# ruff: noqa: B009
import warnings
import numpy as np
import pulp
from geopandas import GeoDataFrame
from scipy.spatial.distance import cdist
from .base import BaseOutputMixin, FacilityModelBuilder, LocateSolver
[docs]
class PCenter(LocateSolver, BaseOutputMixin):
r"""
Implement the :math:`p`-center optimization model and solve it. The
:math:`p`-center problem, as adapted from :cite:`daskin_2013`,
can be formulated as:
.. math::
\begin{array}{lllll}
\displaystyle \textbf{Minimize} & \displaystyle W && & (1) \\
\displaystyle \textbf{Subject To} & \displaystyle \sum_{j \in J}{X_{ij} = 1} && \forall i \in I & (2) \\
& \displaystyle \sum_{j \in J}{Y_j} = p && & (3) \\
& X_{ij} \leq Y_{j} && \forall i \in I \quad \forall j \in J & (4) \\
& W \geq \displaystyle \sum_{j \in J}{d_{ij}X_{ij}} && \forall i \in I & (5) \\
& X_{ij} \in \{0, 1\} && \forall i \in I \quad \forall j \in J & (6) \\
& Y_j \in \{0, 1\} && \forall j \in J & (7) \\
& && & \\
\displaystyle \textbf{Where} && i & = & \textrm{index of demand points/areas/objects in set } I \\
&& j & = & \textrm{index of potential facility sites in set } J \\
&& p & = & \textrm{the number of facilities to be sited} \\
&& d_{ij} & = & \textrm{shortest distance or travel time between locations } i \textrm{ and } j \\
&& X_{ij} & = & \begin{cases}
1, \textrm{if client location } i \textrm{ is served by facility } j \\
0, \textrm{otherwise} \\
\end{cases} \\
&& Y_j & = & \begin{cases}
1, \textrm{if a facility is sited at location } j \\
0, \textrm{otherwise} \\
\end{cases} \\
&& W & = & \textrm{maximum distance between any demand site and its associated facility}
\end{array}
Parameters
----------
name : str
The problem name.
problem : pulp.LpProblem
A ``pulp`` instance of an optimization model that contains
constraints, variables, and an objective function.
aij : numpy.array
A cost matrix in the form of a 2D array between origins and destinations.
Attributes
----------
name : str
The problem name.
problem : pulp.LpProblem
A ``pulp`` instance of an optimization model that contains
constraints, variables, and an objective function.
fac2cli : numpy.array
A 2D array storing facility to client relationships where each
row represents a facility and contains an array of client indices
with which it is associated. An empty client array indicates
the facility is associated with no clients.
cli2fac : numpy.array
The inverse of ``fac2cli`` where client to facility relationships
are shown.
aij : numpy.array
A cost matrix in the form of a 2D array between origins and destinations.
""" # noqa: E501
[docs]
def __init__(self, name: str, problem: pulp.LpProblem, aij: np.array):
self.problem = problem
self.name = name
self.aij = aij
def __add_obj(self) -> None:
"""
Add the objective function to the model.
Minimize W
Returns
-------
None
"""
weight = getattr(self, "weight_var")
self.problem += weight, "objective function"
[docs]
@classmethod
def from_cost_matrix(
cls,
cost_matrix: np.array,
p_facilities: int,
predefined_facilities_arr: np.array = None,
name: str = "p-center",
):
"""
Create a ``PCenter`` object based on a cost matrix.
Parameters
----------
cost_matrix: numpy.array
A cost matrix in the form of a 2D array between origins and destinations.
p_facilities : int
The number of facilities to be located.
predefined_facilities_arr : numpy.array (default None)
A binary 1D array of service facilities that must appear in the
solution. For example, consider 3 facilites ``['A', 'B', 'C']``.
If facility ``'B'`` must be in the model solution, then the passed
in array should be ``[0, 1, 0]``.
name : str (default 'p-center')
The problem name.
Returns
-------
spopt.locate.p_center.PCenter
Examples
--------
>>> from spopt.locate import PCenter
>>> from spopt.locate.util import simulated_geo_points
>>> import geopandas
>>> import pulp
>>> import spaghetti
Create a regular lattice.
>>> lattice = spaghetti.regular_lattice((0, 0, 10, 10), 9, exterior=True)
>>> ntw = spaghetti.Network(in_data=lattice)
>>> streets = spaghetti.element_as_gdf(ntw, arcs=True)
>>> streets_buffered = geopandas.GeoDataFrame(
... geopandas.GeoSeries(streets["geometry"].buffer(0.2).unary_union),
... crs=streets.crs,
... columns=["geometry"]
... )
Simulate points about the lattice.
>>> demand_points = simulated_geo_points(streets_buffered, needed=100, seed=5)
>>> facility_points = simulated_geo_points(streets_buffered, needed=5, seed=6)
Snap the points to the network of lattice edges.
>>> ntw.snapobservations(demand_points, "clients", attribute=True)
>>> clients_snapped = spaghetti.element_as_gdf(
... ntw, pp_name="clients", snapped=True
... )
>>> ntw.snapobservations(facility_points, "facilities", attribute=True)
>>> facilities_snapped = spaghetti.element_as_gdf(
... ntw, pp_name="facilities", snapped=True
... )
Calculate the cost matrix from origins to destinations.
>>> cost_matrix = ntw.allneighbordistances(
... sourcepattern=ntw.pointpatterns["clients"],
... destpattern=ntw.pointpatterns["facilities"]
... )
Create and solve a ``PCenter`` instance from the cost matrix.
>>> pcenter_from_cost_matrix = PCenter.from_cost_matrix(
... cost_matrix, p_facilities=4
... )
>>> pcenter_from_cost_matrix = pcenter_from_cost_matrix.solve(
... pulp.PULP_CBC_CMD(msg=False)
... )
Get the facility-client associations.
>>> for fac, cli in enumerate(pcenter_from_cost_matrix.fac2cli):
... print(f"facility {fac} serving {len(cli)} clients")
facility 0 serving 15 clients
facility 1 serving 24 clients
facility 2 serving 33 clients
facility 3 serving 0 clients
facility 4 serving 28 clients
"""
r_cli = range(cost_matrix.shape[0])
r_fac = range(cost_matrix.shape[1])
model = pulp.LpProblem(name, pulp.LpMinimize)
p_center = PCenter(name, model, cost_matrix)
FacilityModelBuilder.add_facility_integer_variable(p_center, r_fac, "y[{i}]")
FacilityModelBuilder.add_client_assign_variable(
p_center, r_cli, r_fac, "z[{i}_{j}]"
)
FacilityModelBuilder.add_weight_continuous_variable(p_center)
if predefined_facilities_arr is not None:
FacilityModelBuilder.add_predefined_facility_constraint(
p_center, predefined_facilities_arr
)
p_center.__add_obj()
FacilityModelBuilder.add_facility_constraint(p_center, p_facilities)
FacilityModelBuilder.add_assignment_constraint(p_center, r_fac, r_cli)
FacilityModelBuilder.add_opening_constraint(p_center, r_fac, r_cli)
FacilityModelBuilder.add_minimized_maximum_constraint(
p_center, cost_matrix, r_fac, r_cli
)
return p_center
[docs]
@classmethod
def from_geodataframe(
cls,
gdf_demand: GeoDataFrame,
gdf_fac: GeoDataFrame,
demand_col: str,
facility_col: str,
p_facilities: int,
predefined_facility_col: str = None,
distance_metric: str = "euclidean",
name: str = "p-center",
):
"""
Create an ``PCenter`` object from ``geopandas.GeoDataFrame`` objects.
Calculate the cost matrix between demand and facility locations
before building the problem within the ``from_cost_matrix()`` method.
Parameters
----------
gdf_demand : geopandas.GeoDataFrame
Demand locations.
gdf_fac : geopandas.GeoDataFrame
Facility locations.
demand_col : str
Demand sites geometry column name.
facility_col : str
Facility candidate sites geometry column name.
p_facilities: int
The number of facilities to be located.
predefined_facility_col : str (default None)
Column name representing facilities are already defined.
This a binary assignment per facility. For example, consider 3 facilites
``['A', 'B', 'C']``. If facility ``'B'`` must be in the model solution,
then the column should be ``[0, 1, 0]``.
distance_metric : str (default 'euclidean')
A metric used for the distance calculations supported by
`scipy.spatial.distance.cdist <https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.distance.cdist.html>`_.
name : str (default 'p-center')
The name of the problem.
Returns
-------
spopt.locate.p_center.PCenter
Examples
--------
>>> from spopt.locate import PCenter
>>> from spopt.locate.util import simulated_geo_points
>>> import geopandas
>>> import pulp
>>> import spaghetti
Create a regular lattice.
>>> lattice = spaghetti.regular_lattice((0, 0, 10, 10), 9, exterior=True)
>>> ntw = spaghetti.Network(in_data=lattice)
>>> streets = spaghetti.element_as_gdf(ntw, arcs=True)
>>> streets_buffered = geopandas.GeoDataFrame(
... geopandas.GeoSeries(streets["geometry"].buffer(0.2).unary_union),
... crs=streets.crs,
... columns=["geometry"]
... )
Simulate points about the lattice.
>>> demand_points = simulated_geo_points(streets_buffered, needed=100, seed=5)
>>> facility_points = simulated_geo_points(streets_buffered, needed=5, seed=6)
Snap the points to the network of lattice edges
and extract as ``GeoDataFrame`` objects.
>>> ntw.snapobservations(demand_points, "clients", attribute=True)
>>> clients_snapped = spaghetti.element_as_gdf(
... ntw, pp_name="clients", snapped=True
... )
>>> ntw.snapobservations(facility_points, "facilities", attribute=True)
>>> facilities_snapped = spaghetti.element_as_gdf(
... ntw, pp_name="facilities", snapped=True
... )
Create and solve a ``PCenter`` instance from the ``GeoDataFrame`` objects.
>>> pcenter_from_geodataframe = PCenter.from_geodataframe(
... clients_snapped,
... facilities_snapped,
... "geometry",
... "geometry",
... p_facilities=4,
... distance_metric="euclidean"
... )
>>> pcenter_from_geodataframe = pcenter_from_geodataframe.solve(
... pulp.PULP_CBC_CMD(msg=False)
... )
Get the facility-client associations.
>>> for fac, cli in enumerate(pcenter_from_geodataframe.fac2cli):
... print(f"facility {fac} serving {len(cli)} clients")
facility 0 serving 14 clients
facility 1 serving 26 clients
facility 2 serving 34 clients
facility 3 serving 0 clients
facility 4 serving 26 clients
""" # noqa: E501
predefined_facilities_arr = None
if predefined_facility_col is not None:
predefined_facilities_arr = gdf_fac[predefined_facility_col].to_numpy()
dem = gdf_demand[demand_col]
fac = gdf_fac[facility_col]
dem_type_geom = dem.geom_type.unique()
fac_type_geom = fac.geom_type.unique()
_msg = (
" geodataframe contains mixed type geometries or is not a point. Be "
"sure deriving centroid from geometries doesn't affect the results."
)
if len(dem_type_geom) > 1 or "Point" not in dem_type_geom:
warnings.warn(f"Demand{_msg}", UserWarning, stacklevel=2)
dem = dem.centroid
if len(fac_type_geom) > 1 or "Point" not in fac_type_geom:
warnings.warn(f"Facility{_msg}", UserWarning, stacklevel=2)
fac = fac.centroid
dem_data = np.array([dem.x.to_numpy(), dem.y.to_numpy()]).T
fac_data = np.array([fac.x.to_numpy(), fac.y.to_numpy()]).T
if gdf_demand.crs != gdf_fac.crs:
raise ValueError(
"Geodataframes crs are different: "
f"gdf_demand-{gdf_demand.crs}, gdf_fac-{gdf_fac.crs}"
)
distances = cdist(dem_data, fac_data, distance_metric)
return cls.from_cost_matrix(
distances, p_facilities, predefined_facilities_arr, name
)
[docs]
def facility_client_array(self) -> None:
"""
Create a 2D array storing **facility to client relationships** where each
row represents a facility and contains an array of client indices
with which it is associated. An empty client array indicates
the facility is associated with no clients.
Returns
-------
None
"""
fac_vars = getattr(self, "fac_vars")
cli_vars = getattr(self, "cli_assgn_vars")
len_fac_vars = len(fac_vars)
self.fac2cli = []
for j in range(len_fac_vars):
array_cli = []
if fac_vars[j].value() > 0:
for i in range(len(cli_vars)):
if cli_vars[i, j].value() > 0:
array_cli.append(i)
self.fac2cli.append(array_cli)
[docs]
def solve(self, solver: pulp.LpSolver, results: bool = True):
"""
Solve the ``PCenter`` model.
Parameters
----------
solver : pulp.LpSolver
A solver supported by ``pulp``.
results : bool (default True)
If ``True`` it will create metainfo (which facilities cover
which demand) and vice-versa, and the uncovered demand.
Returns
-------
spopt.locate.p_center.PCenter
"""
self.problem.solve(solver)
self.check_status()
if results:
self.facility_client_array()
self.client_facility_array()
return self