optimization module

class ezclimate.optimization.CoordinateDescent(utility, var_nums, accuracy=0.0001, iterations=100)

Bases: object

Coordinate descent optimization algorithm for the EZ-Climate model.

Parameters:

• utility (Utility object) – object of utility class
• var_nums (int) – number of elements in array to optimize
• accuracy (float) – stop value for the utility increase
• iterations (int) – maximum number of iterations

utility

Utility object – object of utility class

var_nums

int – number of elements in array to optimize

accuracy

float – stop value for the utility increase

iterations

int – maximum number of iterations

run(m)

Run the coordinate descent iterations.

Parameters:m (initial point) – Returns:best mitigation point and the utility of the best mitigation point Return type:tuple

Note

Uses the scipy package.

class ezclimate.optimization.GeneticAlgorithm(pop_amount, num_generations, cx_prob, mut_prob, bound, num_feature, utility, fixed_values=None, fixed_indicies=None, print_progress=False)

Bases: object

Optimization algorithm for the EZ-Climate model.

Parameters:

• pop_amount (int) – number of individuals in the population
• num_feature (int) – number of elements in each individual, i.e. number of nodes in tree-model
• num_generations (int) – number of generations of the populations to be evaluated
• bound (float) – upper bound of mitigation in each node
• cx_prob (float) – probability of mating
• mut_prob (float) – probability of mutation.
• utility (Utility object) – object of utility class
• fixed_values (ndarray, optional) – nodes to keep fixed
• fixed_indicies (ndarray, optional) – indicies of nodes to keep fixed
• print_progress (bool, optional) – if the progress of the evolution should be printed

pop_amount

int – number of individuals in the population

num_feature

int – number of elements in each individual, i.e. number of nodes in tree-model

num_generations

int – number of generations of the populations to be evaluated

bound

float – upper bound of mitigation in each node

cx_prob

float – probability of mating

mut_prob

float – probability of mutation.

u

Utility object – object of utility class

fixed_values

ndarray, optional – nodes to keep fixed

fixed_indicies

ndarray, optional – indicies of nodes to keep fixed

print_progress

bool, optional – if the progress of the evolution should be printed

run()

Start the evolution process.

The evolution steps are:

1. Select the individuals to perform cross-over and mutation.
2. Cross over among the selected candidate.
3. Mutate result as offspring.
4. Combine the result of offspring and parent together. And selected the top 80 percent of original population amount.
5. Random Generate 20 percent of original population amount new individuals and combine the above new population.

Returns:final population and the fitness for the final population Return type:tuple

Note

Uses the multiprocessing package.

class ezclimate.optimization.GradientSearch(utility, var_nums, accuracy=1e-06, iterations=100, fixed_values=None, fixed_indicies=None, print_progress=False, scale_alpha=None)

Bases: object

Gradient search optimization algorithm for the EZ-Climate model.

Parameters:

• utility (Utility object) – object of utility class
• learning_rate (float) – starting learning rate of gradient descent
• var_nums (int) – number of elements in array to optimize
• accuracy (float) – stop value for the gradient descent
• fixed_values (ndarray, optional) – nodes to keep fixed
• fixed_indicies (ndarray, optional) – indicies of nodes to keep fixed
• print_progress (bool, optional) – if the progress of the evolution should be printed
• scale_alpha (ndarray, optional) – array to scale the learning rate

utility

Utility object – object of utility class

learning_rate

float – starting learning rate of gradient descent

var_nums

int – number of elements in array to optimize

accuracy

float – stop value for the gradient descent

fixed_values

ndarray, optional – nodes to keep fixed

fixed_indicies

ndarray, optional – indicies of nodes to keep fixed

print_progress

bool, optional – if the progress of the evolution should be printed

scale_alpha

ndarray, optional – array to scale the learning rate

gradient_descent(initial_point, return_last=False)

Gradient descent algorithm. The initial_point is updated using the Adam algorithm. Adam uses the history of the gradient to compute individual step sizes for each element in the mitigation vector. The vector of step sizes are calculated using estimates of the first and second moments of the gradient.

Parameters:

• initial_point (ndarray) – initial guess of the mitigation
• return_last (bool, optional) –

  if True the function returns the last point, else the point

  with highest utility

Returns:

(best point, best utility)

Return type:

tuple

numerical_gradient(m, delta=1e-08, fixed_indicies=None)

Calculate utility gradient numerically.

Parameters:

• m (ndarray or list) – array of mitigation
• delta (float, optional) – change in mitigation
• fixed_indicies (ndarray or list, optional) – indicies of gradient that should not be calculated

Returns:

gradient

Return type:

ndarray

run(initial_point_list, topk=4)

Initiate the gradient search algorithm.

Parameters:

• initial_point_list (list) – list of initial points to select from
• topk (int, optional) – select and run gradient descent on the topk first points of initial_point_list

Returns:

best mitigation point and the utility of the best mitigation point

Return type:

tuple

Raises:

ValueError – If topk is larger than the length of initial_point_list.

Note

Uses the multiprocessing package.