MOBO package

Submodules

MOBO.BO module

class MOBO.BO.BayesianOptimizationProblem(mogp)

Bases: object

pyGMO wrapper for gaussian process regression

fitness(x)
get_bounds()
get_nobj()
set_bounds(bounds)
class MOBO.BO.MultiObjectiveBayesianOptimization

Bases: object

run_kmeans(n_clusters=8, init='k-means++', n_init=10, max_iter=300, tol=0.0001, precompute_distances='auto', verbose=0, random_state=None, copy_x=True, n_jobs=1)

clustering parate front solutions by k-means

Parameters:
  • n_clusters (int) – optional, default 8 The number of clusters to form as well as the number of centroids to generate.
  • init – (‘k-means++’, ‘random’ or an ndarray) Method for initialization, defaults to ‘k-means++’: ‘k-means++’ : selects initial cluster centers for k-mean clustering in a smart way to speed up convergence. See section Notes in k_init for more details. ‘random’: choose k observations (rows) at random from data for the initial centroids. If an ndarray is passed, it should be of shape (n_clusters, n_features) and gives the initial centers.
  • n_init (int) – default 10 Number of time the k-means algorithm will be run with different centroid seeds. The final results will be the best output of n_init consecutive runs in terms of inertia.
  • max_iter (int) – default 300 Maximum number of iterations of the k-means algorithm for a single run.
  • tol – float, default: 1e-4 Relative tolerance with regards to inertia to declare convergence
  • precompute_distances – {‘auto’, True, False} Precompute distances (faster but takes more memory). ‘auto’ : do not precompute distances if n_samples * n_clusters > 12 million. This corresponds to about 100MB overhead per job using double precision. True : always precompute distances False : never precompute distances
  • verbose – int, default 0 Verbosity mode.
  • random_state – int, RandomState instance or None (default) Determines random number generation for centroid initialization. Use an int to make the randomness deterministic.
  • copy_x – boolean, optional When pre-computing distances it is more numerically accurate to center the data first. If copy_x is True (default), then the original data is not modified, ensuring X is C-contiguous. If False, the original data is modified, and put back before the function returns, but small numerical differences may be introduced by subtracting and then adding the data mean, in this case it will also not ensure that data is C-contiguous which may cause a significant slowdown.
  • n_jobs – int or None, optional (default=None) The number of jobs to use for the computation. This works by computing each of the n_init runs in parallel. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors.
  • algorithm – “auto”, “full” or “elkan”, default=”auto” K-means algorithm to use. The classical EM-style algorithm is “full”. The “elkan” variation is more efficient by using the triangle inequality, but currently doesn’t support sparse data. “auto” chooses “elkan” for dense data and “full” for sparse data.

Examples:

mobo = MOBO.MultiObjectiveBayesianOptimization()
mobo.set_train_data(x_observed, y_observed)
mobo.train_GPModel()

See also

https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html

run_mobo(func=None, args=[], n_dv=0, n_obj_cons=0, n_init_lhs_samples=24, n_iter=10, n_new_ind=16, ga_pop_size=100, ga_gen=50, n_cons=0, mutation=0.03)

runs multi-objective bayesian optimization

Parameters:
  • func – multi objective function you want to minimize. y = f(x, agrs=[]) 0 <= x[i] <=1
  • args (list) – parameters for the function.
  • n_dv (int) – number of design variabels
  • n_obj (int) – number of objective functions n_init_lhs_sampling (int): initial population of bayesian optimization
  • n_iter (int) – number of iteration of bayesian optimization n_new_ind (int): number of new indivisuals in each iteration.
  • ga_pop_size (int) – population size of multi objective genetic algorithm (NSGA2) ga_pop_size must be multiply number of four.
  • ga_gen (int) – generation number of multi objective genetic algorithm (NSGA2)
  • n_cons (int) – number of constraints functions
run_moead(size=48, gen=100)

runs multi-objective genetic algorithm using gaussian process regression. objective function is Expected Improvement. :param size: population size (default=48) :type size: int :param gen: generation size (default=100) :type gen: int

Examples:

mobo = MOBO.MultiObjectiveBayesianOptimization()
mobo.set_train_data(x_observed, y_observed)
mobo.train_GPModel()
run_moga(size=48, gen=100, m=0.03)

runs multi-objective genetic algorithm using gaussian process regression. objective function is Expected Improvement. :param size: population size (default=48) :type size: int :param gen: generation size (default=100) :type gen: int

Examples:

mobo = MOBO.MultiObjectiveBayesianOptimization()
mobo.set_train_data(x_observed, y_observed)
mobo.train_GPModel()
set_number_of_cpu_core(n_multiprocessing=4)

sets number of cpu cores you use in multi-objective EI calculation (default all cpu) Examples:

cpu = 4
mobo.set_number_of_cpu_core(cpu)
set_optimum_direction(direction_list)
Parameters:direction_list (list) – list of 1 and -1 which expresses the direction of optimum

Examples:

direction_list = [-1, 1, -1]
mobo.set_optimum_direction(direction_list)
set_train_data(x_observed, y_observed, n_cons=0)
Parameters:
  • x_observed – np.array (n_samples, n_params)
  • y_observed – np.array (n_samples, n_obj + n_cons)

Example:

mobo = MOBO.MultiObjectiveBayesianOptimization()
mobo.set_train_data(x_observed, y_observed)
train_GPModel(kernel=Matern(length_scale=1, nu=1.5))

Examples:

mobo = MOBO.MultiObjectiveBayesianOptimization()
mobo.set_train_data(x_observed, y_observed)
mobo.train_GPModel()

MOBO.GP module

class MOBO.GP.GaussianProcess

Bases: object

Multi-Objective Gaussian Process core class

Note

Set parameters first before train

(https://thuijskens.github.io/2016/12/29/bayesian-optimisation/)

Example:

mogp = MOBO.GaussianProcess()
mogp.set_train_data(x_observed, y_observed)
mogp.train()
x = np.array([[-5, -5]])
print(mogp.predict(x))

x = np.array([[-4.9, -4.9]])
print(mogp.expected_improvement(x))
constrained_EI(x)

uses probability of g(x) <= 0. g > 0 is infeasible.

expected_hypervolume_improvement(x)

Expected hypervolume improvement function.

Note

under construction!

expected_improvement(x)

Expected improvement function.

Parameters:x (array-like) – shape = [n_samples, n_params]

Examples:

x = np.array([[-4.9, -4.9]])
ei = mogp.expected_improvement(x)
print(ei)
predict_original_coor(x)

Note

use it after training

Parameters:x – np.array, size = [n_input, n_params]
Returns:mean and std size = [2, n_obj]
Return type:mu, sigma (float or list)

Example:

x = np.array([-5, -5])
mu, sigma = mogp.predict(x)
print(mu, sigma)
predict_standarize_value(x)

Note

use it after training

Parameters:x – np.array, size = [n_input, n_params]
Returns:mean and std size = [2, n_obj]
Return type:mu, sigma (float or list)

Example:

x = np.array([-5, -5])
mu, sigma = mogp.predict(x)
print(mu, sigma)
probability_of_feasibility(x)

calculates the probability of feasibility. uses probability of g(x) <= 0. g > 0 is infeasible.

set_number_of_cpu_core(n_multiprocessing)
set_optimum_direction(direction_list)
Parameters:
  • direction_list (list) – list of 1 and -1
  • expresses the direction of optimum (which) –

Examples:

direction_list = [-1, 1, -1]
mogp.set_optimum_direction(direction_list)
set_train_data(x_observed, y_observed, n_cons=0)
Parameters:
  • x_observed – np.array (n_samples, n_params)
  • y_observed – np.array (n_samples, n_obj)

Example:

mogp = MOBO.GaussianProcess()
mogp.set_train_data(x_observed, y_observed)
train(kernel=Matern(length_scale=1, nu=1.5))

trains Gaussian process for regression

Note

multi-objective optimization (n_obj > 1) is also available.

Parameters:kernel – kernel implemented in sklearn.gp (default: gp.kernels.Matern())

Example:

mogp = MOBO.GaussianProcess()
mogp.set_train_data(x_observed, y_observed)
mogp.train()
wrapper_mp(i_obj)
class MOBO.GP.MpHelper(cls, mtd_name)

Bases: object

helper function for multiprocessing to call class method

Note

japanese site http://aflc.hatenablog.com/entry/20110825/1314366131

Module contents