Sphere 4D benchmark

Import required modules



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# Init matplotlib

%matplotlib inline

import matplotlib
matplotlib.rcParams['figure.figsize'] = (8, 8)



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# Setup PyAI
import sys
sys.path.insert(0, '/Users/jdecock/git/pub/jdhp/pyai')



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import numpy as np
import time
import warnings

from scipy import optimize



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# Plot functions
from pyai.optimize.utils import array_list_to_array
from pyai.optimize.utils import plot_err_wt_num_feval

Define the objective function



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## Objective function: Rosenbrock function (Scipy's implementation)
#func = scipy.optimize.rosen



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# Set the objective function
#from pyai.optimize.functions import sphere as func
from pyai.optimize.functions import Sphere
#from pyai.optimize.functions import additive_gaussian_noise as noise
from pyai.optimize.functions import multiplicative_gaussian_noise as noise
#from pyai.optimize.functions import additive_poisson_noise as noise

func = Sphere(ndim=4)

func.noise = noise      # Comment this line to use a deterministic objective function



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print(func)
print(func.bounds)
print(func.ndim)
print(func.arg_min)
print(func(func.arg_min))

The "basin-hopping" algorithm (Scipy)



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%%time

bh_eval_error_array_list = []

NUM_RUNS = 100

for run_index in range(NUM_RUNS):
    x_init = np.random.random(func.ndim)   # draw samples in [0.0, 1.0)
    min_bounds = func.bounds[0]
    max_bounds = func.bounds[1]
    x_init *= (max_bounds - min_bounds)
    x_init += min_bounds

    func.do_eval_logs = True
    func.reset_eval_counters()
    func.reset_eval_logs()

    init_time = time.time()

    with warnings.catch_warnings():
        warnings.simplefilter("ignore")
        res = optimize.basinhopping(func,
                                    x_init,            # The initial point
                                    niter=100,         # The number of basin hopping iterations
                                    disp=False)        # Print status messages

    func.do_eval_logs = False

    eval_error_array = np.array(func.eval_logs_dict['fx']) - func(func.arg_min)

    print("x* =", res.x)
    print("f(x*) =", res.fun)
    #print("Cause of the termination:", ";".join(res.message))
    #print("Number of evaluations of the objective functions:", res.nfev)
    #print("Number of evaluations of the jacobian:", res.njev)
    #print("Number of iterations performed by the optimizer:", res.nit)
    
    bh_eval_error_array_list.append(eval_error_array);

The "Differential Evolution" (DE) algorithm (Scipy)



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%%time

de_eval_error_array_list = []

NUM_RUNS = 100

for run_index in range(NUM_RUNS):
    bounds = func.bounds.T.tolist()

    func.do_eval_logs = True
    func.reset_eval_counters()
    func.reset_eval_logs()

    init_time = time.time()

    with warnings.catch_warnings():
        warnings.simplefilter("ignore")
        res = optimize.differential_evolution(func,
                                              bounds,              # The initial point
                                              maxiter=100,         # The number of DE iterations
                                              polish=False,
                                              disp=False)          # Print status messages

    func.do_eval_logs = False

    eval_error_array = np.array(func.eval_logs_dict['fx']) - func(func.arg_min)

    print("x* =", res.x)
    print("f(x*) =", res.fun)
    #print("Cause of the termination:", ";".join(res.message))
    #print("Number of evaluations of the objective functions:", res.nfev)
    #print("Number of evaluations of the jacobian:", res.njev)
    #print("Number of iterations performed by the optimizer:", res.nit)
    
    de_eval_error_array_list.append(eval_error_array);

SAES (PyAI)



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from pyai.optimize import SAES



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%%time

saes_eval_error_array_list = []

NUM_RUNS = 100

for run_index in range(NUM_RUNS):
    saes = SAES()

    func.do_eval_logs = True
    func.reset_eval_counters()
    func.reset_eval_logs()

    res = saes.minimize(func, init_pop_mu=0., init_pop_sigma=6., mu=3, lmb=6)

    func.do_eval_logs = False

    eval_error_array = np.array(func.eval_logs_dict['fx']) - func(func.arg_min)

    print("x* =", res)
    
    saes_eval_error_array_list.append(eval_error_array);



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fig, ax = plt.subplots(figsize=(12, 8))

#plot_err_wt_num_feval(array_list_to_array(bh_eval_error_array_list), x_log=True, y_log=True, ax=ax, label="Basin Hopping", plot_option="mean")
plot_err_wt_num_feval(array_list_to_array(de_eval_error_array_list), x_log=True, y_log=True, ax=ax, label="Differential Evolution", plot_option="mean")
plot_err_wt_num_feval(array_list_to_array(saes_eval_error_array_list), x_log=True, y_log=True, ax=ax, label="SAES", plot_option="mean")

ax.legend(fontsize='x-large')

plt.show()