class HyperVolume(AbstractConvergenceMetric):
'''Hypervolume convergence metric class
This metric is derived from a hyper-volume measure, which describes the
multi-dimensional volume of space contained within the pareto front. When
computed with minimum and maximums, it describes the ratio of dominated
outcomes to all possible outcomes in the extent of the space. Getting this
number to be high or low is not necessarily important, as not all outcomes
within the min-max range will be feasible. But, having the hypervolume remain
fairly stable over multiple generations of the evolutionary algorithm provides
an indicator of convergence.
Parameters
---------
minimum : numpy array
maximum : numpy array
'''
def __init__(self, minimum, maximum):
super(HyperVolume, self).__init__("hypervolume")
self.hypervolume_func = Hypervolume(minimum=minimum, maximum=maximum)
def __call__(self, optimizer):
self.results.append(
self.hypervolume_func.calculate(optimizer.algorithm.archive))
@classmethod
def from_outcomes(cls, outcomes):
ranges = [_.expected_range() for _ in outcomes]
return cls([_[0] for _ in ranges], [_[1] for _ in ranges])
class HyperVolume(AbstractConvergenceMetric):
'''Hypervolume convergence metric class
This metric is derived from a hyper-volume measure, which describes the
multi-dimensional volume of space contained within the pareto front. When
computed with minimum and maximums, it describes the ratio of dominated
outcomes to all possible outcomes in the extent of the space. Getting this
number to be high or low is not necessarily important, as not all outcomes
within the min-max range will be feasible. But, having the hypervolume remain
fairly stable over multiple generations of the evolutionary algorithm provides
an indicator of convergence.
Parameters
---------
minimum : numpy array
maximum : numpy array
'''
def __init__(self, minimum, maximum):
super(HyperVolume, self).__init__("hypervolume")
self.hypervolume_func = Hypervolume(minimum=minimum, maximum=maximum)
def __call__(self, optimizer):
self.results.append(self.hypervolume_func.calculate(
optimizer.algorithm.archive))
@classmethod
def from_outcomes(cls, outcomes):
ranges = [o.expected_range for o in outcomes if o.kind != o.INFO]
minimum, maximum = np.asarray(list(zip(*ranges)))
return cls(minimum, maximum)
class HyperVolume(AbstractConvergenceMetric):
'''Hypervolume convergence metric class
Parameters
---------
minimum : numpy array
maximum : numpy array
'''
def __init__(self, minimum, maximum):
super(HyperVolume, self).__init__("hypervolume")
self.hypervolume_func = Hypervolume(minimum=minimum, maximum=maximum)
def __call__(self, optimizer):
self.results.append(self.hypervolume_func.calculate(optimizer.algorithm.archive))
class HyperVolume(AbstractConvergenceMetric):
'''Hypervolume convergence metric class
Parameters
---------
minimum : numpy array
maximum : numpy array
'''
def __init__(self, minimum, maximum):
super(HyperVolume, self).__init__("hypervolume")
self.hypervolume_func = Hypervolume(minimum=minimum, maximum=maximum)
def __call__(self, optimizer):
self.results.append(
self.hypervolume_func.calculate(optimizer.algorithm.archive))
for _ in range(1000):
solution = Solution(problem)
solution.variables = [random.uniform(0,1) if i < problem.nobjs-1 else 0.5 for i in range(problem.nvars)]
solution.evaluate()
reference_set.add(solution)
# compute the indicators
gd = GenerationalDistance(reference_set)
print("Generational Distance:", gd.calculate(algorithm.result))
igd = InvertedGenerationalDistance(reference_set)
print("Inverted Generational Distance:", igd.calculate(algorithm.result))
hyp = Hypervolume(reference_set)
print("Hypervolume:", hyp.calculate(algorithm.result))
ei = EpsilonIndicator(reference_set)
print("Epsilon Indicator:", ei.calculate(algorithm.result))
sp = Spacing()
print("Spacing:", sp.calculate(algorithm.result))
# plot the result versus the reference set
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1, projection='3d')
ax.scatter([s.objectives[0] for s in reference_set],
[s.objectives[1] for s in reference_set],
constraint.append(Real(vd,vcap)) #x3 (range from vdead to vcapacity), check condition later
constraint.append(Real(0.0001,(math.pi/2-0.0001))) #x4 (0-pi/2), but avoid 0 and pi (90 degree)
num_var+=48
reservoirs[i][1] = 5
# Call optimization function
problem = Problem(num_var, totalobs)
problem.types[:] = constraint
problem.function = viccall
problem.constraints[:] = ">=0"
start = datetime.datetime.now()
hyp = Hypervolume(minimum=minvar, maximum=maxvar)
allresults = []
with ProcessPoolEvaluator(number_of_cores) as evaluator:
algorithm = EpsNSGAII(problem, eps, population_size=population, evaluator = evaluator)
while algorithm.nfe<number_of_functions:
algorithm.step()
one_step_result = hyp.calculate(algorithm.result) #this param stores information of hypervolume indicator, save as a file if needed
allresults.append(one_step_result)
end = datetime.datetime.now()
nondominated_solutions = nondominated(algorithm.result)
os.chdir('../Results')
# Finish and save results to files
print("Start",start)
print("End",end)
print("Finish running simulations! See opt_objectives.txt and opt_variables.txt for results.")
np.savetxt("optimization_objectives.txt",[s.objectives[:] for s in nondominated_solutions],fmt="%s")
np.savetxt("optimization_variables.txt",[s.variables[:] for s in nondominated_solutions],fmt="%s")
# END OF FILE
# ------------------------------------------------------------------------------------------------------------------------------------------------
for _ in range(1000):
solution = Solution(problem)
solution.variables = [random.uniform(0,1) if i < problem.nobjs-1 else 0.5 for i in range(problem.nvars)]
solution.evaluate()
reference_set.add(solution)
# compute the indicators
gd = GenerationalDistance(reference_set)
print("Generational Distance:", gd.calculate(algorithm.result))
igd = InvertedGenerationalDistance(reference_set)
print("Inverted Generational Distance:", igd.calculate(algorithm.result))
hyp = Hypervolume(reference_set)
print("Hypervolume:", hyp.calculate(algorithm.result))
ei = EpsilonIndicator(reference_set)
print("Epsilon Indicator:", ei.calculate(algorithm.result))
sp = Spacing()
print("Spacing:", sp.calculate(algorithm.result))
# plot the result versus the reference set
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1, projection='3d')
ax.scatter([s.objectives[0] for s in reference_set],
[s.objectives[1] for s in reference_set],
# Setup optimization parameters
problem = Problem(no_vars, no_of_obj)
problem.types[:] = VIC_types
problem.function = viccall
hyp = Hypervolume(minimum=minobj, maximum=maxobj)
x = []
# Start simulations
with ProcessPoolEvaluator(number_of_core) as evaluator:
algorithm = EpsNSGAII(problem,
eps,
population_size=pop_size,
evaluator=evaluator)
while algorithm.nfe <= number_functions:
algorithm.step()
y = hyp.calculate(algorithm.result)
x.append(y)
end = datetime.datetime.now()
nondominated_solutions = nondominated(algorithm.result)
os.chdir('../Results')
# Finish and save results to files
print("Start", start)
print("End", end)
print(
"Finish running simulations! See opt_objectives.txt and opt_variables.txt for results."
)
np.savetxt("calibration_objectives.txt",
[s.objectives[:] for s in nondominated_solutions],
fmt="%s")
np.savetxt("calibration_variables.txt",