spopt.locate.PCenter¶
- class spopt.locate.PCenter(name: str, problem: LpProblem, aij: array)[source]¶
Implement the \(p\)-center optimization model and solve it. The \(p\)-center problem, as adapted from [Das13], can be formulated as:
\[\begin{split}\begin{array}{lllll} \displaystyle \textbf{Minimize} & \displaystyle W && & (1) \\ \displaystyle \textbf{Subject To} & \displaystyle \sum_{j \in J}{X_{ij} = 1} && \forall i \in I & (2) \\ & \displaystyle \sum_{j \in J}{Y_j} = p && & (3) \\ & X_{ij} \leq Y_{j} && \forall i \in I \quad \forall j \in J & (4) \\ & W \geq \displaystyle \sum_{j \in J}{d_{ij}X_{ij}} && \forall i \in I & (5) \\ & X_{ij} \in \{0, 1\} && \forall i \in I \quad \forall j \in J & (6) \\ & Y_j \in \{0, 1\} && \forall j \in J & (7) \\ & && & \\ \displaystyle \textbf{Where} && i & = & \textrm{index of demand points/areas/objects in set } I \\ && j & = & \textrm{index of potential facility sites in set } J \\ && p & = & \textrm{the number of facilities to be sited} \\ && d_{ij} & = & \textrm{shortest distance or travel time between locations } i \textrm{ and } j \\ && X_{ij} & = & \begin{cases} 1, \textrm{if client location } i \textrm{ is served by facility } j \\ 0, \textrm{otherwise} \\ \end{cases} \\ && Y_j & = & \begin{cases} 1, \textrm{if a facility is sited at location } j \\ 0, \textrm{otherwise} \\ \end{cases} \\ && W & = & \textrm{maximum distance between any demand site and its associated facility} \end{array}\end{split}\]- 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.
- name
- 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.
- name
- __init__(name: str, problem: LpProblem, aij: array)[source]¶
Initialize.
- Parameters:
- name
str
The desired name for the model.
- name
Methods
__init__
(name, problem, aij)Initialize.
check_status
()Ensure a model is solved.
client_facility_array
()Create a 2D array storing client to facility relationships where each row represents a client and contains an array of facility indices with which it is associated.
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.
from_cost_matrix
(cost_matrix, p_facilities)Create a
PCenter
object based on a cost matrix.from_geodataframe
(gdf_demand, gdf_fac, ...)Create an
PCenter
object fromgeopandas.GeoDataFrame
objects.solve
(solver[, results])Solve the
PCenter
model.- facility_client_array() None [source]¶
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:
- classmethod from_cost_matrix(cost_matrix: array, p_facilities: int, predefined_facilities_arr: array = None, name: str = 'p-center')[source]¶
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
(defaultNone
) 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:
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
- classmethod from_geodataframe(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')[source]¶
Create an
PCenter
object fromgeopandas.GeoDataFrame
objects. Calculate the cost matrix between demand and facility locations before building the problem within thefrom_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
(defaultNone
) 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.
- name
str
(default ‘p-center’) The name of the problem.
- gdf_demand
- Returns:
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 theGeoDataFrame
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