkeOwIULiZ/6FvaA9CyUaf6gJjmLZMkb/KhW238qlfb/escg9hy/\nqEDKa6eXUa34PAo/kaz4R32bzfafNWuW5/dBrOkueW1cqlHgNoWfSF5Wr4bNm1PP78t6BUeW1x5m\nCj+RrHhL3i5cgBtucJ7f54WTf1cXyK87W+bA81P4iWQpaJ1vD0HLy7Ke1Kyw603P8BDJm/csj61b\nqa1ZQ6VS6fmoySSPrgxao5v1tJc9e/aM3NPdVPmJ5MF71ke1urzLc6XS3vS0I4turV+WYVeGKS+q\n/ESy5j3istlsh92FC+3wA+auuYbWnj2ZPJwcsqvwonZ5OXTo0MhNfVHlJ5K3ahXWr4drrkk91cWj\nKS/pKfxEsuZ/xOX69dFb23fJeiCk+7plDbtuCj+RPAQ94rKHPKa6dF9bgbeS7vmJ9Is36jszQ61W\nWzHq68lrl+asR4CHnSo/kTx1j/quW0ft0CHmfad4gZRm2yjN8YtP4SeSF2/UF5ZHfptNAMZXr2bu\n4sXUH5H3lJduo7TNlbq9Iv3Sebbv3J49iYLP687mOeUl6DNHkSo/kbzkNOrr1+/9/Eah4vMo/ETy\nFGPU15PXVJfu63vXcxkRTrrLdJEp/EQGqFarLW1pn8dUF//nuFyzTAMkCj+Rfli3Di5epNZqMd9q\nMT4+DsD8/PyKU/Oq8IKuX6bA89OAh0jevD3+mk3wHhXb2fF5fHycVquVeFeXbprj506Vn0gfzUF7\nje8f/VGswY9e/JVdP6e8jMp0F4WfSN68HZ4vXoTrr4+9rT1EB50nr8Cr1+tUq9WRqh4VfiL9EGOH\nZ4g/zaWfU16GveLz6J6fSEHU6/Wle3bdAyH+e3Z53L+Lmsycxf3IolH4ifTLzp3tSc8zMwCXbW5Q\nq9VYWFhYOtV7qHnWQecPubDAK8MAicJPpB927oR/+Adqzz9P5dAhKpXKiupubGws98ALUoaw66Z7\nfiID4lV3nrSrKHoNioTN6Stb2HVT5SfSD8eOwW//NnMvfzmtPXuW5vYl5dp9hXJWdS5U+Yn0y7Fj\nid866NHfXoZ9vp/CT6SAXO7R9fo5T6P2OEuFn8iA+ae2+Nf8ej/D4ALO+/3o0aMrzh3Wis+j8BPp\ns0qlEnlO92BIluJsaeU3KhWfJzT8jDFV4ADwBuAC8B5r7ZO+47cBdwGXgB8Cd1prW/k1V2T0eEGX\n5hkeUZIG3Cjv5xc12rsbuMJauwP4MHCvd8AYMwZ8DPgDa+0u4CXA2/JqqMioaLVal/3Ja7WG6w4v\nZR0Njgq/ncARAGvtceBG37HzwJuttd6ixdXAAiLSN1FB5ylrwIWJuud3JXDW9/uiMaZqrW12urfP\nAxhj9gHj1trHcmqnSGnF3dZeIeem0moF36IzxtwLfM9a+0jn99PW2ut8x6vAJ4CtwDt9VWBPjUZD\n9wNFQtTr9RWvLSwsMDY2tuL12dnZfjRpBa+Ns7Oz7NmzB4BDhw4NpC1+U1NT0SNJPlGV3zHgZuAR\nY8ybgB90Hb+fdvf3FteBjrxu6GYhzxvOWVD70ilS+8JGfP1TXLzfB1nN1Wo1ms0m586dA1h6zsjU\n1NRSWwf97zXJgExU+H0NuMkY401N39sZ4a0BJ4B3A98GvmGMAfi0tfZw7FaICDC4oHNZF+zxvz7M\nc/1Cw6+lPY7uAAAGKklEQVRTzb2/6+Wf+n5elXmLREqg1+2mflSmcULO403DGTWa5CwyIoKCzSXk\nyrjbi8JPZEi5bHbQrYwhF0ThJ1JQ/nBzWesbFGxlD7kgCj+RAer1vI6gzQ26KdTSUfiJDEjUBgeD\nnuISxn8fcVj39dNOziIDNj4+TqvV4sSJE0trfQexHC1sd2jvyXKjRJWfyICEra7KU5LpLt1GYa6f\nKj+RERJUvcV9glt35TmKz+1V5ScyJLrDy1+5xaGR4DaFn0hB1Ov1FQ8u94sa/QVNd4lD4ScyQC5b\n2nt6jf4q1JJT+IkUxNjY2NLOKcNmGKe7KPxEBsg/4lu0zQPCHnQ0Co+xVPiJlExYiCUNtWGq+DwK\nP5ER4TIaHCfUwu4vDnPF51H4iRRU2MYG3ZKGWpkHUBR+IgMWZ0v7MFE7vcjlFH4iBVXkjQ1GgZa3\niQyY9/Byb2ODvB5mLpdT+IlIIt3rhaenp5fm+w0DhZ9ICblugBB3c4Rhont+IkMqKIiCprhkPTG5\n+zrDNtdP4ScyYKtWraLZbK543XU7+yRcN0Dwfm80GiN3D1LhJzKkXB9F6XJ+GSn8RAZscXER6M9D\ny2WZBjxEpJQUfiJSSgo/EblM0qkvwzbPT/f8RArEW+frH+n1/+6ie1pL1LSXUdibLwmFn0gBxNnO\nPm+9pr54G62GTYvRPD8RSSyrzQyi9t4btb35ktA9P5EC8DY2KGsQDUJo5WeMqQIHgDcAF4D3WGuf\n9B2/GfgIcAn4vLX2czm2VUQkM1GV327gCmvtDuDDwL3eAWPMGuCTwE3A7wP/yRhzdV4NFRHJUlT4\n7QSOAFhrjwM3+o69Bjhprf21tfYi8Djwe7m0UkQkY1EDHlcCZ32/LxpjqtbaZufYr33HXgReknH7\nREqhe7R3fHx8xTQXl+d4uD7EyPUJbt7PR48eXXGs+/dhe3Zvxf/c0G7GmHuB71lrH+n8ftpae13n\n59cDH7fW/nHn908Cj1trvxp0vUajEfxhIiIpTE1NxZovFFX5HQNuBh4xxrwJ+IHv2E+AVxtjXgrM\n0+7y/vcsGycikpeoyq/C8mgvwF5gCqhZax80xrwN+Cjte4cPWWv/V87tFRHJRGj4iYiMKk1yFpFS\nUviJSCkp/ESklBR+IlJKuezqUvQ1wQ7tuw24q9O+HwJ3Wmv7MjIU1TbfeQ8AZ6y1d/ejXa7tM8b8\nLu1lkBXgn4A/s9b+pkDtuwX4S6BF+7+9z/arbb42TNOeI/uWrtcLsVY+pH0D+164tM933Om7kVfl\nV/Q1wWHtGwM+BvyBtXYX7VUrbytC23xtfB/wOtpf4H4L+3dXAR4AZqy1deD/AtcXpX0d3n97O4E/\nN8b0dVWSMeZDwIPA2q7Xi/C9CGvfoL8Xoe3zHXf+buQVfkVfExzWvvPAm6215zu/rwYWCtI2jDE7\ngO3A/bSrq34La98kcAb4oDHmW8BGa60tUPsALgIbgTHa//76/X8gJ4G3s/LvrgjfCwhu36C/F56g\n9sX+buQVfj3XBPuODXpNcGD7rLUta+3zAMaYfcC4tfaxIrTNGLOJ9qTyDzCY4IPwv9sJYAdwH/Dv\ngH9rjOnZNRlQ+6BdCTaAHwF/ba31n5u7zvLPSz0OFeF7Edi+AnwvQtuX5LuR107OZ4ENvt+9zRCg\n/RfsP7YB+Nec2hEkrH3efaNPAFuBdxSobbfSDpi/BV4BrDfG/KO19osFad8Z2tWLBTDGHKFdeX2z\nCO0zxmym/eX4LeAc8CVjzK3W2kf72L4gRfhehBrw9yJK7O9GXpXfMeCtAGFrgo0xV9Au7b+bUzuS\ntA/aZfNa4BZfmT/wtllr77PW3ti50ftx4OE+B19o+4CfAzVjzA2d3+u0K6x+CmvfOmARuNAJxOdo\nd4GLoAjfiyiD/F6ESvLdyKvy+xpwkzHmWOf3vZ2RIm9N8AeBv2d5TfAzObUjdvuAE8C7gW8D3zDG\nAHzaWnt40G2z1j7Yde4gBjyi/m7vAB7uDH4cs9b+XcHadwj4jjHmPO37Rwf73D5PC5ZGUIvyvQhs\nH4P/XoS2L8l3Q2t7RaSUNMlZREpJ4ScipaTwE5FSUviJSCkp/ESklBR+IlJKCj8RKaX/D0+mdB2k\nlP+mAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10a013048>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "What about decision space?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(5,5))\n",
      "for ind in dominators:\n",
      "    plt.plot(ind[0], ind[1], 'r.', alpha=0.5)\n",
      "for ind in dominated:\n",
      "    plt.plot(ind[0], ind[1], 'g.', alpha=0.5)\n",
      "for ind in others:\n",
      "    plt.plot(ind[0], ind[1], 'k.', ms=4)\n",
      "plt.plot(a_given_individual[0], a_given_individual[1], 'bo', ms=11);"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109e59be0>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Obtain the nondominated front"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "non_dom = tools.sortNondominated(example_pop, k=len(example_pop),  first_front_only=True)[0]"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(5,5))\n",
      "for ind in example_pop:\n",
      "    plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'k.', ms=4)\n",
      "for ind in non_dom:\n",
      "    plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'ro', alpha=0.74, ms=7)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109e59390>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
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     "source": [
      "# The Non-dominated Sorting Genetic Algorithm (NSGA-II)\n",
      "\n",
      "* NSGA-II algorithm is one of the pillars of the EMO field.\n",
      "    * Deb, K., Pratap, A., Agarwal, S., Meyarivan, T., *A fast and elitist multiobjective genetic algorithm: NSGA-II*, IEEE Transactions on Evolutionary Computation, vol.6, no.2, pp.182,197, Apr 2002 doi: [10.1109/4235.996017](http://dx.doi.org/10.1109/4235.996017).\n",
      "* Fitness assignment relies on the Pareto dominance relation:\n",
      "    1. Rank individuals according the dominance relations established between them. \n",
      "    2. Individuals with the same domination rank are then compared using a local crowding distance."
     ]
    },
    {
     "cell_type": "markdown",
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     "source": [
      "## NSGA-II fitness in detail\n",
      "\n",
      "* The first step consists in classifying the individuals in a series of categories $\\mathcal{F}_1,\\ldots,\\mathcal{F}_L$. \n",
      "* Each of these categories store individuals that are only dominated by the elements of the previous categories,\n",
      "$$\n",
      "\\begin{array}{rl}\n",
      "\t\\forall \\vec{x}\\in\\set{F}_i: &\\exists \\vec{y}\\in\\set{F}_{i-1} \\text{ such that } \\vec{y}\\dom\\vec{x},\\text{ and }\\\\ \n",
      "\t                            &\\not\\exists\\vec{z}\\in \\set{P}_t\\setminus\\left( \\set{F}_1\\cup\\ldots\\cup\\set{F}_{i-1}\n",
      "\t                            \\right)\\text{ that }\\vec{z}\\dom\\vec{x}\\,;\n",
      "\\end{array}\n",
      "$$\n",
      "with $\\mathcal{F}_1$ equal to $\\mathcal{P}_t^\\ast$, the set of non-dominated individuals of $\\mathcal{P}_t$.\n",
      "\n",
      "* After all individuals are ranked a local crowding distance is assigned to them. \n",
      "* The use of this distance primes individuals more isolated with respect to others. "
     ]
    },
    {
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     "source": [
      "## Crowding distance\n",
      "\n",
      "The assignment process goes as follows,\n",
      "\n",
      "* for each category set $\\set{F}_l$, having $f_l=|\\set{F}_l|$,\n",
      "    * for each individual $\\vec{x}_i\\in\\set{F}_l$, set $d_{i}=0$.\n",
      "    * for each objective function $m=1,\\ldots,M$,\n",
      "        * $\\vec{I}=\\mathrm{sort}\\left(\\set{F}_l,m\\right)$ (generate index vector).\n",
      "        * $d_{I_1}^{(l)}=d_{I_{f_l}}^{(l)}=\\infty$.\n",
      "        * for $i=2,\\ldots,f_l-1$,\n",
      "            * Update the remaining distances as,\n",
      "                $$\n",
      "                d_i = d_i + \\frac{f_m\\left(\\vec{x}_{I_{i+1}}\\right)-f_m\\left(\\vec{x}_{I_{i+1}}\\right)}\n",
      "\t\t\t                   {f_m\\left(\\vec{x}_{I_{1}}\\right)-f_m\\left(\\vec{x}_{I_{f_l}}\\right)}\\,.\n",
      "                $$\n",
      "\n",
      "Here the $\\mathrm{sort}\\left(\\set{F},m\\right)$ function produces an ordered index vector $\\vec{I}$ with respect to objective function $m$. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Sorting the population by rank and distance.\n",
      "\n",
      "* Having the individual ranks and their local distances they are sorted using the crowded comparison operator, stated as: \n",
      "    * An individual $\\vec{x}_i$ _is better than_ $\\vec{x}_j$ if:\n",
      "        * $\\vec{x}_i$ has a better rank: $\\vec{x}_i\\in\\set{F}_k$, $\\vec{x}_j\\in\\set{F}_l$ and $k<l$, or;\n",
      "        * if $k=l$ and $d_i>d_j$.\n",
      "        \n",
      "**Now we have key element of the the non-dominated sorting GA.**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## Implementing NSGA-II"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "toolbox = base.Toolbox()"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "Let's try DTLZ3, a more complex problem that DTLZ2 as it has many local Pareto-optimal fronts that run parallel to global one.\n",
      "\n",
      "* As in DTLZ2, the Pareto-optimal front lies in the first [orthant](http://en.wikipedia.org/wiki/Orthant) of a unit (radius 1) hypersphere located at the coordinate origin ($\\vec{0}$)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "toolbox.register(\"evaluate\", lambda ind: benchmarks.dtlz3(ind, 2))"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "toolbox.register(\"attr_float\", uniform, BOUND_LOW, BOUND_UP, NDIM)\n",
      "toolbox.register(\"individual\", tools.initIterate, creator.Individual, toolbox.attr_float)\n",
      "toolbox.register(\"population\", tools.initRepeat, list, toolbox.individual)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "toolbox.register(\"mate\", tools.cxSimulatedBinaryBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0)\n",
      "toolbox.register(\"mutate\", tools.mutPolynomialBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0, indpb=1.0/NDIM)\n",
      "toolbox.register(\"select\", tools.selNSGA2)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "Let's also use the `toolbox` to pass other configuration to our function. This will show itself usefull when performing massive experiments."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "toolbox.pop_size = 50\n",
      "toolbox.max_gen = 3000\n",
      "toolbox.mut_prob = 0.2"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## A compact NSGA-II implementation\n",
      "\n",
      "Storing all the required information in the `toolbox` and using DEAP's `algorithms.eaMuPlusLambda` function allows us to create a very compact -albeit not a 100% exact copy of the original- implementation of NSGA-II."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def nsga_ii(toolbox, stats=None, verbose=False):\n",
      "    pop = toolbox.population(n=toolbox.pop_size)\n",
      "    pop = toolbox.select(pop, len(pop))\n",
      "    return algorithms.eaMuPlusLambda(pop, toolbox, mu=toolbox.pop_size, \n",
      "                                     lambda_=toolbox.pop_size, \n",
      "                                     cxpb=1-toolbox.mut_prob,\n",
      "                                     mutpb=toolbox.mut_prob, \n",
      "                                     stats=stats, \n",
      "                                     ngen=toolbox.max_gen, \n",
      "                                     verbose=verbose)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## Running the algorithm"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "We are now ready to run our NSGA-II."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%time res, logbook = nsga_ii(toolbox)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 51.8 s, sys: 130 ms, total: 52 s\n",
        "Wall time: 52.2 s\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "We can now get the Pareto fronts in the results (`res`)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fronts = tools.emo.sortLogNondominated(res, len(res))"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## Resulting Pareto fronts"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_colors = ('b','r', 'g', 'm', 'y', 'k', 'c')\n",
      "fig, ax = plt.subplots(1, figsize=(4,4))\n",
      "for i,inds in enumerate(fronts):\n",
      "    par = [toolbox.evaluate(ind) for ind in inds]\n",
      "    df = pd.DataFrame(par)\n",
      "    df.plot(ax=ax, kind='scatter', label='Front ' + str(i+1), \n",
      "                 x=df.columns[0], y=df.columns[1], \n",
      "                 color=plot_colors[i % len(plot_colors)])\n",
      "plt.xlabel('$f_1(\\mathbf{x})$');plt.ylabel('$f_2(\\mathbf{x})$');"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1105f6b00>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "* Results are far from the optimum and in only one front.\n",
      "* It is better to make an animated plot of the evolution as it takes place."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## Animating the evolutionary process"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "We create a `stats` to store the individuals not only their objective function values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "stats = tools.Statistics()\n",
      "stats.register(\"pop\", copy.deepcopy)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "toolbox.max_gen = 4000 # we need more generations!"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "Re-run the algorithm to get the data necessary for plotting."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%time res, logbook = nsga_ii(toolbox, stats=stats)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "subslide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 1min 16s, sys: 564 ms, total: 1min 17s\n",
        "Wall time: 1min 19s\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from JSAnimation import IPython_display\n",
      "import matplotlib.colors as colors\n",
      "from matplotlib import animation"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def animate(frame_index, logbook):\n",
      "    'Updates all plots to match frame _i_ of the animation.'\n",
      "    ax.clear()    \n",
      "    fronts = tools.emo.sortLogNondominated(logbook.select('pop')[frame_index], \n",
      "                                           len(logbook.select('pop')[frame_index]))\n",
      "    for i,inds in enumerate(fronts):\n",
      "        par = [toolbox.evaluate(ind) for ind in inds]\n",
      "        df = pd.DataFrame(par)\n",
      "        df.plot(ax=ax, kind='scatter', label='Front ' + str(i+1), \n",
      "                 x=df.columns[0], y =df.columns[1], alpha=0.47,\n",
      "                 color=plot_colors[i % len(plot_colors)])\n",
      "        \n",
      "    ax.set_title('$t=$' + str(frame_index))\n",
      "    ax.set_xlabel('$f_1(\\mathbf{x})$');ax.set_ylabel('$f_2(\\mathbf{x})$')\n",
      "    return None"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(4,4))\n",
      "ax = fig.gca()\n",
      "anim = animation.FuncAnimation(fig, lambda i: animate(i, logbook), \n",
      "                               frames=len(logbook), interval=60, \n",
      "                               blit=True)\n",
      "anim"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "The previous animation makes the notebook too big for on-line viewing. To circumvent this, it is better to save the animation as video and upload it to YouTube."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "anim.save('nsgaii-dtlz3.mp4', fps=15, bitrate=-1, dpi=500)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import YouTubeVideo\n",
      "YouTubeVideo('Cm7r4cJq59s')"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "html": [
        "\n",
        "        <iframe\n",
        "            width=\"400\"\n",
        "            height=300\"\n",
        "            src=\"https://www.youtube.com/embed/Cm7r4cJq59s\"\n",
        "            frameborder=\"0\"\n",
        "            allowfullscreen\n",
        "        ></iframe>\n",
        "        "
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "<IPython.lib.display.YouTubeVideo at 0x110a47cf8>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "Here it is clearly visible how the algorithm \"jumps\" from one local-optimum to a better one as evolution takes place."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "# MOP benchmark problem toolkits\n",
      "\n",
      "Each problem instance is meant to test the algorithms with regard with a given feature: local optima, convexity, discontinuity, bias, or a combination of them.\n",
      "\n",
      "* [*ZDT1-6*](http://www.tik.ee.ethz.ch/sop/download/supplementary/testproblems/): Two-objective problems with a fixed number of decision variables.\n",
      "     * E. Zitzler, K. Deb, and L. Thiele. Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation, 8(2):173-195, 2000. ([pdf](http://www.tik.ee.ethz.ch/sop/publicationListFiles/zdt2000a.pdf))\n",
      "* [*DTLZ1-7*](http://www.tik.ee.ethz.ch/sop/download/supplementary/testproblems/): $m$-objective problems with $n$ variables.\n",
      "     * K. Deb, L. Thiele, M. Laumanns and E. Zitzler. Scalable Multi-Objective Optimization Test Problems. CEC 2002, p. 825 - 830, IEEE Press, 2002. ([pdf](http://www.tik.ee.ethz.ch/sop/publicationListFiles/dtlz2002a.pdf))"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "* [*CEC'09*](http://dces.essex.ac.uk/staff/zhang/moeacompetition09.htm): Two- and three- objective problems that very complex Pareto sets.\n",
      "    * Zhang, Q., Zhou, A., Zhao, S., & Suganthan, P. N. (2009). Multiobjective optimization test instances for the CEC 2009 special session and competition. In 2009 IEEE Congress on Evolutionary Computation (pp. 1\u201330). ([pdf](http://dces.essex.ac.uk/staff/zhang/MOEAcompetition/cec09testproblem0904.pdf.pdf))\n",
      "* [*WFG1-9*](http://www.wfg.csse.uwa.edu.au/publications.html#toolkit): $m$-objective problems with $n$ variables, very complex.\n",
      "    * Huband, S., Hingston, P., Barone, L., & While, L. (2006). A review of multiobjective test problems and a scalable test problem toolkit. IEEE Transactions on Evolutionary Computation, 10(5), 477\u2013506. doi:10.1109/TEVC.2005.861417"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "DEAP still lacks some of these problems so I will grab the DTLZ5, DTLZ6 and DTLZ7 problems from inspyred and adapt them for DEAP. \n",
      "\n",
      "*Note to self*: sent these problems to the DEAP guys."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "DTLZ5 and DTLZ6 have an $m-1$-dimensional Pareto-optimal front.\n",
      "* This means that in 3D the Pareto optimal front is a 2D curve.\n",
      "<div align='center'><img src='http://www.cs.cinvestav.mx/~emoobook/apendix-e/galeria4/dtlz5a.jpg' width=\"38%\" align='center'/></div>\n",
      "* In two dimensions the front is **a point**."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def dtlz5(ind, n_objs):\n",
      "    from functools import reduce\n",
      "    g = lambda x: sum([(a - 0.5)**2 for a in x])\n",
      "    gval = g(ind[n_objs-1:])\n",
      "    \n",
      "    theta = lambda x: math.pi / (4.0 * (1 + gval)) * (1 + 2 * gval * x)\n",
      "    fit = [(1 + gval) * math.cos(math.pi / 2.0 * ind[0]) *\n",
      "           reduce(lambda x,y: x*y, [math.cos(theta(a)) for a in ind[1:]])]\n",
      "    for m in reversed(range(1, n_objs)):\n",
      "        if m == 1:\n",
      "            fit.append((1 + gval) * math.sin(math.pi / 2.0 * ind[0]))\n",
      "        else:\n",
      "            fit.append((1 + gval) * math.cos(math.pi / 2.0 * ind[0]) *\n",
      "                       reduce(lambda x,y: x*y, [math.cos(theta(a)) for a in ind[1:m-1]], 1) *\n",
      "                       math.sin(theta(ind[m-1])))\n",
      "    return fit"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def dtlz6(ind, n_objs):\n",
      "    from functools import reduce\n",
      "    gval = sum([a**0.1 for a in ind[n_objs-1:]])\n",
      "    theta = lambda x: math.pi / (4.0 * (1 + gval)) * (1 + 2 * gval * x)\n",
      "    fit = [(1 + gval) * math.cos(math.pi / 2.0 * ind[0]) * \n",
      "           reduce(lambda x,y: x*y, [math.cos(theta(a)) for a in ind[1:]])]\n",
      "    for m in reversed(range(1, n_objs)):\n",
      "        if m == 1:\n",
      "            fit.append((1 + gval) * math.sin(math.pi / 2.0 * ind[0]))\n",
      "        else:\n",
      "            fit.append((1 + gval) * math.cos(math.pi / 2.0 * ind[0]) *\n",
      "                       reduce(lambda x,y: x*y, [math.cos(theta(a)) for a in ind[1:m-1]], 1) *\n",
      "                       math.sin(theta(ind[m-1])))\n",
      "    return fit            "
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "DTLZ7 has many disconnected Pareto-optimal fronts.\n",
      "\n",
      "<div align='center'><img src='http://www.cs.cinvestav.mx/~emoobook/apendix-e/galeria4/dtlz7b.jpg' width=\"38%\" align='center'/></div>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def dtlz7(ind, n_objs):\n",
      "    gval = 1 + 9.0 / len(ind[n_objs-1:]) * sum([a for a in ind[n_objs-1:]])\n",
      "    fit = [ind for ind in ind[:n_objs-1]]\n",
      "    fit.append((1 + gval) * (n_objs - sum([a / (1.0 + gval) * (1 + math.sin(3 * math.pi * a)) for a in ind[:n_objs-1]])))\n",
      "    return fit"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "How does our NSGA-II behaves when faced with different benchmark problems?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "problem_instances = {'ZDT1': benchmarks.zdt1, 'ZDT2': benchmarks.zdt2,\n",
      "                     'ZDT3': benchmarks.zdt3, 'ZDT4': benchmarks.zdt4,\n",
      "                     'DTLZ1': lambda ind: benchmarks.dtlz1(ind,2),\n",
      "                     'DTLZ2': lambda ind: benchmarks.dtlz2(ind,2),\n",
      "                     'DTLZ3': lambda ind: benchmarks.dtlz3(ind,2),\n",
      "                     'DTLZ4': lambda ind: benchmarks.dtlz4(ind,2, 100),\n",
      "                     'DTLZ5': lambda ind: dtlz5(ind,2),\n",
      "                     'DTLZ6': lambda ind: dtlz6(ind,2),\n",
      "                     'DTLZ7': lambda ind: dtlz7(ind,2)}"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "toolbox.max_gen = 1000\n",
      "\n",
      "stats = tools.Statistics(lambda ind: ind.fitness.values)\n",
      "stats.register(\"obj_vals\", np.copy)\n",
      "\n",
      "def run_problem(toolbox, problem):\n",
      "    toolbox.register('evaluate', problem)\n",
      "    return nsga_ii(toolbox, stats=stats)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 11
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "Running NSGA-II solving all problems. Now it takes longer."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%time results = {problem: run_problem(toolbox, problem_instances[problem]) for problem in problem_instances}"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 3min 16s, sys: 675 ms, total: 3min 17s\n",
        "Wall time: 3min 18s\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Creating this animation takes more programming effort."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class MultiProblemAnimation:\n",
      "    def init(self, fig, results):\n",
      "        self.results = results\n",
      "        self.axs = [fig.add_subplot(3,4,i+1) for i in range(len(results))]\n",
      "        self.plots =[]\n",
      "        for i, problem in enumerate(sorted(results)):\n",
      "            (res, logbook) = self.results[problem]\n",
      "            pop = pd.DataFrame(data=logbook.select('obj_vals')[0])\n",
      "            plot = self.axs[i].plot(pop[0], pop[1], 'b.', alpha=0.47)[0]\n",
      "            self.plots.append(plot)\n",
      "        fig.tight_layout()\n",
      "            \n",
      "    def animate(self, t):\n",
      "        'Updates all plots to match frame _i_ of the animation.'\n",
      "        for i, problem in enumerate(sorted(results)):\n",
      "            #self.axs[i].clear()\n",
      "            (res, logbook) = self.results[problem]\n",
      "            pop = pd.DataFrame(data=logbook.select('obj_vals')[t])\n",
      "            self.plots[i].set_data(pop[0], pop[1])\n",
      "            self.axs[i].set_title(problem + '; $t=' + str(t)+'$') \n",
      "            self.axs[i].set_xlim((0, max(1,pop.max()[0])))\n",
      "            self.axs[i].set_ylim((0, max(1,pop.max()[1])))\n",
      "        return self.axs"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mpa = MultiProblemAnimation()"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(14,6))\n",
      "anim = animation.FuncAnimation(fig, mpa.animate, init_func=mpa.init(fig,results), \n",
      "                               frames=toolbox.max_gen, interval=60, blit=True)\n",
      "anim"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Saving the animation as video and uploading it to youtube."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "anim.save('nsgaii-benchmarks.mp4', fps=15, bitrate=-1, dpi=500)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "YouTubeVideo('8t-aWcpDH0U')"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "html": [
        "\n",
        "        <iframe\n",
        "            width=\"400\"\n",
        "            height=300\"\n",
        "            src=\"https://www.youtube.com/embed/8t-aWcpDH0U\"\n",
        "            frameborder=\"0\"\n",
        "            allowfullscreen\n",
        "        ></iframe>\n",
        "        "
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 41,
       "text": [
        "<IPython.lib.display.YouTubeVideo at 0x110a79d68>"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "* It is interesting how the algorithm deals with each problem: clearly some problems are harder than others.\n",
      "* In some cases it \"hits\" the Pareto front and then slowly explores it.\n",
      "\n",
      "**Read more about this in the class materials.**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "# Experiment design and reporting results\n",
      "\n",
      "* Watching an animation of an EMO algorithm solve a problem is certainly fun. \n",
      "* It also allows us to understand many particularities of the problem being solved.\n",
      "* But, as [Carlos Coello](http://delta.cs.cinvestav.mx/~ccoello/) would say, we are *not* in an art appreciation class.\n",
      "* We should follow the key concepts provided by the [scientific method](http://en.wikipedia.org/wiki/Scientific_method).\n",
      "* I urge you to study the [experimental design](http://en.wikipedia.org/wiki/Design_of_experiments) topic in depth as it is an essential knowledge.\n",
      "\n",
      "**Evolutionary algorithms are stochastic algorithms, therefore their results must be assessed by repeating experiments until you reach an statistically valid conclusion.** "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## An illustrative simple/sample experiment\n",
      "\n",
      "Let's make a relatively simple experiment:\n",
      "\n",
      "* **Hypothesis**: The mutation probability of NSGA-II matters when solving the DTLZ3 problem.\n",
      "* **Procedure**: We must perform an experiment testing different mutation probabilities while keeping the other parameters constant."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### Notation\n",
      "\n",
      "As usual we need to establish some notation:\n",
      "\n",
      "* *Multi-objective problem* (or just *problem*): A multi-objective optimization problem, as defined above.\n",
      "* *MOEA*: An evolutionary computation method used to solve multi-objective problems.\n",
      "* *Experiment*: a combination of problem and MOEA and a set of values of their parameters.\n",
      "* *Experiment run*: The result of running an experiment.\n",
      "* We will use `toolbox` instances to define experiments. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "We start by creating a `toolbox` that will contain the configuration that will be shared across all experiments."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "toolbox = base.Toolbox()"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "BOUND_LOW, BOUND_UP = 0.0, 1.0\n",
      "NDIM = 30\n",
      "\n",
      "# the explanation of this... a few lines bellow\n",
      "def eval_helper(ind):\n",
      "    return benchmarks.dtlz3(ind, 2)\n",
      "\n",
      "toolbox.register(\"evaluate\", eval_helper)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def uniform(low, up, size=None):\n",
      "    try:\n",
      "        return [random.uniform(a, b) for a, b in zip(low, up)]\n",
      "    except TypeError:\n",
      "        return [random.uniform(a, b) for a, b in zip([low] * size, [up] * size)]\n",
      "\n",
      "toolbox.register(\"attr_float\", uniform, BOUND_LOW, BOUND_UP, NDIM)\n",
      "toolbox.register(\"individual\", tools.initIterate, creator.Individual, toolbox.attr_float)\n",
      "toolbox.register(\"population\", tools.initRepeat, list, toolbox.individual)\n",
      "\n",
      "toolbox.register(\"mate\", tools.cxSimulatedBinaryBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0)\n",
      "toolbox.register(\"mutate\", tools.mutPolynomialBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0, indpb=1.0/NDIM)\n",
      "\n",
      "toolbox.register(\"select\", tools.selNSGA2)\n",
      "\n",
      "toolbox.pop_size = 200\n",
      "toolbox.max_gen = 500"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "We add a `experiment_name` to `toolbox` that we will fill up later on."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "toolbox.experiment_name = \"$P_\\mathrm{mut}=\""
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "We can now replicate this toolbox instance and then modify the mutation probabilities."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "mut_probs = (0.05, 0.15, 0.3)\n",
      "number_of_experiments = len(mut_probs)\n",
      "toolboxes=list([copy.copy(toolbox) for _ in range(number_of_experiments)])"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "Now `toolboxes` is a list of copies of the same toolbox. One for each experiment configuration (population size)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "...but we still have to set the population sizes in the elements of `toolboxes`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i, toolbox in enumerate(toolboxes):\n",
      "    toolbox.mut_prob = mut_probs[i]\n",
      "    toolbox.experiment_name = toolbox.experiment_name + str(mut_probs[i]) +'$'"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 89
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for toolbox in toolboxes:\n",
      "    print(toolbox.experiment_name, toolbox.mut_prob)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "$P_\\mathrm{mut}=0.05$ 0.05\n",
        "$P_\\mathrm{mut}=0.15$ 0.15\n",
        "$P_\\mathrm{mut}=0.3$ 0.3\n"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## Experiment design\n",
      "\n",
      "As we are dealing with stochastic methods their results should be reported relying on an statistical analysis.\n",
      "\n",
      "* A given  experiment (a `toolbox` instance in our case) should be repeated a *sufficient* amount of times. \n",
      "* In theory, the more runs the better, but how much in enough? In practice, we could say that about *30* runs is enough.\n",
      "* The non-dominated fronts produced by each experiment run should be compared to each other. \n",
      "* We have seen in class that a number of *performance indicators*, like the *hypervolume*, *additive* and *multiplicative epsilon indicators*, among others, have been proposed for that task.\n",
      "* We can use statistical visualizations like [box plots](http://en.wikipedia.org/wiki/Box_plot) or [violin plots](http://en.wikipedia.org/wiki/Violin_plot) to make a visual assessment of the indicator values produced in each run.\n",
      "* We must apply a set of [statistical hypothesis tests](http://en.wikipedia.org/wiki/Statistical_hypothesis_testing) in order to reach an statistically valid judgment of the results of an algorithms. \n",
      "\n",
      "\n",
      "_Note_: I personally like the number [42](http://en.wikipedia.org/wiki/42_%28number%29) as it is the [answer to The Ultimate Question of Life, the Universe, and Everything](http://en.wikipedia.org/wiki/Phrases_from_The_Hitchhiker%27s_Guide_to_the_Galaxy#Answer_to_the_Ultimate_Question_of_Life.2C_the_Universe.2C_and_Everything_.2842.29)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "number_of_runs = 42"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 49
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### Running experiments in parallel \n",
      "As we are now solving more demanding problems it would be nice to make our algorithms to run in parallel and profit from modern multi-core CPUs.\n",
      "\n",
      "* In DEAP it is very simple to parallelize an algorithm (if it has been properly programmed) by providing a parallel `map()` function throu the `toolbox`.\n",
      "* Local parallelization can be achieved using Python's [`multiprocessing`](https://docs.python.org/2/library/multiprocessing.html) or [`concurrent.futures`](https://docs.python.org/3/library/concurrent.futures.html) modules.\n",
      "* Cluster parallelization can be achived using IPython Parallel or [SCOOP](http://en.wikipedia.org/wiki/Python_SCOOP_%28software%29), that seems to be recommended by the DEAP guys as it was part of it.\n",
      "\n",
      "*Note*: While preparing this notebook I why process-based parallelization is much faster than thread-based parallelization. You can have a very good summary about this in http://blog.liang2.tw/2014-handy-dist-computing/."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### Progress feedback\n",
      "\n",
      "* Another issue with these long experiments has to do being patient.\n",
      "* A little bit of feedback on the experiment execution would be cool.\n",
      "* We can use the integer progress bar from [IPython widgets](http://nbviewer.ipython.org/github/jvns/ipython/blob/master/examples/Interactive%20Widgets/Index.ipynb) and report every time an experiment run is finished."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.html import widgets\n",
      "from IPython.display import display"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "progress_bar = widgets.IntProgressWidget(description=\"Starting...\", \n",
      "                                         max=len(toolboxes)*number_of_runs)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 51
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### A side-effect of using process-based parallelization\n",
      "\n",
      "Process-based parallelization based on `multiprocessing` requires that the parameters passed to `map()` be [pickleable](https://docs.python.org/3.4/library/pickle.html).\n",
      "\n",
      "* The direct consequence is that `lambda` functions can not be directly used. \n",
      "* This is will certainly ruin the party to all `lambda` fans out there! *-me included*.\n",
      "* Hence we need to write some wrapper functions instead.\n",
      "* But, that wrapper function can take care of filtering out dominated individuals in the results."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def run_algo_wrapper(toolboox):\n",
      "    result,a = nsga_ii(toolbox)\n",
      "    pareto_sets = tools.emo.sortLogNondominated(result, len(result))\n",
      "    return pareto_sets[0]"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "<div class=\"alert alert-info\" role=\"alert\">\n",
      "Ideally, I would had ran this code at this point, but it is not working. Sometimes the `for future in...` loop never ends. I don't have much time to look into it, but if you have any idea I would appreciate it.  \n",
      "</div>\n",
      "\n",
      "```python\n",
      "%%time\n",
      "import concurrent.futures\n",
      "display(progress_bar)\n",
      "\n",
      "results = {toolbox.experiment_name:[] for toolbox in toolboxes}\n",
      "with concurrent.futures.ProcessPoolExecutor() as executor:\n",
      "    # Submit all the tasks...\n",
      "    futures = {executor.submit(run_algo_wrapper, toolbox): toolbox\n",
      "               for _ in range(number_of_runs)\n",
      "               for toolbox in toolboxes}\n",
      "    \n",
      "    # ...and wait for them to finish.\n",
      "    for future in concurrent.futures.as_completed(futures):\n",
      "        tb = futures[future]\n",
      "        results[tb.experiment_name].append(future.result())\n",
      "        progress_bar.value +=1\n",
      "        progress_bar.description = \"Finished %03d of %03d:\" % (progress_bar.value, progress_bar.max)\n",
      "```"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "# All set! Run the experiments..."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "This is not a perfect implementation but... works!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%time\n",
      "from multiprocessing import Pool\n",
      "display(progress_bar)\n",
      "\n",
      "results = {}\n",
      "pool = Pool()\n",
      "for toolbox in toolboxes:\n",
      "    results[toolbox.experiment_name] = pool.map(run_algo_wrapper, [toolbox] * number_of_runs)\n",
      "    progress_bar.value +=number_of_runs\n",
      "    progress_bar.description = \"Finished %03d of %03d:\" % (progress_bar.value, progress_bar.max)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 3.2 s, sys: 781 ms, total: 3.98 s\n",
        "Wall time: 1h 31min 9s\n"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "As you can see, even this relatively small experiment took lots of time!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "As running the experiments takes so long, lets save the results so we can use them whenever we want."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pickle"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pickle.dump(results, open('nsga_ii_dtlz3-results.pickle', 'wb'), \n",
      "            pickle.HIGHEST_PROTOCOL)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 112
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 55
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 129
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "In case you need it, this file is included in the github repository.\n",
      "\n",
      "To load the results we would just have to:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "loaded_results = pickle.load(open('nsga_ii_dtlz3-results.pickle', 'rb'))\n",
      "#results = loaded_results # <-- uncomment if needed"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 129,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 56
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 129,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "`results` is a dictionary, but a pandas `DataFrame` is a more handy container for the results."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "res = pd.DataFrame(loaded_results)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 129,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 57
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 129,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Headers may come out unsorted. Let's fix that first. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "res.head()"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 129,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "subslide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
        "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
        "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> [[1.0, 0.5000269727348605, 0.4999616400061205,...</td>\n",
        "      <td> [[0.9999999999999867, 0.4001150913352416, 0.40...</td>\n",
        "      <td> [[0.9999999999999996, 0.5000103341990221, 0.59...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> [[0.9999999999999996, 0.5000347245740564, 0.50...</td>\n",
        "      <td> [[0.9999999999999994, 0.3000864089066496, 0.50...</td>\n",
        "      <td> [[0.9999999999999021, 0.4004161957652541, 0.49...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> [[0.999999999813255, 0.5999721288215643, 0.499...</td>\n",
        "      <td> [[0.9999999999999981, 0.4995172500410508, 0.49...</td>\n",
        "      <td> [[0.9999999999999997, 0.4001590675284601, 0.50...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> [[0.9999999998399098, 0.4998310912965175, 0.49...</td>\n",
        "      <td> [[0.9999999999415495, 0.5000078089803229, 0.39...</td>\n",
        "      <td> [[0.9999999999999546, 0.5000090989133338, 0.39...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> [[0.9999999999999997, 0.5011132736209546, 0.50...</td>\n",
        "      <td> [[0.9999999999997499, 0.50003632075969, 0.5001...</td>\n",
        "      <td> [[1.0, 0.49942156718161346, 0.4998754336732803...</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 58,
       "text": [
        "                               $P_\\mathrm{mut}=0.05$  \\\n",
        "0  [[1.0, 0.5000269727348605, 0.4999616400061205,...   \n",
        "1  [[0.9999999999999996, 0.5000347245740564, 0.50...   \n",
        "2  [[0.999999999813255, 0.5999721288215643, 0.499...   \n",
        "3  [[0.9999999998399098, 0.4998310912965175, 0.49...   \n",
        "4  [[0.9999999999999997, 0.5011132736209546, 0.50...   \n",
        "\n",
        "                               $P_\\mathrm{mut}=0.15$  \\\n",
        "0  [[0.9999999999999867, 0.4001150913352416, 0.40...   \n",
        "1  [[0.9999999999999994, 0.3000864089066496, 0.50...   \n",
        "2  [[0.9999999999999981, 0.4995172500410508, 0.49...   \n",
        "3  [[0.9999999999415495, 0.5000078089803229, 0.39...   \n",
        "4  [[0.9999999999997499, 0.50003632075969, 0.5001...   \n",
        "\n",
        "                                $P_\\mathrm{mut}=0.3$  \n",
        "0  [[0.9999999999999996, 0.5000103341990221, 0.59...  \n",
        "1  [[0.9999999999999021, 0.4004161957652541, 0.49...  \n",
        "2  [[0.9999999999999997, 0.4001590675284601, 0.50...  \n",
        "3  [[0.9999999999999546, 0.5000090989133338, 0.39...  \n",
        "4  [[1.0, 0.49942156718161346, 0.4998754336732803...  "
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "res = res.reindex_axis([toolbox.experiment_name for toolbox in toolboxes], axis=1)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 129,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "res.head()"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 129,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
        "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
        "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> [[1.0, 0.5000269727348605, 0.4999616400061205,...</td>\n",
        "      <td> [[0.9999999999999867, 0.4001150913352416, 0.40...</td>\n",
        "      <td> [[0.9999999999999996, 0.5000103341990221, 0.59...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> [[0.9999999999999996, 0.5000347245740564, 0.50...</td>\n",
        "      <td> [[0.9999999999999994, 0.3000864089066496, 0.50...</td>\n",
        "      <td> [[0.9999999999999021, 0.4004161957652541, 0.49...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> [[0.999999999813255, 0.5999721288215643, 0.499...</td>\n",
        "      <td> [[0.9999999999999981, 0.4995172500410508, 0.49...</td>\n",
        "      <td> [[0.9999999999999997, 0.4001590675284601, 0.50...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> [[0.9999999998399098, 0.4998310912965175, 0.49...</td>\n",
        "      <td> [[0.9999999999415495, 0.5000078089803229, 0.39...</td>\n",
        "      <td> [[0.9999999999999546, 0.5000090989133338, 0.39...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> [[0.9999999999999997, 0.5011132736209546, 0.50...</td>\n",
        "      <td> [[0.9999999999997499, 0.50003632075969, 0.5001...</td>\n",
        "      <td> [[1.0, 0.49942156718161346, 0.4998754336732803...</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 60,
       "text": [
        "                               $P_\\mathrm{mut}=0.05$  \\\n",
        "0  [[1.0, 0.5000269727348605, 0.4999616400061205,...   \n",
        "1  [[0.9999999999999996, 0.5000347245740564, 0.50...   \n",
        "2  [[0.999999999813255, 0.5999721288215643, 0.499...   \n",
        "3  [[0.9999999998399098, 0.4998310912965175, 0.49...   \n",
        "4  [[0.9999999999999997, 0.5011132736209546, 0.50...   \n",
        "\n",
        "                               $P_\\mathrm{mut}=0.15$  \\\n",
        "0  [[0.9999999999999867, 0.4001150913352416, 0.40...   \n",
        "1  [[0.9999999999999994, 0.3000864089066496, 0.50...   \n",
        "2  [[0.9999999999999981, 0.4995172500410508, 0.49...   \n",
        "3  [[0.9999999999415495, 0.5000078089803229, 0.39...   \n",
        "4  [[0.9999999999997499, 0.50003632075969, 0.5001...   \n",
        "\n",
        "                                $P_\\mathrm{mut}=0.3$  \n",
        "0  [[0.9999999999999996, 0.5000103341990221, 0.59...  \n",
        "1  [[0.9999999999999021, 0.4004161957652541, 0.49...  \n",
        "2  [[0.9999999999999997, 0.4001590675284601, 0.50...  \n",
        "3  [[0.9999999999999546, 0.5000090989133338, 0.39...  \n",
        "4  [[1.0, 0.49942156718161346, 0.4998754336732803...  "
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 129,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## A first glace at the results"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = res.applymap(lambda pop: [toolbox.evaluate(ind) for ind in pop])\n",
      "plt.figure(figsize=(15,3))\n",
      "for i, col in enumerate(a.columns):\n",
      "    plt.subplot(1,len(a.columns), i+1)\n",
      "    for pop in a[col]:\n",
      "        x = pd.DataFrame(data= pop)\n",
      "        plt.scatter(x[0], x[1], alpha=0.5)\n",
      "    plt.title(col)   "
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 129
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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yAVi1Kp8xY5poby/AMJKYPv12ioqKgEQUxY7F4gMi0HXQ9Sp0fSoej0pLi4LH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9VoJEQMyIc6MnN7cZOTltKSgYTFJSH154YS+urqNp0WIyycn5XLw4h5iYvooachwhLZXYqvgs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\nn30PHo+HuDgbNls0zz9/A6mpqeF9tLW1sWjRgwA88cS3cDqd4e1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       "text": [
        "<matplotlib.figure.Figure at 0x1134c7c18>"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 129,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "The local Pareto-optimal fronts are clearly visible!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 129,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## Calculating performance indicators\n",
      "\n",
      "* As already mentioned, we need to evaluate the quality of the solutions produced in every execution of the algorithm. \n",
      "* We will use the hypervolumne indicator for that.\n",
      "* We already filtered each population a leave only the non-dominated individuals."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 129,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Calculating *nadir point*: an individual that is \u201cworse\u201d than any other individual in each of the objectives."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def calculate_nadir(results):\n",
      "    alldata = np.concatenate(np.concatenate(results.values))\n",
      "    obj_vals = [toolbox.evaluate(ind) for ind in alldata]\n",
      "    return np.max(obj_vals, axis=0)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 129
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nadir = calculate_nadir(res)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 143
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nadir"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 143,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 64,
       "text": [
        "array([ 24.1078374 ,  23.24556811])"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 143,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "We can now compute the hypervolume of the Pareto-optimal fronts yielded by each algorithm run."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import deap.benchmarks.tools as bt"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 143
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 65
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hypervols = res.applymap(lambda pop: bt.hypervolume(pop, nadir))"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 143
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 66
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hypervols.head()"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 148,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
        "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
        "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 479.299366</td>\n",
        "      <td> 471.090265</td>\n",
        "      <td> 462.265758</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 465.688953</td>\n",
        "      <td> 444.166523</td>\n",
        "      <td> 500.285145</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 493.253702</td>\n",
        "      <td> 538.765728</td>\n",
        "      <td> 461.301381</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 493.875035</td>\n",
        "      <td> 452.831973</td>\n",
        "      <td> 506.646024</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 491.986397</td>\n",
        "      <td> 532.318474</td>\n",
        "      <td> 417.450301</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 67,
       "text": [
        "   $P_\\mathrm{mut}=0.05$  $P_\\mathrm{mut}=0.15$  $P_\\mathrm{mut}=0.3$\n",
        "0             479.299366             471.090265            462.265758\n",
        "1             465.688953             444.166523            500.285145\n",
        "2             493.253702             538.765728            461.301381\n",
        "3             493.875035             452.831973            506.646024\n",
        "4             491.986397             532.318474            417.450301"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 148,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "##\u00a0How can we interpret the indicators?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 150
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "###\u00a0Option A: Tabular form"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hypervols.describe()"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 150,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
        "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
        "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>count</th>\n",
        "      <td>  42.000000</td>\n",
        "      <td>  42.000000</td>\n",
        "      <td>  42.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>mean</th>\n",
        "      <td> 462.425110</td>\n",
        "      <td> 444.683926</td>\n",
        "      <td> 457.372139</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>std</th>\n",
        "      <td>  85.074852</td>\n",
        "      <td>  67.852181</td>\n",
        "      <td>  68.171960</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>min</th>\n",
        "      <td> 211.210104</td>\n",
        "      <td> 261.538491</td>\n",
        "      <td> 136.654403</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>25%</th>\n",
        "      <td> 446.959790</td>\n",
        "      <td> 407.811816</td>\n",
        "      <td> 437.208398</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>50%</th>\n",
        "      <td> 493.564368</td>\n",
        "      <td> 449.807904</td>\n",
        "      <td> 462.348260</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>75%</th>\n",
        "      <td> 515.485198</td>\n",
        "      <td> 495.389646</td>\n",
        "      <td> 496.541831</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>max</th>\n",
        "      <td> 552.279112</td>\n",
        "      <td> 539.961884</td>\n",
        "      <td> 546.582980</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 68,
       "text": [
        "       $P_\\mathrm{mut}=0.05$  $P_\\mathrm{mut}=0.15$  $P_\\mathrm{mut}=0.3$\n",
        "count              42.000000              42.000000             42.000000\n",
        "mean              462.425110             444.683926            457.372139\n",
        "std                85.074852              67.852181             68.171960\n",
        "min               211.210104             261.538491            136.654403\n",
        "25%               446.959790             407.811816            437.208398\n",
        "50%               493.564368             449.807904            462.348260\n",
        "75%               515.485198             495.389646            496.541831\n",
        "max               552.279112             539.961884            546.582980"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 150,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "###\u00a0Option B: Visualization"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(15,3))\n",
      "plt.subplot(1,2,1, title='Violin plots of NSGA-II with $P_{\\mathrm{mut}}$')\n",
      "seaborn.violinplot(hypervols, alpha=0.74)\n",
      "plt.ylabel('Hypervolume'); plt.xlabel('Mutation probabilities')\n",
      "plt.subplot(1,2,2, title='Box plots of NSGA-II with $P_{\\mathrm{mut}}$')\n",
      "seaborn.boxplot(hypervols, alpha=0.74)\n",
      "plt.ylabel('Hypervolume'); plt.xlabel('Mutation probabilities');"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 150,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 69,
       "text": [
        "<matplotlib.text.Text at 0x1173910f0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gQHxwML2DgjhwIo8tWUf47LPP+Pqrrxg2bBhXjBtH586dmzwuAVrrCuC28zyU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\nWA5cCnzVzNQ5t5+KigrWrFnD2rVrdRdPRATdycsqUyafwvb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XIPsn28E++7l9ktOdwN+Z\n2QLgSeApd78V2ExwpVVERDJPOVI5UnKMijzJdb3J6McEbewHaoby+fD1XwFb+ix/nKBJiBE07fi9\nmT1D0FG9xMzKgKeA1WZ2E4f7KtQQJK0fmNkrBB3abxwktsGae8w2s43h/v+sz6hnvSN1tRM0q/kn\nM3sZ+GT4vHedcWFTkH8GrnH3LoJ+AP9qZr8CriFIqjPD9R34KbAR+E93/+++++sTa9+YB/rs+4CP\nAv9hZi8BZwF/GTaJ+TXwSvi5tgOPDfLZRUQkPZQjlSMlR8USieGaFItIOpnZz4HPuftzmY5FREQk\nSpQjRZKjO3kiIiIiIiI5RHfyREREREREcoju5ImIiIiIiOQQFXkiIiIiIiI5REWeiIiIiIhIDlGR\nJyIiIiIikkNU5ImIiIiIiOQQFXkiIiIiIiI55P8DWUs3juzijlcAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x116939f98>"
       ]
      }
     ],
     "prompt_number": 69
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 150,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## Option C: Statistical hypothesis test"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 150,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "* Choosing the correct statistical test is essential to properly report the results.\n",
      "* [Nonparametric statistics](http://en.wikipedia.org/wiki/Nonparametric_statistics) can lend a helping hand.\n",
      "* [Parametric statistics](http://en.wikipedia.org/wiki/Parametric_statistics) could be a better choice in some cases. \n",
      "* Parametric statistics require that *all* data follow a known distribution (frequently a normal one).\n",
      "* Some tests -like the [normality test](http://en.wikipedia.org/wiki/Normality_test)- can be apply to verify that data meet the parametric stats requirements.\n",
      "* In my experience that is very unlikely that all your EMO result meet those characteristics."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 150,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "We start by writing a function that helps us tabulate the results of the application of an statistical hypothesis test."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import itertools\n",
      "import scipy.stats as stats"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 150
      },
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 70
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def compute_stat_matrix(data, stat_func, alpha=0.05):\n",
      "    '''A function that applies `stat_func` to all combinations of columns in `data`.\n",
      "    Returns a squared matrix with the p-values'''\n",
      "    p_values = pd.DataFrame(columns=data.columns, index=data.columns)\n",
      "    for a,b in itertools.combinations(data.columns,2):\n",
      "        s,p = stat_func(data[a], data[b]) \n",
      "        p_values[a].ix[b] = p\n",
      "        p_values[b].ix[a] = p\n",
      "    return p_values"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 150,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [],
     "prompt_number": 71
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 150,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "The [Kruskal-Wallis H-test](http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.kruskal.html) tests the null hypothesis that the population median of all of the groups are equal.\n",
      "\n",
      "* It is a non-parametric version of [ANOVA](http://en.wikipedia.org/wiki/Analysis_of_variance). \n",
      "* The test works on 2 or more independent samples, which may have different sizes. \n",
      "* Note that rejecting the null hypothesis does not indicate which of the groups differs. \n",
      "* Post-hoc comparisons between groups are required to determine which groups are different."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "stats.kruskal(*[hypervols[col] for col in hypervols.columns])"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 160
      },
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 72,
       "text": [
        "(4.1170925062938863, 0.12763939044708175)"
       ]
      }
     ],
     "prompt_number": 72
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 160,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "We now can assert that the results are not the same but which ones are different or similar to the others the others?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 160,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "In case that the null hypothesis of the Kruskal-Wallis is rejected the Conover\u2013Inman procedure (Conover, 1999, pp. 288-290) can be applied in a pairwise manner in order to determine if the results of one algorithm were significantly better than those of the other.\n",
      "\n",
      "* Conover, W. J. (1999). *Practical Nonparametric Statistics*. John Wiley & Sons, New York, 3rd edition.\n",
      "\n",
      "_Note_: If you want to get an extended summary of this method check out my [PhD thesis](http://lmarti.com/pubs). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def conover_inman_procedure(data, alpha=0.05):\n",
      "    num_runs = len(data)\n",
      "    num_algos = len(data.columns)\n",
      "    N = num_runs*num_algos\n",
      "\n",
      "    _,p_value = stats.kruskal(*[data[col] for col in data.columns])\n",
      "    \n",
      "    ranked =  stats.rankdata(np.concatenate([data[col] for col in data.columns]))\n",
      "    \n",
      "    ranksums = []\n",
      "    for i in range(num_algos):\n",
      "        ranksums.append(np.sum(ranked[num_runs*i:num_runs*(i+1)]))\n",
      "\n",
      "    S_sq = (np.sum(ranked**2) - N*((N+1)**2)/4)/(N-1)\n",
      "\n",
      "    right_side = stats.t.cdf(1-(alpha/2), N-num_algos) * \\\n",
      "                 math.sqrt((S_sq*((N-1-p_value)/(N-1)))*2/num_runs)\n",
      "    \n",
      "    res = pd.DataFrame(columns=data.columns, index=data.columns)\n",
      "\n",
      "    for i,j in itertools.combinations(np.arange(num_algos),2):\n",
      "        res[res.columns[i]].ix[j] = abs(ranksums[i] - ranksums[j]/num_runs) > right_side\n",
      "        res[res.columns[j]].ix[i] = abs(ranksums[i] - ranksums[j]/num_runs) > right_side\n",
      "    return res"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 160,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [],
     "prompt_number": 73
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "conover_inman_procedure(hypervols)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 160,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
        "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
        "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
        "      <td>  NaN</td>\n",
        "      <td> True</td>\n",
        "      <td> True</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
        "      <td> True</td>\n",
        "      <td>  NaN</td>\n",
        "      <td> True</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
        "      <td> True</td>\n",
        "      <td> True</td>\n",
        "      <td>  NaN</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 74,
       "text": [
        "                      $P_\\mathrm{mut}=0.05$ $P_\\mathrm{mut}=0.15$  \\\n",
        "$P_\\mathrm{mut}=0.05$                   NaN                  True   \n",
        "$P_\\mathrm{mut}=0.15$                  True                   NaN   \n",
        "$P_\\mathrm{mut}=0.3$                   True                  True   \n",
        "\n",
        "                      $P_\\mathrm{mut}=0.3$  \n",
        "$P_\\mathrm{mut}=0.05$                 True  \n",
        "$P_\\mathrm{mut}=0.15$                 True  \n",
        "$P_\\mathrm{mut}=0.3$                   NaN  "
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 160,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "We now know in what cases the difference is sufficient as to say that one result is better than the other."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 160,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Another alternative is the [Friedman test](http://en.wikipedia.org/wiki/Friedman_test).\n",
      "\n",
      "* Its null hypothesis that repeated measurements of the same individuals have the same distribution. \n",
      "* It is often used to test for consistency among measurements obtained in different ways. \n",
      "    * For example, if two measurement techniques are used on the same set of individuals, the Friedman test can be used to determine if the two measurement techniques are consistent."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hyp_transp = hypervols.transpose()\n",
      "measurements = [list(hyp_transp[col]) for col in hyp_transp.columns]\n",
      "stats.friedmanchisquare(*measurements)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 160,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 75,
       "text": [
        "(41.4318936877076, 0.45177834097859693)"
       ]
      }
     ],
     "prompt_number": 75
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 160,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "[Mann\u2013Whitney U test](http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test) (also called the Mann\u2013Whitney\u2013Wilcoxon (MWW), Wilcoxon rank-sum test (WRS), or Wilcoxon\u2013Mann\u2013Whitney test) is a nonparametric test of the null hypothesis that two populations are the same against an alternative hypothesis, especially that a particular population tends to have larger values than the other.\n",
      "\n",
      "It has greater efficiency than the $t$-test on non-normal distributions, such as a mixture of normal distributions, and it is nearly as efficient as the $t$-test on normal distributions."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "raw_p_values=compute_stat_matrix(hypervols, stats.mannwhitneyu)\n",
      "raw_p_values"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 169,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
        "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
        "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
        "      <td>        NaN</td>\n",
        "      <td> 0.03572306</td>\n",
        "      <td> 0.08074789</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
        "      <td> 0.03572306</td>\n",
        "      <td>        NaN</td>\n",
        "      <td>  0.1549628</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
        "      <td> 0.08074789</td>\n",
        "      <td>  0.1549628</td>\n",
        "      <td>        NaN</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 76,
       "text": [
        "                      $P_\\mathrm{mut}=0.05$ $P_\\mathrm{mut}=0.15$  \\\n",
        "$P_\\mathrm{mut}=0.05$                   NaN            0.03572306   \n",
        "$P_\\mathrm{mut}=0.15$            0.03572306                   NaN   \n",
        "$P_\\mathrm{mut}=0.3$             0.08074789             0.1549628   \n",
        "\n",
        "                      $P_\\mathrm{mut}=0.3$  \n",
        "$P_\\mathrm{mut}=0.05$           0.08074789  \n",
        "$P_\\mathrm{mut}=0.15$            0.1549628  \n",
        "$P_\\mathrm{mut}=0.3$                   NaN  "
       ]
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 169,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "The [familywise error rate](http://en.wikipedia.org/wiki/Familywise_error_rate) (FWER) is the probability of making one or more false discoveries, or [type I errors](http://en.wikipedia.org/wiki/Type_I_and_type_II_errors), among all the hypotheses when performing multiple hypotheses tests.\n",
      "\n",
      "_Example_: When performing a test, there is a $\\alpha$ chance of making a type I error. If we make $m$ tests, then the probability of making one type I error is $m\\alpha$. Therefore, if an $\\alpha=0.05$ is used and 5 pairwise comparisons are made, we will have a $5\\times0.05 = 0.25$ chance of making a type I error.\n",
      "\n",
      "* FWER procedures (such as the [Bonferroni correction](http://en.wikipedia.org/wiki/Bonferroni_correction)) exert a more stringent control over false discovery compared to False discovery rate controlling procedures. \n",
      "* FWER controlling seek to reduce the probability of even one false discovery, as opposed to the expected proportion of false discoveries. \n",
      "* Thus, FDR procedures have greater power at the cost of increased rates of type I errors, i.e., rejecting the null hypothesis of no effect when it should be accepted."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 169,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "One of these corrections is the [\u0160id\u00e1k correction](http://en.wikipedia.org/wiki/%C5%A0id%C3%A1k_correction) as it is less conservative than the [Bonferroni correction](http://en.wikipedia.org/wiki/Bonferroni_correction):\n",
      "$$\\alpha_{SID} = 1-(1-\\alpha)^\\frac{1}{m},$$\n",
      "where $m$ is the number of tests.\n",
      "\n",
      "* In our case $m$ is the number of combinations of algorithm configurations taken two at a time.\n",
      "* There are other corrections that can be used."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.misc import comb\n",
      "alpha=0.05\n",
      "alpha_sid = 1 - (1-alpha)**(1/comb(len(hypervols.columns), 2))\n",
      "print(alpha_sid)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 169,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.0169524275084\n"
       ]
      }
     ],
     "prompt_number": 77
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 169,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Let's apply the corrected alpha to `raw_p_values`. If we have a cell with a `True` value that means that those two results are the same."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "raw_p_values.applymap(lambda value: value <= alpha_sid)"
     ],
     "language": "python",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 169,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
        "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
        "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
        "      <td> False</td>\n",
        "      <td> False</td>\n",
        "      <td> False</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
        "      <td> False</td>\n",
        "      <td> False</td>\n",
        "      <td> False</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
        "      <td> False</td>\n",
        "      <td> False</td>\n",
        "      <td> False</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 78,
       "text": [
        "                      $P_\\mathrm{mut}=0.05$ $P_\\mathrm{mut}=0.15$  \\\n",
        "$P_\\mathrm{mut}=0.05$                 False                 False   \n",
        "$P_\\mathrm{mut}=0.15$                 False                 False   \n",
        "$P_\\mathrm{mut}=0.3$                  False                 False   \n",
        "\n",
        "                      $P_\\mathrm{mut}=0.3$  \n",
        "$P_\\mathrm{mut}=0.05$                False  \n",
        "$P_\\mathrm{mut}=0.15$                False  \n",
        "$P_\\mathrm{mut}=0.3$                 False  "
       ]
      }
     ],
     "prompt_number": 78
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 169,
       "slide_helper": "subslide_end",
       "slide_type": "subslide"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## Further -and highly recommended- reading\n",
      "\n",
      "* Cohen, P. R. (1995). _Empirical Methods for Artificial Intelligence_ (Vol. 139). Cambridge: MIT press. [link](http://mitpress.mit.edu/books/empirical-methods-artificial-intelligence)\n",
      "* Bartz-Beielstein, Thomas (2006). _Experimental Research in Evolutionary Computation: The New Experimentalism_. Springer [link](http://link.springer.com/book/10.1007%2F3-540-32027-X)\n",
      "* Garc\u00eda, S., & Herrera, F. (2008). _An Extension on \u201cStatistical Comparisons of Classifiers over Multiple Data Sets\u201d for all Pairwise Comparisons_. Journal of Machine Learning Research, 9, 2677\u20132694. [pdf](http://www.jmlr.org/papers/v9/garcia08a.html)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 169,
       "slide_type": "subslide"
      },
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "# Final remarks\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "internals": {
       "frag_helper": "fragment_end",
       "frag_number": 169,
       "slide_helper": "subslide_end"
      },
      "slide_helper": "slide_end",
      "slideshow": {
       "slide_type": "-"
      }
     },
     "source": [
      "In this class/notebook we have seen some key elements:\n",
      "\n",
      "1. The Pareto dominance relation in action.\n",
      "2. The NSGA-II algorithm.\n",
      "3. Some of the existing MOP benchmarks. \n",
      "4. How to perform experiments and draw statistically valid conclusions from them.\n",
      "\n",
      "Bear in mind that:\n",
      "\n",
      "* When working in EMO topics problems like those of the CEC'09 or WFG toolkits are usually involved.\n",
      "* The issue of devising a proper experiment design and interpreting the results is a fundamental one.\n",
      "* The experimental setup presented here can be used with little modifications to single-objective optimization and even to other machine learning or stochastic algorithms."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}