vis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import jijmodeling as jm\n",
    "\n",
    "# define variables\n",
    "d = jm.Placeholder(\"d\", ndim=2)\n",
    "N = d.shape[0]\n",
    "N.set_latex(\"N\")\n",
    "i = jm.Element(\"i\", belong_to=(0, N))\n",
    "j = jm.Element(\"j\", belong_to=(0, N))\n",
    "t = jm.Element(\"t\", belong_to=(0, N))\n",
    "x = jm.BinaryVar(\"x\", shape=(N, N))\n",
    "\n",
    "# set problem\n",
    "problem = jm.Problem(\"Traveling Salesman Problem\")\n",
    "problem += jm.sum([i, j], d[i, j] * jm.sum(t, x[i, t] * x[j, (t + 1) % N]))\n",
    "problem += jm.Constraint(\"one-city\", jm.sum(i, x[i, t]) == 1, forall=t)\n",
    "problem += jm.Constraint(\"one-time\", jm.sum(t, x[i, t]) == 1, forall=i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\begin{array}{cccc}\\text{Problem:} & \\text{Traveling Salesman Problem} & & \\\\& & \\min \\quad \\displaystyle \\sum_{i = 0}^{N - 1} \\sum_{j = 0}^{N - 1} d_{i, j} \\cdot \\sum_{t = 0}^{N - 1} x_{i, t} \\cdot x_{j, \\left(t + 1\\right) \\bmod N} & \\\\\\text{{s.t.}} & & & \\\\ & \\text{one-city} & \\displaystyle \\sum_{i = 0}^{N - 1} x_{i, t} = 1 & \\forall t \\in \\left\\{0,\\ldots,N - 1\\right\\} \\\\ & \\text{one-time} & \\displaystyle \\sum_{t = 0}^{N - 1} x_{i, t} = 1 & \\forall i \\in \\left\\{0,\\ldots,N - 1\\right\\} \\\\\\text{{where}} & & & \\\\& x & 2\\text{-dim binary variable}\\\\\\end{array}$$"
      ],
      "text/plain": [
       "<jijmodeling.Problem at 0x562b63081ba0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "problem"
   ]
  }
 ],
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