start planning notebook

aimacode · norvig · May 24, 2017 · Apr 17, 2017 · Apr 17, 2017 · Apr 22, 2017
commit 94babf0ed61ed260f3ea6c2a4e99b06489e5e849
diff --git a/planning.ipynb b/planning.ipynb
@@ -1,24 +1,311 @@
 {
  "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "# Planning: planning.py; chapters 10-11"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This notebook describes the [planning.py](https://github.com/aimacode/aima-python/blob/master/planning.py) module, which covers Chapters 10 (Classical Planning) and  11 (Planning and Acting in the Real World) of *[Artificial Intelligence: A Modern Approach](http://aima.cs.berkeley.edu)*. See the [intro notebook](https://github.com/aimacode/aima-python/blob/master/intro.ipynb) for instructions.\n",
+    "\n",
+    "We'll start by looking at `PDDL` and `Action` data types for defining problems and actions. Then, we will see how to use them by trying to plan a trip across the familiar map of Romania, from [search.ipynb](https://github.com/aimacode/aima-python/blob/master/search.ipynb). Finally, we will look at the implementation of the GraphPlan algorithm.\n",
+    "\n",
+    "The first step is to load the code:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "from planning import *"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Lets first think about modelling an Action in this context. We need at least 3 things to be able to do so:\n",
+    "* preconditions that the action must meet\n",
+    "* the effects of executing the action\n",
+    "* some expression that represents the action"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Lets look at the source for `Action` and see how these are implemented."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "%psource Action"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "It is interesting to see the way preconditions and effects are represented here. Instead of just being a list of expressions each, they consist of two lists. This is to workaround the fact that PDDL doesn't allow for negations. Thus, for each precondition, we maintain a seperate list of those preconditions that must hold true, and those whose negations must hold true. Similarly, we track the effects in terms of the statements that become true, should an action be executed, and those that become false, once the action is executed."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now lets look at problems, represented by the `PDDL` class. We would expect to need the following to be able to define a problem:\n",
+    "* a goal test\n",
+    "* an initial state\n",
+    "* a set of viable actions that can be executed in the search space of the problem"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "%psource PDDL"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This class defines all three of these. The initial_state is a list of `Expr` expressions that forms the initial knowledge base for the problem. Next, actions contains a list of `Action` objects that may be executed in the search space of the problem. Lastly, we pass a `goal_test` function as a parameter - this typically takes a knowledge base as parameter, returns whether or not the goal has been reached."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now lets try to define a planning problem using these tools. Since we already know about the map of Romania, lets see if we can plan a trip across a simplified map of Romania.\n",
+    "\n",
+    "We start by defining the map."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "from utils import *\n",
+    "# this imports the required expr so we can create our knowledge base\n",
+    "\n",
+    "knowledge_base = [\n",
+    "    expr(\"Connected(Bucharest,Pitesti)\"),\n",
+    "    expr(\"Connected(Pitesti,Rimnicu)\"),\n",
+    "    expr(\"Connected(Rimnicu,Sibiu)\"),\n",
+    "    expr(\"Connected(Sibiu,Fagaras)\"),\n",
+    "    expr(\"Connected(Fagaras,Bucharest)\"),\n",
+    "    expr(\"Connected(Pitesti,Craiova)\"),\n",
+    "    expr(\"Connected(Craiova,Rimnicu)\")\n",
+    "    ]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now lets add some logic propositions to complete our knowledge about travelling around the map. These would be the typical symmetry and transitivity properties of connections on a map.\n",
+    "\n",
+    "Lets also add our starting location - *Sibiu* to the map."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "knowledge_base.extend([\n",
+    "     expr(\"Connected(x,y) ==> Connected(y,x)\"),\n",
+    "     expr(\"Connected(x,y) & Connected(y,z) ==> Connected(x,z)\"),\n",
+    "     expr(\"At(Sibiu)\")\n",
+    "    ])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We now have a complete knowledge base:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Connected(Bucharest, Pitesti),\n",
+       " Connected(Pitesti, Rimnicu),\n",
+       " Connected(Rimnicu, Sibiu),\n",
+       " Connected(Sibiu, Fagaras),\n",
+       " Connected(Fagaras, Bucharest),\n",
+       " Connected(Pitesti, Craiova),\n",
+       " Connected(Craiova, Rimnicu),\n",
+       " (Connected(x, y) ==> Connected(y, x)),\n",
+       " ((Connected(x, y) & Connected(y, z)) ==> Connected(x, z)),\n",
+       " At(Sibiu)]"
+      ]
+     },
+     "execution_count": 34,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "knowledge_base"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now lets start adding possible actions to our problem. We know we can drive between any connected places. But, as clear from [this](https://en.wikipedia.org/wiki/List_of_airports_in_Romania) list of airports, we can also fly directly between Sibiu, Bucharest, and Craiova.\n",
+    "\n",
+    "Lets start by defining these flights."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 38,
    "metadata": {
     "collapsed": false
    },
    "outputs": [],
    "source": [
-    "import planning"
+    "#Sibiu to Bucharest\n",
+    "precond_pos = [expr('At(Sibiu)')]\n",
+    "precond_neg = []\n",
+    "effect_add = [expr('At(Bucharest)')]\n",
+    "effect_rem = [expr('At(Sibiu)')]\n",
+    "fly_s_b = Action(expr('Fly(Sibiu, Bucharest)'), [precond_pos, precond_neg], [effect_add, effect_rem])\n",
+    "\n",
+    "#Bucharest to Sibiu\n",
+    "precond_pos = [expr('At(Bucharest)')]\n",
+    "precond_neg = []\n",
+    "effect_add = [expr('At(Sibiu)')]\n",
+    "effect_rem = [expr('At(Bucharest)')]\n",
+    "fly_b_s = Action(expr('Fly(Bucharest, Sibiu)'), [precond_pos, precond_neg], [effect_add, effect_rem])\n",
+    "\n",
+    "#Sibiu to Craiova\n",
+    "precond_pos = [expr('At(Sibiu)')]\n",
+    "precond_neg = []\n",
+    "effect_add = [expr('At(Craiova)')]\n",
+    "effect_rem = [expr('At(Sibiu)')]\n",
+    "fly_s_c = Action(expr('Fly(Sibiu, Craiova)'), [precond_pos, precond_neg], [effect_add, effect_rem])\n",
+    "\n",
+    "#Craiova to Sibiu\n",
+    "precond_pos = [expr('At(Craiova)')]\n",
+    "precond_neg = []\n",
+    "effect_add = [expr('At(Sibiu)')]\n",
+    "effect_rem = [expr('At(Craiova)')]\n",
+    "fly_c_s = Action(expr('Fly(Craiova, Sibiu)'), [precond_pos, precond_neg], [effect_add, effect_rem])\n",
+    "\n",
+    "#Bucharest to Craiova\n",
+    "precond_pos = [expr('At(Bucharest)')]\n",
+    "precond_neg = []\n",
+    "effect_add = [expr('At(Craiova)')]\n",
+    "effect_rem = [expr('At(Bucharest)')]\n",
+    "fly_b_c = Action(expr('Fly(Bucharest, Craiova)'), [precond_pos, precond_neg], [effect_add, effect_rem])\n",
+    "\n",
+    "#Craiova to Bucharest\n",
+    "precond_pos = [expr('At(Craiova)')]\n",
+    "precond_neg = []\n",
+    "effect_add = [expr('At(Bucharest)')]\n",
+    "effect_rem = [expr('At(Craiova)')]\n",
+    "fly_c_b = Action(expr('Fly(Craiova, Bucharest)'), [precond_pos, precond_neg], [effect_add, effect_rem])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now lets define all the drive actions."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 39,
    "metadata": {
     "collapsed": true
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "#Drive\n",
+    "precond_pos = [expr('At(x)')]\n",
+    "precond_neg = []\n",
+    "effect_add = [expr('At(y)')]\n",
+    "effect_rem = [expr('At(x)')]\n",
+    "drive = Action(expr('Drive(x, y)'), [precond_pos, precond_neg], [effect_add, effect_rem])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Finally, lets define our goal: travel to Bucharest."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def goal_test(kb):\n",
+    "    return kb.ask(expr(\"At(Bucharest)\"))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We are now finally ready to define our problem."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "prob = PDDL(knowledge_base, [fly_s_b, fly_b_s, fly_s_c, fly_c_s, fly_b_c, fly_c_b, drive], goal_test)"
+   ]
   }
  ],
  "metadata": {
@@ -37,7 +324,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.1"
+   "version": "3.4.3"
   }
  },
  "nbformat": 4,