def execAZPSA(y, w, pRegions, initialSolution=[], maxit=1):
"""Simulated Annealing variant of Automatic Zoning Procedure (AZP-SA)
AZP-SA aggregates N zones (areas) into M regions. "The M output regions
should be formed of internally connected, contiguous, zones." ([Openshaw_Rao1995]_ pp 428).
AZP-SA is a variant of the AZP algorithm that incorporates a seach
process, called Simulated Annealing algorithm [Kirkpatrick_Gelatt_Vecchi1983]_.
Simulated annealing algorithm "permits moves which result in a worse value
of the objective function but with a probability that diminishes
gradually, through iteration time" ([Openshaw_Rao1995]_ pp 431).
In Openshaw and Rao (1995) the objective function is not defined because
AZP-Tabu can be applied to any function, F(Z). "F(Z) can be any function
defined on data for the M regions in Z, and Z is the allocation of each of
N zones to one of M regions such that each zone is assigned to only one
region" ([Openshaw_Rao1995]_ pp 428)." In clusterPy we Minimize F(Z),
where Z is the within-cluster sum of squares from each area to the
attribute centroid of its cluster.
In order to make the cooling schedule robust the units of measure of the
objective function, we set the Boltzmann's equation as: R(0,1) <
exp((-(Candidate Solution - Current Solution) / Current Solution)/T(k)).
The cooling schedule is T(k) = 0.85 T(k-1) ([Openshaw_Rao1995]_ pp
431), with an initial temperature T(0)=1.
NOTE: The original algorithm proposes to start from a random initial
feasible solution. Previous computational experience showed us that this
approach leads to poor quality solutions. In clusterPy we started from an
initial solution that starts with a initial set of seeds (as many seed as
regions) selected using the K-means++ algorithm. From those seeds, other
neighbouring areas are assigned to its closest (in attribute space)
growing region. This strategy has proven better results. ::
layer.cluster('azpSa',vars,regions,<wType>,<std>,<initialSolution>,<maxit>,<dissolve>,<dataOperations>)
:keyword vars: Area attribute(s) (e.g. ['SAR1','SAR2'])
:type vars: list
:keyword regions: Number of regions
:type regions: integer
:keyword wType: Type of first-order contiguity-based spatial matrix: 'rook' or 'queen'. Default value wType = 'rook'.
:type wType: string
:keyword std: If = 1, then the variables will be standardized.
:type std: binary
:keyword initialSolution: List with a initial solution vector. It is useful when the user wants a solution that is not very different from a preexisting solution (e.g. municipalities,districts, etc.). Note that the number of regions will be the same as the number of regions in the initial feasible solution (regardless the value you assign to parameter "regions"). IMPORTANT: make sure you are entering a feasible solution and according to the W matrix you selected, otherwise the algorithm will not converge.
:type initialSolution: list
:keyword maxit: For a given temperature, perform SA maxit times (see Openshaw and Rao (1995) pp 431, Step b). Default value maxit = 1. NOTE: the parameter Ik, in Step d was fixed at 3.
:type maxit: integer
:keyword dissolve: If = 1, then you will get a "child" instance of the layer that contains the new regions. Default value = 0. Note:. Each child layer is saved in the attribute layer.results. The first algorithm that you run with dissolve=1 will have a child layer in layer.results[0]; the second algorithm that you run with dissolve=1 will be in layer.results[1], and so on. You can export a child as a shapefile with layer.result[<1,2,3..>].exportArcData('filename')
:type dissolve: binary
:keyword dataOperations: Dictionary which maps a variable to a list of operations to run on it. The dissolved layer will contains in it's data all the variables specified in this dictionary. Be sure to check the input layer's fieldNames before use this utility.
:type dataOperations: dictionary
The dictionary structure must be as showed bellow.
>>> X = {}
>>> X[variableName1] = [function1, function2,....]
>>> X[variableName2] = [function1, function2,....]
Where functions are strings wich represents the name of the
functions to be used on the given variableName. Functions
could be,'sum','mean','min','max','meanDesv','stdDesv','med',
'mode','range','first','last','numberOfAreas. By deffault just
ID variable is added to the dissolved map.
"""
print "Running original AZP-SA algorithm (Openshaw and Rao, 1995)"
print "Number of areas: ", len(y)
if initialSolution != []:
print "Number of regions: ", len(numpy.unique(initialSolution))
pRegions = len(numpy.unique(initialSolution))
else:
print "Number of regions: ", pRegions
print "Boltzmann's equation: "
print " R(0,1) < exp((-(Candidate Soution - Current Solution) / Current Solution)/T(k))"
print "Cooling schedule: T(k) = 0.85 T(k-1)"
if pRegions >= len(y):
message = "\n WARNING: You are aggregating "+str(len(y))+" into"+\
str(pRegions)+" regions!!. The number of regions must be an integer"+\
" number lower than the number of areas being aggregated"
raise Exception, message
distanceType = "EuclideanSquared"
distanceStat = "Centroid"
objectiveFunctionType = "SS"
selectionType = "Minimum"
alpha = 0.85
am = AreaManager(w, y, distanceType)
start = tm.time()
# CONSTRUCTION
rm = RegionMaker(am,
pRegions,
initialSolution=initialSolution,
distanceType=distanceType,
distanceStat=distanceStat,
selectionType=selectionType,
objectiveFunctionType=objectiveFunctionType)
print "initial solution: ", rm.returnRegions()
print "initial O.F: ", rm.objInfo
# LOCAL SEARCH
rm.AZPSA(alpha, maxit)
time = tm.time() - start
Sol = rm.returnRegions()
Of = rm.objInfo
print "FINAL SOLUTION: ", Sol
print "FINAL OF: ", Of
output = {
"objectiveFunction": Of,
"runningTime": time,
"algorithm": "azpSa",
"regions": len(Sol),
"r2a": Sol,
"distanceType": distanceType,
"distanceStat": distanceStat,
"selectionType": selectionType,
"ObjectiveFuncionType": objectiveFunctionType
}
print "Done"
return output
