97 lines
3.7 KiB
Plaintext
97 lines
3.7 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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"#!/usr/bin/env python\n",
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"# This Python file uses the following encoding: utf-8\n",
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"# Copyright 2018 Google LLC\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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"\"\"\"Linear optimization example\"\"\"\n",
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"\n",
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"from __future__ import print_function\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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"\"\"\"Entry point of the program\"\"\"\n",
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"# Instantiate a Glop solver, naming it LinearExample.\n",
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"solver = pywraplp.Solver('LinearExample',\n",
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" pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)\n",
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"\n",
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"# Create the two variables and let them take on any value.\n",
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"x = solver.NumVar(-solver.infinity(), solver.infinity(), 'x')\n",
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"y = solver.NumVar(-solver.infinity(), solver.infinity(), 'y')\n",
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"\n",
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"# Objective function: Maximize 3x + 4y.\n",
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"objective = solver.Objective()\n",
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"objective.SetCoefficient(x, 3)\n",
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"objective.SetCoefficient(y, 4)\n",
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"objective.SetMaximization()\n",
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"\n",
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"# Constraint 0: x + 2y <= 14.\n",
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"constraint0 = solver.Constraint(-solver.infinity(), 14)\n",
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"constraint0.SetCoefficient(x, 1)\n",
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"constraint0.SetCoefficient(y, 2)\n",
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"\n",
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"# Constraint 1: 3x - y >= 0.\n",
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"constraint1 = solver.Constraint(0, solver.infinity())\n",
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"constraint1.SetCoefficient(x, 3)\n",
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"constraint1.SetCoefficient(y, -1)\n",
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"\n",
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"# Constraint 2: x - y <= 2.\n",
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"constraint2 = solver.Constraint(-solver.infinity(), 2)\n",
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"constraint2.SetCoefficient(x, 1)\n",
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"constraint2.SetCoefficient(y, -1)\n",
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"\n",
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"print('Number of variables =', solver.NumVariables())\n",
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"print('Number of constraints =', solver.NumConstraints())\n",
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"\n",
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"# Solve the system.\n",
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"status = solver.Solve()\n",
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"# Check that the problem has an optimal solution.\n",
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"if status != pywraplp.Solver.OPTIMAL:\n",
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" print(\"The problem does not have an optimal solution!\")\n",
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" exit(1)\n",
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"\n",
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"print('Solution:')\n",
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"print('x =', x.solution_value())\n",
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"print('y =', y.solution_value())\n",
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"print('Optimal objective value =', objective.Value())\n",
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"print('')\n",
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"print('Advanced usage:')\n",
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"print('Problem solved in ', solver.wall_time(), ' milliseconds')\n",
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"print('Problem solved in ', solver.iterations(), ' iterations')\n",
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"print('x: reduced cost =', x.reduced_cost())\n",
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"print('y: reduced cost =', y.reduced_cost())\n",
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"activities = solver.ComputeConstraintActivities()\n",
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"print('constraint0: dual value =',\n",
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" constraint0.dual_value(), ' activities =',\n",
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" activities[constraint0.index()])\n",
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"print('constraint1: dual value =',\n",
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" constraint1.dual_value(), ' activities =',\n",
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" activities[constraint1.index()])\n",
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"print('constraint2: dual value =',\n",
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" constraint2.dual_value(), ' activities =',\n",
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" activities[constraint2.index()])\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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