Source code for qiskit_optimization.applications.graph_partition

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# (C) Copyright IBM 2018, 2021.
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
# Any modifications or derivative works of this code must retain this
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"""An application class for the graph partitioning."""

from typing import Dict, List, Optional, Union

import networkx as nx
import numpy as np
from docplex.mp.model import Model

from qiskit_optimization.algorithms import OptimizationResult
from qiskit_optimization.problems.quadratic_program import QuadraticProgram
from qiskit_optimization.translators import from_docplex_mp
from .graph_optimization_application import GraphOptimizationApplication

[docs]class GraphPartition(GraphOptimizationApplication): """Optimization application for the "graph partition" [1] problem based on a NetworkX graph. References: [1]: "Graph partition", https://en.wikipedia.org/wiki/Graph_partition """
[docs] def to_quadratic_program(self) -> QuadraticProgram: """Convert a graph partition instance into a :class:`~qiskit_optimization.problems.QuadraticProgram` Returns: The :class:`~qiskit_optimization.problems.QuadraticProgram` created from the graph partition instance. """ mdl = Model(name="Graph partition") n = self._graph.number_of_nodes() x = {i: mdl.binary_var(name=f"x_{i}") for i in range(n)} for w, v in self._graph.edges: self._graph.edges[w, v].setdefault("weight", 1) objective = mdl.sum( self._graph.edges[i, j]["weight"] * (x[i] + x[j] - 2 * x[i] * x[j]) for i, j in self._graph.edges ) mdl.minimize(objective) mdl.add_constraint(mdl.sum([x[i] for i in x]) == n // 2) op = from_docplex_mp(mdl) return op
[docs] def interpret(self, result: Union[OptimizationResult, np.ndarray]) -> List[List[int]]: """Interpret a result as a list of node indices Args: result : The calculated result of the problem Returns: A list of node indices divided into two groups. """ x = self._result_to_x(result) partition = [[], []] # type: List[List[int]] for i, value in enumerate(x): if value == 0: partition[0].append(i) else: partition[1].append(i) return partition
def _draw_result( self, result: Union[OptimizationResult, np.ndarray], pos: Optional[Dict[int, np.ndarray]] = None, ) -> None: """Draw the result with colors Args: result : The calculated result for the problem pos: The positions of nodes """ x = self._result_to_x(result) nx.draw(self._graph, node_color=self._node_colors(x), pos=pos, with_labels=True) def _node_colors(self, x: np.ndarray) -> List[str]: # Return a list of strings for draw. # Color a node with red when the corresponding variable is 1. # Otherwise color it with blue. return ["r" if x[node] else "b" for node in self._graph.nodes]

© Copyright 2018, 2021, Qiskit Optimization Development Team.

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