250 lines
8.6 KiB
Plaintext
250 lines
8.6 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "google",
|
|
"metadata": {},
|
|
"source": [
|
|
"##### Copyright 2025 Google LLC."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "apache",
|
|
"metadata": {},
|
|
"source": [
|
|
"Licensed under the Apache License, Version 2.0 (the \"License\");\n",
|
|
"you may not use this file except in compliance with the License.\n",
|
|
"You may obtain a copy of the License at\n",
|
|
"\n",
|
|
" http://www.apache.org/licenses/LICENSE-2.0\n",
|
|
"\n",
|
|
"Unless required by applicable law or agreed to in writing, software\n",
|
|
"distributed under the License is distributed on an \"AS IS\" BASIS,\n",
|
|
"WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
|
|
"See the License for the specific language governing permissions and\n",
|
|
"limitations under the License.\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "basename",
|
|
"metadata": {},
|
|
"source": [
|
|
"# soft_constraints_sat"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "link",
|
|
"metadata": {},
|
|
"source": [
|
|
"<table align=\"left\">\n",
|
|
"<td>\n",
|
|
"<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/sat/soft_constraints_sat.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
|
|
"</td>\n",
|
|
"<td>\n",
|
|
"<a href=\"https://github.com/google/or-tools/blob/main/ortools/sat/samples/soft_constraints_sat.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
|
|
"</td>\n",
|
|
"</table>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "doc",
|
|
"metadata": {},
|
|
"source": [
|
|
"First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "install",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"%pip install ortools"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "description",
|
|
"metadata": {},
|
|
"source": [
|
|
"\n",
|
|
"The sample shows multiple ways to model soft constraints in CP-SAT.\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "code",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"from ortools.sat.python import cp_model\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"def infeasible_model() -> None:\n",
|
|
" \"\"\"Base model that is infeasible.\"\"\"\n",
|
|
" # Creates the model.\n",
|
|
" model = cp_model.CpModel()\n",
|
|
"\n",
|
|
" # Creates the variables.\n",
|
|
" x = model.new_int_var(0, 10, \"x\")\n",
|
|
" y = model.new_int_var(0, 10, \"y\")\n",
|
|
" z = model.new_int_var(0, 10, \"z\")\n",
|
|
"\n",
|
|
" # Creates the constraints.\n",
|
|
" model.add(x > y)\n",
|
|
" model.add(y > z)\n",
|
|
" model.add(z > x)\n",
|
|
"\n",
|
|
" # Creates a solver and solves.\n",
|
|
" solver = cp_model.CpSolver()\n",
|
|
" status = solver.solve(model)\n",
|
|
"\n",
|
|
" # Print solution.\n",
|
|
" print(f\" Status = {solver.status_name(status)}\")\n",
|
|
"\n",
|
|
"\n",
|
|
"def model_with_enforcement_literals() -> None:\n",
|
|
" \"\"\"Adds fixed costs to violated constraints.\"\"\"\n",
|
|
" # Creates the model.\n",
|
|
" model = cp_model.CpModel()\n",
|
|
"\n",
|
|
" # Creates the variables.\n",
|
|
" x = model.new_int_var(0, 10, \"x\")\n",
|
|
" y = model.new_int_var(0, 10, \"y\")\n",
|
|
" z = model.new_int_var(0, 10, \"z\")\n",
|
|
" a = model.new_bool_var(\"a\")\n",
|
|
" b = model.new_bool_var(\"b\")\n",
|
|
"\n",
|
|
" # Creates the constraints. Adds enforcement literals to the first two\n",
|
|
" # constraints, we assume the third constraint is always enforced.\n",
|
|
" model.add(x > y).only_enforce_if(a)\n",
|
|
" model.add(y > z).only_enforce_if(b)\n",
|
|
" model.add(z > x)\n",
|
|
"\n",
|
|
" # Adds an objective to maximize the number of enforced constraints.\n",
|
|
" model.maximize(a + 2 * b)\n",
|
|
"\n",
|
|
" # Creates a solver and solves.\n",
|
|
" solver = cp_model.CpSolver()\n",
|
|
" status = solver.solve(model)\n",
|
|
"\n",
|
|
" # Print solution.\n",
|
|
" print(f\" Status = {solver.status_name(status)}\")\n",
|
|
" if status == cp_model.OPTIMAL:\n",
|
|
" print(f\" Objective value = {solver.objective_value}\")\n",
|
|
" print(f\" Value of x = {solver.value(x)}\")\n",
|
|
" print(f\" Value of y = {solver.value(y)}\")\n",
|
|
" print(f\" Value of z = {solver.value(z)}\")\n",
|
|
" print(f\" Value of a = {solver.boolean_value(a)}\")\n",
|
|
" print(f\" Value of b = {solver.boolean_value(b)}\")\n",
|
|
"\n",
|
|
"\n",
|
|
"def model_with_linear_violations() -> None:\n",
|
|
" \"\"\"Adds fixed costs to violated constraints.\"\"\"\n",
|
|
" # Creates the model.\n",
|
|
" model = cp_model.CpModel()\n",
|
|
"\n",
|
|
" # Creates the variables.\n",
|
|
" x = model.new_int_var(0, 10, \"x\")\n",
|
|
" y = model.new_int_var(0, 10, \"y\")\n",
|
|
" z = model.new_int_var(0, 10, \"z\")\n",
|
|
" a = model.new_int_var(0, 10, \"a\")\n",
|
|
" b = model.new_int_var(0, 10, \"b\")\n",
|
|
"\n",
|
|
" # Creates the constraints. Adds enforcement literals to the first two\n",
|
|
" # constraints, we assume the third constraint is always enforced.\n",
|
|
" model.add(x > y - a)\n",
|
|
" model.add(y > z - b)\n",
|
|
" model.add(z > x)\n",
|
|
"\n",
|
|
" # Adds an objective to minimize the added slacks.\n",
|
|
" model.minimize(a + 2 * b)\n",
|
|
"\n",
|
|
" # Creates a solver and solves.\n",
|
|
" solver = cp_model.CpSolver()\n",
|
|
" status = solver.solve(model)\n",
|
|
"\n",
|
|
" # Print solution.\n",
|
|
" print(f\" Status = {solver.status_name(status)}\")\n",
|
|
" if status == cp_model.OPTIMAL:\n",
|
|
" print(f\" Objective value = {solver.objective_value}\")\n",
|
|
" print(f\" Value of x = {solver.value(x)}\")\n",
|
|
" print(f\" Value of y = {solver.value(y)}\")\n",
|
|
" print(f\" Value of z = {solver.value(z)}\")\n",
|
|
" print(f\" Value of a = {solver.value(a)}\")\n",
|
|
" print(f\" Value of b = {solver.value(b)}\")\n",
|
|
"\n",
|
|
"\n",
|
|
"def model_with_quadratic_violations() -> None:\n",
|
|
" \"\"\"Adds fixed costs to violated constraints.\"\"\"\n",
|
|
" # Creates the model.\n",
|
|
" model = cp_model.CpModel()\n",
|
|
"\n",
|
|
" # Creates the variables.\n",
|
|
" x = model.new_int_var(0, 10, \"x\")\n",
|
|
" y = model.new_int_var(0, 10, \"y\")\n",
|
|
" z = model.new_int_var(0, 10, \"z\")\n",
|
|
" a = model.new_int_var(0, 10, \"a\")\n",
|
|
" b = model.new_int_var(0, 10, \"b\")\n",
|
|
" square_a = model.new_int_var(0, 100, \"square_a\")\n",
|
|
" square_b = model.new_int_var(0, 100, \"square_b\")\n",
|
|
"\n",
|
|
" # Creates the constraints. Adds enforcement literals to the first two\n",
|
|
" # constraints, we assume the third constraint is always enforced.\n",
|
|
" model.add(x > y - a)\n",
|
|
" model.add(y > z - b)\n",
|
|
" model.add(z > x)\n",
|
|
"\n",
|
|
" model.add_multiplication_equality(square_a, a, a)\n",
|
|
" model.add_multiplication_equality(square_b, b, b)\n",
|
|
"\n",
|
|
" # Adds an objective to minimize the added slacks.\n",
|
|
" model.minimize(square_a + 2 * square_b)\n",
|
|
"\n",
|
|
" # Creates a solver and solves.\n",
|
|
" solver = cp_model.CpSolver()\n",
|
|
" status = solver.solve(model)\n",
|
|
"\n",
|
|
" # Print solution.\n",
|
|
" print(f\" Status = {solver.status_name(status)}\")\n",
|
|
" if status == cp_model.OPTIMAL:\n",
|
|
" print(f\" Objective value = {solver.objective_value}\")\n",
|
|
" print(f\" Value of x = {solver.value(x)}\")\n",
|
|
" print(f\" Value of y = {solver.value(y)}\")\n",
|
|
" print(f\" Value of z = {solver.value(z)}\")\n",
|
|
" print(f\" Value of a = {solver.value(a)}\")\n",
|
|
" print(f\" Value of b = {solver.value(b)}\")\n",
|
|
"\n",
|
|
"\n",
|
|
"def main() -> None:\n",
|
|
" print(\"Infeasible model:\")\n",
|
|
" infeasible_model()\n",
|
|
" print(\"Model with enforcement literals:\")\n",
|
|
" model_with_enforcement_literals()\n",
|
|
" print(\"Model with linear violations:\")\n",
|
|
" model_with_linear_violations()\n",
|
|
" print(\"Model with quadratic violations:\")\n",
|
|
" model_with_quadratic_violations()\n",
|
|
"\n",
|
|
"\n",
|
|
"main()\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"language_info": {
|
|
"name": "python"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|