223 lines
7.0 KiB
Plaintext
223 lines
7.0 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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"# assignment6_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/assignment6_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/assignment6_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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" Assignment problem using MIP in Google or-tools.\n",
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"\n",
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" From GLPK:s example assign.mod:\n",
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" '''\n",
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" The assignment problem is one of the fundamental combinatorial\n",
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" optimization problems.\n",
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"\n",
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" In its most general form, the problem is as follows:\n",
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"\n",
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" There are a number of agents and a number of tasks. Any agent can be\n",
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" assigned to perform any task, incurring some cost that may vary\n",
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" depending on the agent-task assignment. It is required to perform all\n",
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" tasks by assigning exactly one agent to each task in such a way that\n",
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" the total cost of the assignment is minimized.\n",
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"\n",
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" (From Wikipedia, the free encyclopedia.)\n",
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" '''\n",
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"\n",
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" Compare with the Comet model:\n",
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" http://www.hakank.org/comet/assignment6.co\n",
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"\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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"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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"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",
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"# number of agents\n",
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"m = 8\n",
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"\n",
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"# number of tasks\n",
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"n = 8\n",
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"\n",
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"# set of agents\n",
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"I = list(range(m))\n",
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"\n",
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"# set of tasks\n",
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"J = list(range(n))\n",
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"\n",
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"# cost of allocating task j to agent i\n",
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"# \"\"\"\n",
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"# These data correspond to an example from [Christofides].\n",
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"#\n",
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"# Optimal solution is 76\n",
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"# \"\"\"\n",
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"c = [[13, 21, 20, 12, 8, 26, 22, 11], [12, 36, 25, 41, 40, 11, 4, 8],\n",
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" [35, 32, 13, 36, 26, 21, 13, 37], [34, 54, 7, 8, 12, 22, 11, 40],\n",
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" [21, 6, 45, 18, 24, 34, 12, 48], [42, 19, 39, 15, 14, 16, 28, 46],\n",
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" [16, 34, 38, 3, 34, 40, 22, 24], [26, 20, 5, 17, 45, 31, 37, 43]]\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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"# For the output: the assignment as task number.\n",
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"assigned = [solver.IntVar(0, 10000, 'assigned[%i]' % j) for j in J]\n",
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"\n",
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"costs = [solver.IntVar(0, 10000, 'costs[%i]' % i) for i in I]\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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"# total cost, to be minimized\n",
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"z = solver.Sum([c[i][j] * x[i, j] for i in I for j in J])\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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"# each agent can perform at most one task\n",
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"for i in I:\n",
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" solver.Add(solver.Sum([x[i, j] for j in J]) <= 1)\n",
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"\n",
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"# each task must be assigned exactly to one agent\n",
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"for j in J:\n",
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" solver.Add(solver.Sum([x[i, j] for i in I]) == 1)\n",
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"\n",
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"# to which task and what cost is person i assigned (for output in MiniZinc)\n",
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"for i in I:\n",
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" solver.Add(assigned[i] == solver.Sum([j * x[i, j] for j in J]))\n",
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" solver.Add(costs[i] == solver.Sum([c[i][j] * x[i, j] for j in J]))\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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"print('Assigned')\n",
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"for j in J:\n",
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" print(int(assigned[j].SolutionValue()), end=' ')\n",
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"print()\n",
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"\n",
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"print('Matrix:')\n",
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"for i in I:\n",
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" for j in J:\n",
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" print(int(x[i, j].SolutionValue()), end=' ')\n",
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" print()\n",
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"print()\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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