238 lines
7.3 KiB
Plaintext
238 lines
7.3 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"##### Copyright 2020 Google LLC."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Licensed under the Apache License, Version 2.0 (the \"License\");\n",
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"you may not use this file except in compliance with the License.\n",
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"You may obtain a copy of the License at\n",
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"\n",
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" http://www.apache.org/licenses/LICENSE-2.0\n",
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"\n",
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"Unless required by applicable law or agreed to in writing, software\n",
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"distributed under the License is distributed on an \"AS IS\" BASIS,\n",
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"WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
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"See the License for the specific language governing permissions and\n",
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"limitations under the License.\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# 3_jugs_mip"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<table align=\"left\">\n",
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"<td>\n",
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"<a href=\"https://colab.research.google.com/github/google/or-tools/blob/master/examples/notebook/contrib/3_jugs_mip.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
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"</td>\n",
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"<td>\n",
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"<a href=\"https://github.com/google/or-tools/blob/master/examples/contrib/3_jugs_mip.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/tools/github_32px.png\"/>View source on GitHub</a>\n",
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"</td>\n",
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"</table>"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"!pip install ortools"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Copyright 2011 Hakan Kjellerstrand hakank@gmail.com\n",
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"#\n",
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"# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
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"# you may not use this file except in compliance with the License.\n",
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"# You may obtain a copy of the License at\n",
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"#\n",
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"# http://www.apache.org/licenses/LICENSE-2.0\n",
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"#\n",
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"# Unless required by applicable law or agreed to in writing, software\n",
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"# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
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"# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
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"# See the License for the specific language governing permissions and\n",
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"# limitations under the License.\n",
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"\"\"\"\n",
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"\n",
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" 3 jugs problem using MIP in Google or-tools.\n",
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"\n",
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" A.k.a. water jugs problem.\n",
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"\n",
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" Problem from Taha 'Introduction to Operations Research',\n",
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" page 245f .\n",
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"\n",
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" Compare with the CP model:\n",
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" http://www.hakank.org/google_or_tools/3_jugs_regular\n",
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"\n",
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" This model was created by Hakan Kjellerstrand (hakank@gmail.com)\n",
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" Also see my other Google CP Solver models:\n",
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" http://www.hakank.org/google_or_tools/\n",
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"\"\"\"\n",
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"from __future__ import print_function\n",
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"import sys\n",
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"from ortools.linear_solver import pywraplp\n",
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"\n",
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"\n",
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"\n",
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"# Create the solver.\n",
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"\n",
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"print('Solver: ', sol)\n",
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"\n",
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"# using GLPK\n",
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"if sol == 'GLPK':\n",
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" solver = pywraplp.Solver('CoinsGridGLPK',\n",
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" pywraplp.Solver.GLPK_MIXED_INTEGER_PROGRAMMING)\n",
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"else:\n",
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" # Using CBC\n",
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" solver = pywraplp.Solver('CoinsGridCBC',\n",
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" pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)\n",
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"\n",
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"#\n",
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"# data\n",
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"#\n",
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"n = 15\n",
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"start = 0 # start node\n",
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"end = 14 # end node\n",
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"M = 999 # a large number\n",
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"\n",
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"nodes = [\n",
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" '8,0,0', # start\n",
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" '5,0,3',\n",
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" '5,3,0',\n",
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" '2,3,3',\n",
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" '2,5,1',\n",
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" '7,0,1',\n",
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" '7,1,0',\n",
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" '4,1,3',\n",
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" '3,5,0',\n",
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" '3,2,3',\n",
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" '6,2,0',\n",
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" '6,0,2',\n",
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" '1,5,2',\n",
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" '1,4,3',\n",
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" '4,4,0' # goal!\n",
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"]\n",
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"\n",
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"# distance\n",
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"d = [[M, 1, M, M, M, M, M, M, 1, M, M, M, M, M, M],\n",
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" [M, M, 1, M, M, M, M, M, M, M, M, M, M, M, M],\n",
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" [M, M, M, 1, M, M, M, M, 1, M, M, M, M, M, M],\n",
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" [M, M, M, M, 1, M, M, M, M, M, M, M, M, M, M],\n",
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" [M, M, M, M, M, 1, M, M, 1, M, M, M, M, M, M],\n",
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" [M, M, M, M, M, M, 1, M, M, M, M, M, M, M, M],\n",
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" [M, M, M, M, M, M, M, 1, 1, M, M, M, M, M, M],\n",
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" [M, M, M, M, M, M, M, M, M, M, M, M, M, M, 1],\n",
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" [M, M, M, M, M, M, M, M, M, 1, M, M, M, M, M],\n",
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" [M, 1, M, M, M, M, M, M, M, M, 1, M, M, M, M],\n",
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" [M, M, M, M, M, M, M, M, M, M, M, 1, M, M, M],\n",
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" [M, 1, M, M, M, M, M, M, M, M, M, M, 1, M, M],\n",
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" [M, M, M, M, M, M, M, M, M, M, M, M, M, 1, M],\n",
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" [M, 1, M, M, M, M, M, M, M, M, M, M, M, M, 1],\n",
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" [M, M, M, M, M, M, M, M, M, M, M, M, M, M, M]]\n",
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"\n",
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"#\n",
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"# variables\n",
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"#\n",
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"\n",
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"# requirements (right hand statement)\n",
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"rhs = [solver.IntVar(-1, 1, 'rhs[%i]' % i) for i in range(n)]\n",
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"\n",
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"x = {}\n",
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"for i in range(n):\n",
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" for j in range(n):\n",
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" x[i, j] = solver.IntVar(0, 1, 'x[%i,%i]' % (i, j))\n",
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"\n",
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"out_flow = [solver.IntVar(0, 1, 'out_flow[%i]' % i) for i in range(n)]\n",
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"in_flow = [solver.IntVar(0, 1, 'in_flow[%i]' % i) for i in range(n)]\n",
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"\n",
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"# length of path, to be minimized\n",
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"z = solver.Sum(\n",
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" [d[i][j] * x[i, j] for i in range(n) for j in range(n) if d[i][j] < M])\n",
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"\n",
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"#\n",
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"# constraints\n",
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"#\n",
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"\n",
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"for i in range(n):\n",
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" if i == start:\n",
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" solver.Add(rhs[i] == 1)\n",
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" elif i == end:\n",
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" solver.Add(rhs[i] == -1)\n",
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" else:\n",
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" solver.Add(rhs[i] == 0)\n",
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"\n",
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"# outflow constraint\n",
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"for i in range(n):\n",
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" solver.Add(\n",
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" out_flow[i] == solver.Sum([x[i, j] for j in range(n) if d[i][j] < M]))\n",
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"\n",
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"# inflow constraint\n",
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"for j in range(n):\n",
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" solver.Add(\n",
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" in_flow[j] == solver.Sum([x[i, j] for i in range(n) if d[i][j] < M]))\n",
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"\n",
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"# inflow = outflow\n",
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"for i in range(n):\n",
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" solver.Add(out_flow[i] - in_flow[i] == rhs[i])\n",
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"\n",
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"# objective\n",
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"objective = solver.Minimize(z)\n",
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"\n",
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"#\n",
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"# solution and search\n",
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"#\n",
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"solver.Solve()\n",
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"\n",
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"print()\n",
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"print('z: ', int(solver.Objective().Value()))\n",
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"\n",
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"t = start\n",
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"while t != end:\n",
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" print(nodes[t], '->', end=' ')\n",
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" for j in range(n):\n",
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" if x[t, j].SolutionValue() == 1:\n",
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" print(nodes[j])\n",
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" t = j\n",
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" break\n",
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"\n",
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"print()\n",
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"print('walltime :', solver.WallTime(), 'ms')\n",
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"if sol == 'CBC':\n",
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" print('iterations:', solver.Iterations())\n",
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"\n"
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]
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}
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],
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"metadata": {},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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