A simple example showcasing CBX#

[1]:

%load_ext autoreload
%autoreload 2
import cbx as cbx
from cbx.dynamics import CBO
from cbx.objectives import Rastrigin
import cbx.utils.termination as term
from cbx.scheduler import effective_sample_size

The autoreload extension is already loaded. To reload it, use:
  %reload_ext autoreload

Define the parameters#

[2]:

conf = {'alpha': 40.0,
        'dt': 0.1,
        'sigma': 1.,
        'lamda': 1.0,
        'batch_args':{
        'batch_size':200,
        'batch_partial': False},
        'd': 2,
        'term_criteria':[term.max_it_term(50)],
        'N': 50,
        'M': 3,
        'track_args': {'names':
                       ['update_norm',
                        'energy','x',
                        'consensus',
                        'drift']},}

Define the initial positions of the particles and objective function#

[3]:

x = cbx.utils.init_particles(shape=(conf['M'], conf['N'], conf['d']), x_min=-2., x_max = 1.)
f = Rastrigin()

Define the dynamic and scheduler#

[4]:

dyn = CBO(f, x=x, noise='isotropic', f_dim='3D',
          **conf)
sched = effective_sample_size(name='alpha', eta = 0.1)

Run the CBO algorithm#

[5]:

dyn.optimize(sched=sched)

....................
Starting Optimization with dynamic: CBO
....................
Time: 0.100, best current energy: [ 33.68654168 120.71036047  62.80683578]
Number of function evaluations: [100 100 100]
Time: 0.200, best current energy: [28.58152131 81.26971772 34.44364278]
Number of function evaluations: [150 150 150]
Time: 0.300, best current energy: [28.62646872 67.2817824  34.44364278]
Number of function evaluations: [200 200 200]
Time: 0.400, best current energy: [17.48615705 49.59452258 34.44364278]
Number of function evaluations: [250 250 250]
Time: 0.500, best current energy: [17.48616666 19.10682227 13.33378508]
Number of function evaluations: [300 300 300]
Time: 0.600, best current energy: [17.49727879  0.90316275  3.90712534]
Number of function evaluations: [350 350 350]
Time: 0.700, best current energy: [17.49727879  0.90316275  3.90712154]
Number of function evaluations: [400 400 400]
Time: 0.800, best current energy: [13.74853011  0.90316275  2.54385584]
Number of function evaluations: [450 450 450]
Time: 0.900, best current energy: [13.7896205   0.90316275  2.66192072]
Number of function evaluations: [500 500 500]
Time: 1.000, best current energy: [9.56378915 0.85071259 2.53878036]
Number of function evaluations: [550 550 550]
Time: 1.100, best current energy: [1.65695363 0.84499308 1.79225608]
Number of function evaluations: [600 600 600]
Time: 1.200, best current energy: [0.30609722 0.84500232 1.79423101]
Number of function evaluations: [650 650 650]
Time: 1.300, best current energy: [0.34922258 0.44816694 1.79431591]
Number of function evaluations: [700 700 700]
Time: 1.400, best current energy: [0.36915171 0.27820948 1.79484459]
Number of function evaluations: [750 750 750]
Time: 1.500, best current energy: [0.36017227 0.21050182 1.76474269]
Number of function evaluations: [800 800 800]
Time: 1.600, best current energy: [0.21274971 0.23505038 1.72918115]
Number of function evaluations: [850 850 850]
Time: 1.700, best current energy: [0.12348101 0.21199976 1.75816384]
Number of function evaluations: [900 900 900]
Time: 1.800, best current energy: [0.05143352 0.30367209 1.94523642]
Number of function evaluations: [950 950 950]
Time: 1.900, best current energy: [0.0540006  0.35056549 1.72136138]
Number of function evaluations: [1000 1000 1000]
Time: 2.000, best current energy: [0.06110012 0.38862823 0.81879727]
Number of function evaluations: [1050 1050 1050]
Time: 2.100, best current energy: [0.11740263 0.3865363  0.82657734]
Number of function evaluations: [1100 1100 1100]
Time: 2.200, best current energy: [0.11257089 0.39789684 0.80443249]
Number of function evaluations: [1150 1150 1150]
Time: 2.300, best current energy: [0.16063367 0.35253543 0.42259068]
Number of function evaluations: [1200 1200 1200]
Time: 2.400, best current energy: [0.00862797 0.36359695 0.20873996]
Number of function evaluations: [1250 1250 1250]
Time: 2.500, best current energy: [0.00547368 0.31876961 0.22591405]
Number of function evaluations: [1300 1300 1300]
Time: 2.600, best current energy: [0.01746446 0.33732993 0.22473574]
Number of function evaluations: [1350 1350 1350]
Time: 2.700, best current energy: [0.1102633  0.08918512 0.07924495]
Number of function evaluations: [1400 1400 1400]
Time: 2.800, best current energy: [0.12797242 0.05583967 0.03559821]
Number of function evaluations: [1450 1450 1450]
Time: 2.900, best current energy: [0.1343424  0.0026892  0.02978487]
Number of function evaluations: [1500 1500 1500]
Time: 3.000, best current energy: [0.14289871 0.00705355 0.03382854]
Number of function evaluations: [1550 1550 1550]
Time: 3.100, best current energy: [0.04305495 0.00800484 0.04023679]
Number of function evaluations: [1600 1600 1600]
Time: 3.200, best current energy: [0.04527542 0.00193493 0.02004014]
Number of function evaluations: [1650 1650 1650]
Time: 3.300, best current energy: [5.71784399e-02 1.97961671e-05 8.34815345e-03]
Number of function evaluations: [1700 1700 1700]
Time: 3.400, best current energy: [0.04809217 0.00035915 0.00896287]
Number of function evaluations: [1750 1750 1750]
Time: 3.500, best current energy: [0.04800839 0.00152849 0.00664716]
Number of function evaluations: [1800 1800 1800]
Time: 3.600, best current energy: [0.04956155 0.00454781 0.00418105]
Number of function evaluations: [1850 1850 1850]
Time: 3.700, best current energy: [0.04051642 0.00135038 0.00292033]
Number of function evaluations: [1900 1900 1900]
Time: 3.800, best current energy: [0.05082993 0.00160846 0.00114098]
Number of function evaluations: [1950 1950 1950]
Time: 3.900, best current energy: [0.03143296 0.00183167 0.00097155]
Number of function evaluations: [2000 2000 2000]
Time: 4.000, best current energy: [0.0251956  0.00222968 0.00049768]
Number of function evaluations: [2050 2050 2050]
Time: 4.100, best current energy: [0.01983502 0.00140792 0.0002946 ]
Number of function evaluations: [2100 2100 2100]
Time: 4.200, best current energy: [0.01510383 0.00176546 0.00016745]
Number of function evaluations: [2150 2150 2150]
Time: 4.300, best current energy: [1.11427167e-02 2.21863881e-03 8.64473601e-05]
Number of function evaluations: [2200 2200 2200]
Time: 4.400, best current energy: [1.15549719e-02 2.20430974e-03 9.07954948e-05]
Number of function evaluations: [2250 2250 2250]
Time: 4.500, best current energy: [8.89131640e-03 2.07031884e-03 6.34935288e-05]
Number of function evaluations: [2300 2300 2300]
Time: 4.600, best current energy: [7.57794167e-03 2.08297333e-03 6.07676724e-05]
Number of function evaluations: [2350 2350 2350]
Time: 4.700, best current energy: [7.38504044e-03 6.04711827e-04 5.48703731e-05]
Number of function evaluations: [2400 2400 2400]
Time: 4.800, best current energy: [6.28198373e-03 4.49847058e-04 5.19042330e-05]
Number of function evaluations: [2450 2450 2450]
Time: 4.900, best current energy: [1.70746592e-05 3.49771414e-04 4.73239729e-05]
Number of function evaluations: [2500 2500 2500]
Time: 5.000, best current energy: [2.97989245e-05 1.99295912e-04 3.17562532e-05]
Number of function evaluations: [2550 2550 2550]
--------------------
Finished solver.
Best energy: [1.70746592e-05 1.97961671e-05 3.17562532e-05]
--------------------

[5]:

array([[-6.48890754e-05,  9.62647790e-06],
       [-5.99651486e-05,  3.73273810e-05],
       [-4.80953108e-05,  7.54337349e-05]])