136 lines
4.5 KiB
Plaintext
136 lines
4.5 KiB
Plaintext
{
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"cells": [
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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 2010 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 in Google CP Solver.\n",
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"\n",
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" Winston 'Operations Research', Assignment Problems, page 393f\n",
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" (generalized version with added test column)\n",
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"\n",
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" Compare with the following models:\n",
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" * Comet : http://www.hakank.org/comet/assignment.co\n",
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" * ECLiPSE : http://www.hakank.org/eclipse/assignment.ecl\n",
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" * Gecode : http://www.hakank.org/gecode/assignment.cpp\n",
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" * MiniZinc: http://www.hakank.org/minizinc/assignment.mzn\n",
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" * Tailor/Essence': http://www.hakank.org/tailor/assignment.eprime\n",
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" * SICStus: http://hakank.org/sicstus/assignment.pl\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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"from ortools.constraint_solver import pywrapcp\n",
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"\n",
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"\n",
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"# Create the solver.\n",
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"solver = pywrapcp.Solver(\"n-queens\")\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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"# declare variables\n",
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"total_cost = solver.IntVar(0, 100, \"total_cost\")\n",
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"x = []\n",
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"for i in range(rows):\n",
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" t = []\n",
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" for j in range(cols):\n",
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" t.append(solver.IntVar(0, 1, \"x[%i,%i]\" % (i, j)))\n",
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" x.append(t)\n",
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"x_flat = [x[i][j] for i in range(rows) for j in range(cols)]\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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"# total_cost\n",
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"solver.Add(total_cost == solver.Sum(\n",
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" [solver.ScalProd(x_row, cost_row) for (x_row, cost_row) in zip(x, cost)]))\n",
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"\n",
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"# exacly one assignment per row, all rows must be assigned\n",
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"[\n",
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" solver.Add(solver.Sum([x[row][j]\n",
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" for j in range(cols)]) == 1)\n",
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" for row in range(rows)\n",
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"]\n",
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"\n",
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"# zero or one assignments per column\n",
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"[\n",
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" solver.Add(solver.Sum([x[i][col]\n",
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" for i in range(rows)]) <= 1)\n",
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" for col in range(cols)\n",
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"]\n",
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"\n",
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"objective = solver.Minimize(total_cost, 1)\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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"solution = solver.Assignment()\n",
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"solution.Add(x_flat)\n",
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"solution.Add(total_cost)\n",
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"\n",
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"# db: DecisionBuilder\n",
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"db = solver.Phase(x_flat, solver.INT_VAR_SIMPLE, solver.ASSIGN_MIN_VALUE)\n",
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"\n",
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"solver.NewSearch(db, [objective])\n",
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"num_solutions = 0\n",
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"while solver.NextSolution():\n",
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" print(\"total_cost:\", total_cost.Value())\n",
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" for i in range(rows):\n",
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" for j in range(cols):\n",
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" print(x[i][j].Value(), end=\" \")\n",
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" print()\n",
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" print()\n",
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"\n",
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" for i in range(rows):\n",
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" print(\"Task:\", i, end=\" \")\n",
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" for j in range(cols):\n",
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" if x[i][j].Value() == 1:\n",
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" print(\" is done by \", j)\n",
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" print()\n",
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"\n",
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" num_solutions += 1\n",
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"solver.EndSearch()\n",
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"\n",
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"print()\n",
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"print(\"num_solutions:\", num_solutions)\n",
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"print(\"failures:\", solver.Failures())\n",
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"print(\"branches:\", solver.Branches())\n",
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"print(\"WallTime:\", solver.WallTime())\n",
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"\n",
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"\n",
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"# Problem instance\n",
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"# hakank: I added the fifth column to make it more\n",
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"# interestingrows = 4\n",
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"cols = 5\n",
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"cost = [[14, 5, 8, 7, 15], [2, 12, 6, 5, 3], [7, 8, 3, 9, 7], [2, 4, 6, 10, 1]]\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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