class DiscreteOpt(_OptProb):
"""Class for defining discrete-state optimization problems.
Parameters
----------
length: int
Number of elements in state vector.
fitness_fn: fitness function object
Object to implement fitness function for optimization.
maximize: bool, default: True
Whether to maximize the fitness function.
Set :code:`False` for minimization problem.
max_val: int, default: 2
Number of unique values that each element in the state vector
can take. Assumes values are integers in the range 0 to
(max_val - 1), inclusive.
"""
def __init__(self,
length,
fitness_fn,
maximize=True,
max_val=2,
crossover=None,
mutator=None):
self._get_mutual_info_impl = self._get_mutual_info_slow
_OptProb.__init__(self, length, fitness_fn, maximize)
if self.fitness_fn.get_prob_type() == 'continuous':
raise Exception(
"""fitness_fn must have problem type 'discrete',""" +
""" 'either' or 'tsp'. Define problem as""" +
""" ContinuousOpt problem or use alternative""" +
""" fitness function.""")
if max_val < 0:
raise Exception("""max_val must be a positive integer.""")
elif not isinstance(max_val, int):
if max_val.is_integer():
self.max_val = int(max_val)
else:
raise Exception("""max_val must be a positive integer.""")
else:
self.max_val = max_val
self.keep_sample = []
self.node_probs = np.zeros([self.length, self.max_val, self.max_val])
self.parent_nodes = []
self.sample_order = []
self.prob_type = 'discrete'
self.noise = 0
self._crossover = UniformCrossOver(
self) if crossover is None else crossover
self._mutator = SwapMutator(self) if mutator is None else mutator
self._mut_mask = None
self._mut_inf = None
def eval_node_probs(self):
"""Update probability density estimates.
"""
# Create mutual info matrix
mutual_info = self._get_mutual_info_impl()
# Find minimum spanning tree of mutual info matrix
csr_mx = csr_matrix(mutual_info)
mst = minimum_spanning_tree(csr_mx)
# Convert minimum spanning tree to depth first tree with node 0 as root
dft = depth_first_tree(csr_matrix(mst.toarray()), 0, directed=False)
dft = np.round(dft.toarray(), 10)
# Determine parent of each node
parent = np.argmin(dft[:, 1:], axis=0)
# Get probs
probs = np.zeros([self.length, self.max_val, self.max_val])
probs[0, :] = np.histogram(self.keep_sample[:, 0],
np.arange(self.max_val + 1),
density=True)[0]
for i in range(1, self.length):
for j in range(self.max_val):
subset = self.keep_sample[np.where(
self.keep_sample[:, parent[i - 1]] == j)[0]]
if not len(subset):
probs[i, j] = 1 / self.max_val
else:
temp_probs = np.histogram(subset[:, i],
np.arange(self.max_val + 1),
density=True)[0]
# Check if noise argument is not default (in epsilon)
if self.noise > 0:
# Add noise, from the mimic argument "noise"
temp_probs = (temp_probs + self.noise)
# All probability adds up to one
temp_probs = np.divide(temp_probs, np.sum(temp_probs))
# Handle floating point error to ensure probability adds up to 1
if sum(temp_probs) != 1.0:
temp_probs = np.divide(temp_probs,
np.sum(temp_probs))
# Set probability
probs[i, j] = temp_probs
# Update probs and parent
self.node_probs = probs
self.parent_nodes = parent
def set_mimic_fast_mode(self, fast_mode):
if fast_mode:
mut_mask = np.zeros([self.length, self.length], dtype=bool)
for i in range(0, self.length):
for j in range(i, self.length):
mut_mask[i, j] = True
mut_mask = mut_mask.reshape((self.length * self.length))
self._mut_mask = mut_mask
# Set ignore error to ignore dividing by zero
np.seterr(divide='ignore', invalid='ignore')
self._get_mutual_info_impl = self._get_mutual_info_fast
self._mut_inf = np.zeros([self.length * self.length])
else:
self._mut_mask = None
self._get_mutual_info_impl = self._get_mutual_info_slow
self._mut_inf = None
def _get_mutual_info_slow(self):
mutual_info = np.zeros([self.length, self.length])
for i in range(self.length - 1):
for j in range(i + 1, self.length):
mutual_info[i, j] = -1 * mutual_info_score(
self.keep_sample[:, i], self.keep_sample[:, j])
return mutual_info
# adapted from https://github.com/parkds/mlrose/blob/f7154a1d3e3fdcd934bb3c683b943264d2870fd1/mlrose/algorithms.py
# (thanks to David Sejin Park)
def _get_mutual_info_fast(self):
if self._mut_inf is None:
# restore sanity
self._get_mutual_info_impl = self._get_mutual_info_slow
return self._get_mutual_info_impl()
# get length of the sample which survived from mimic iteration
len_sample_kept = self.keep_sample.shape[0]
# get the length of the bit sequence / problem size
len_prob = self.keep_sample.shape[1]
# Expand the matrices to so each row corresponds to a row by row combination of the list of samples
b = np.repeat(self.keep_sample,
self.length).reshape(len_sample_kept,
len_prob * len_prob)
d = np.hstack(([self.keep_sample] * len_prob))
# Compute the mutual information matrix in bulk, by iterating through the list of
# possible feature values ((max_val-1)^2).
# For example, a binary string would go through 00 01 10 11, for a total of 4 iterations.
# First initialize the mutual info matrix.
self._mut_inf.fill(0)
# Pre-compute the U and V which gets computed multiple times in the inner loop.
U = {}
V = {}
U_sum = {}
V_sum = {}
for i in range(0, self.max_val):
U[i] = (d == i)
V[i] = (b == i)
U_sum[i] = np.sum(d == i, axis=0)
V_sum[i] = np.sum(b == i, axis=0)
# Compute the mutual information for all sample to sample combination for each feature combination
# ((max_val-1)^2)
for i in range(0, self.max_val):
for j in range(0, self.max_val):
# This corresponds to U and V of mutual info matrix, for this feature pair
coeff = np.sum(U[i] * V[j], axis=0)
# Compute length N, for the particular feature pair
UV_length = (U_sum[i] * V_sum[j])
# compute the second term of the MI matrix
temp = np.log(coeff) - np.log(UV_length) + np.log(
len_sample_kept)
# remove the nans and negative infinity
temp[np.isnan(temp)] = 0
temp[np.isneginf(temp)] = 0
# combine the first and the second term, divide by the length N.
# Add the whole MI matrix for the feature to the previously computed values
div = temp * np.divide(coeff, len_sample_kept)
div[self._mut_mask] = 0
self._mut_inf += div
# Need to multiply by negative to get the mutual information
self._mut_inf = -self._mut_inf.reshape(self.length, self.length)
# Only get the upper triangle matrix above the identity row.
# Possible enhancements, currently we are doing double the computation required.
# Pre set the matrix so the computation is only done for rows that are needed. To do for the future.
mutual_info = self._mut_inf.T
self._mut_inf = self._mut_inf.reshape(self.length * self.length)
return mutual_info
def find_neighbors(self):
"""Find all neighbors of the current state.
"""
self.neighbors = []
if self.max_val == 2:
for i in range(self.length):
neighbor = np.copy(self.state)
neighbor[i] = np.abs(neighbor[i] - 1)
self.neighbors.append(neighbor)
else:
for i in range(self.length):
vals = list(np.arange(self.max_val))
vals.remove(self.state[i])
for j in vals:
neighbor = np.copy(self.state)
neighbor[i] = j
self.neighbors.append(neighbor)
def find_sample_order(self):
"""Determine order in which to generate sample vector elements.
"""
sample_order = []
last = [0]
parent = np.array(self.parent_nodes)
while len(sample_order) < self.length:
inds = []
# If last nodes list is empty, select random node than has not
# previously been selected
if len(last) == 0:
inds = [
np.random.choice(
list(set(np.arange(self.length)) - set(sample_order)))
]
else:
for i in last:
inds += list(np.where(parent == i)[0] + 1)
sample_order += last
last = inds
self.sample_order = sample_order
def find_top_pct(self, keep_pct):
"""Select samples with fitness in the top keep_pct percentile.
Parameters
----------
keep_pct: float
Proportion of samples to keep.
"""
if (keep_pct < 0) or (keep_pct > 1):
raise Exception("""keep_pct must be between 0 and 1.""")
# Determine threshold
theta = np.percentile(self.pop_fitness, 100 * (1 - keep_pct))
# Determine samples for keeping
keep_inds = np.where(self.pop_fitness >= theta)[0]
# Determine sample for keeping
self.keep_sample = self.population[keep_inds]
def get_keep_sample(self):
""" Return the keep sample.
Returns
-------
self.keep_sample: array
Numpy array containing samples with fitness in the top keep_pct
percentile.
"""
return self.keep_sample
def get_prob_type(self):
""" Return the problem type.
Returns
-------
self.prob_type: string
Returns problem type.
"""
return self.prob_type
def random(self):
"""Return a random state vector.
Returns
-------
state: array
Randomly generated state vector.
"""
state = np.random.randint(0, self.max_val, self.length)
return state
def random_neighbor(self):
"""Return random neighbor of current state vector.
Returns
-------
neighbor: array
State vector of random neighbor.
"""
neighbor = np.copy(self.state)
i = np.random.randint(0, self.length)
if self.max_val == 2:
neighbor[i] = np.abs(neighbor[i] - 1)
else:
vals = list(np.arange(self.max_val))
vals.remove(neighbor[i])
neighbor[i] = vals[np.random.randint(0, self.max_val - 1)]
return neighbor
def random_pop(self, pop_size):
"""Create a population of random state vectors.
Parameters
----------
pop_size: int
Size of population to be created.
"""
if pop_size <= 0:
raise Exception("""pop_size must be a positive integer.""")
elif not isinstance(pop_size, int):
if pop_size.is_integer():
pop_size = int(pop_size)
else:
raise Exception("""pop_size must be a positive integer.""")
population = []
pop_fitness = []
for _ in range(pop_size):
state = self.random()
population.append(state)
fitness = self.eval_fitness(state)
pop_fitness.append(fitness)
self.population = np.array(population)
self.pop_fitness = np.array(pop_fitness)
def reproduce(self, parent_1, parent_2, mutation_prob=0.1):
"""Create child state vector from two parent state vectors.
Parameters
----------
parent_1: array
State vector for parent 1.
parent_2: array
State vector for parent 2.
mutation_prob: float
Probability of a mutation at each state element during
reproduction.
Returns
-------
child: array
Child state vector produced from parents 1 and 2.
"""
if len(parent_1) != self.length or len(parent_2) != self.length:
raise Exception("""Lengths of parents must match problem length""")
if (mutation_prob < 0) or (mutation_prob > 1):
raise Exception("""mutation_prob must be between 0 and 1.""")
# Reproduce parents
child = self._crossover.mate(parent_1, parent_2)
# Mutate child
child = self._mutator.mutate(child, mutation_prob)
return child
def reset(self):
"""Set the current state vector to a random value and get its fitness.
"""
self.state = self.random()
self.fitness = self.eval_fitness(self.state)
def sample_pop(self, sample_size):
"""Generate new sample from probability density.
Parameters
----------
sample_size: int
Size of sample to be generated.
Returns
-------
new_sample: array
Numpy array containing new sample.
"""
if sample_size <= 0:
raise Exception("""sample_size must be a positive integer.""")
elif not isinstance(sample_size, int):
if sample_size.is_integer():
sample_size = int(sample_size)
else:
raise Exception("""sample_size must be a positive integer.""")
# Initialize new sample matrix
new_sample = np.zeros([sample_size, self.length])
# Get value of first element in new samples
new_sample[:, 0] = np.random.choice(self.max_val,
sample_size,
p=self.node_probs[0, 0])
# Get sample order
self.find_sample_order()
sample_order = self.sample_order[1:]
# Get values for remaining elements in new samples
for i in sample_order:
par_ind = self.parent_nodes[i - 1]
for j in range(self.max_val):
inds = np.where(new_sample[:, par_ind] == j)[0]
new_sample[inds, i] = np.random.choice(self.max_val,
len(inds),
p=self.node_probs[i, j])
return new_sample
class DiscreteOpt(_OptProb):
"""Class for defining discrete-state optimization problems.
Parameters
----------
length: int
Number of elements in state vector.
fitness_fn: fitness function object
Object to implement fitness function for optimization.
maximize: bool, default: True
Whether to maximize the fitness function.
Set :code:`False` for minimization problem.
max_val: int, default: 2
Number of unique values that each element in the state vector
can take. Assumes values are integers in the range 0 to
(max_val - 1), inclusive.
"""
def __init__(self, length, fitness_fn, maximize=True, max_val=2,
crossover=None, mutator=None):
_OptProb.__init__(self, length, fitness_fn, maximize)
if self.fitness_fn.get_prob_type() == 'continuous':
raise Exception("""fitness_fn must have problem type 'discrete',"""
+ """ 'either' or 'tsp'. Define problem as"""
+ """ ContinuousOpt problem or use alternative"""
+ """ fitness function."""
)
if max_val < 0:
raise Exception("""max_val must be a positive integer.""")
elif not isinstance(max_val, int):
if max_val.is_integer():
self.max_val = int(max_val)
else:
raise Exception("""max_val must be a positive integer.""")
else:
self.max_val = max_val
self.keep_sample = []
self.node_probs = np.zeros([self.length, self.max_val, self.max_val])
self.parent_nodes = []
self.sample_order = []
self.prob_type = 'discrete'
self._crossover = UniformCrossOver(self) if crossover is None else crossover
self._mutator = SwapMutator(self) if mutator is None else mutator
def eval_node_probs(self):
"""Update probability density estimates.
"""
# Create mutual info matrix
mutual_info = np.zeros([self.length, self.length])
for i in range(self.length - 1):
for j in range(i + 1, self.length):
mutual_info[i, j] = -1 * mutual_info_score(
self.keep_sample[:, i],
self.keep_sample[:, j])
# Find minimum spanning tree of mutual info matrix
mst = minimum_spanning_tree(csr_matrix(mutual_info))
# Convert minimum spanning tree to depth first tree with node 0 as root
dft = depth_first_tree(csr_matrix(mst.toarray()), 0, directed=False)
dft = np.round(dft.toarray(), 10)
# Determine parent of each node
parent = np.argmin(dft[:, 1:], axis=0)
# Get probs
probs = np.zeros([self.length, self.max_val, self.max_val])
probs[0, :] = np.histogram(self.keep_sample[:, 0],
np.arange(self.max_val + 1),
density=True)[0]
for i in range(1, self.length):
for j in range(self.max_val):
subset = self.keep_sample[np.where(
self.keep_sample[:, parent[i - 1]] == j)[0]]
if not len(subset):
probs[i, j] = 1/self.max_val
else:
probs[i, j] = np.histogram(subset[:, i],
np.arange(self.max_val + 1),
density=True)[0]
# Update probs and parent
self.node_probs = probs
self.parent_nodes = parent
def find_neighbors(self):
"""Find all neighbors of the current state.
"""
self.neighbors = []
if self.max_val == 2:
for i in range(self.length):
neighbor = np.copy(self.state)
neighbor[i] = np.abs(neighbor[i] - 1)
self.neighbors.append(neighbor)
else:
for i in range(self.length):
vals = list(np.arange(self.max_val))
vals.remove(self.state[i])
for j in vals:
neighbor = np.copy(self.state)
neighbor[i] = j
self.neighbors.append(neighbor)
def find_sample_order(self):
"""Determine order in which to generate sample vector elements.
"""
sample_order = []
last = [0]
parent = np.array(self.parent_nodes)
while len(sample_order) < self.length:
inds = []
# If last nodes list is empty, select random node than has not
# previously been selected
if len(last) == 0:
inds = [np.random.choice(list(set(np.arange(self.length)) -
set(sample_order)))]
else:
for i in last:
inds += list(np.where(parent == i)[0] + 1)
sample_order += last
last = inds
self.sample_order = sample_order
def find_top_pct(self, keep_pct):
"""Select samples with fitness in the top keep_pct percentile.
Parameters
----------
keep_pct: float
Proportion of samples to keep.
"""
if (keep_pct < 0) or (keep_pct > 1):
raise Exception("""keep_pct must be between 0 and 1.""")
# Determine threshold
theta = np.percentile(self.pop_fitness, 100*(1 - keep_pct))
# Determine samples for keeping
keep_inds = np.where(self.pop_fitness >= theta)[0]
# Determine sample for keeping
self.keep_sample = self.population[keep_inds]
def get_keep_sample(self):
""" Return the keep sample.
Returns
-------
self.keep_sample: array
Numpy array containing samples with fitness in the top keep_pct
percentile.
"""
return self.keep_sample
def get_prob_type(self):
""" Return the problem type.
Returns
-------
self.prob_type: string
Returns problem type.
"""
return self.prob_type
def random(self):
"""Return a random state vector.
Returns
-------
state: array
Randomly generated state vector.
"""
state = np.random.randint(0, self.max_val, self.length)
return state
def random_neighbor(self):
"""Return random neighbor of current state vector.
Returns
-------
neighbor: array
State vector of random neighbor.
"""
neighbor = np.copy(self.state)
i = np.random.randint(0, self.length)
if self.max_val == 2:
neighbor[i] = np.abs(neighbor[i] - 1)
else:
vals = list(np.arange(self.max_val))
vals.remove(neighbor[i])
neighbor[i] = vals[np.random.randint(0, self.max_val-1)]
return neighbor
def random_pop(self, pop_size):
"""Create a population of random state vectors.
Parameters
----------
pop_size: int
Size of population to be created.
"""
if pop_size <= 0:
raise Exception("""pop_size must be a positive integer.""")
elif not isinstance(pop_size, int):
if pop_size.is_integer():
pop_size = int(pop_size)
else:
raise Exception("""pop_size must be a positive integer.""")
population = []
pop_fitness = []
for _ in range(pop_size):
state = self.random()
fitness = self.eval_fitness(state)
population.append(state)
pop_fitness.append(fitness)
self.population = np.array(population)
self.pop_fitness = np.array(pop_fitness)
def reproduce(self, parent_1, parent_2, mutation_prob=0.1):
"""Create child state vector from two parent state vectors.
Parameters
----------
parent_1: array
State vector for parent 1.
parent_2: array
State vector for parent 2.
mutation_prob: float
Probability of a mutation at each state element during
reproduction.
Returns
-------
child: array
Child state vector produced from parents 1 and 2.
"""
if len(parent_1) != self.length or len(parent_2) != self.length:
raise Exception("""Lengths of parents must match problem length""")
if (mutation_prob < 0) or (mutation_prob > 1):
raise Exception("""mutation_prob must be between 0 and 1.""")
# Reproduce parents
child = self._crossover.mate(parent_1, parent_2)
# Mutate child
child = self._mutator.mutate(child, mutation_prob)
return child
def reset(self):
"""Set the current state vector to a random value and get its fitness.
"""
self.state = self.random()
self.fitness = self.eval_fitness(self.state)
def sample_pop(self, sample_size):
"""Generate new sample from probability density.
Parameters
----------
sample_size: int
Size of sample to be generated.
Returns
-------
new_sample: array
Numpy array containing new sample.
"""
if sample_size <= 0:
raise Exception("""sample_size must be a positive integer.""")
elif not isinstance(sample_size, int):
if sample_size.is_integer():
sample_size = int(sample_size)
else:
raise Exception("""sample_size must be a positive integer.""")
# Initialize new sample matrix
new_sample = np.zeros([sample_size, self.length])
# Get value of first element in new samples
new_sample[:, 0] = np.random.choice(self.max_val, sample_size,
p=self.node_probs[0, 0])
# Get sample order
self.find_sample_order()
sample_order = self.sample_order[1:]
# Get values for remaining elements in new samples
for i in sample_order:
par_ind = self.parent_nodes[i-1]
for j in range(self.max_val):
inds = np.where(new_sample[:, par_ind] == j)[0]
new_sample[inds, i] = np.random.choice(self.max_val,
len(inds),
p=self.node_probs[i, j])
return new_sample