Multi-Generation Gaussian Process Optimization¶

TNK function $n=2$ variables: $x_i \in [0, \pi], i=1,2$

Objectives:

• $f_i(x) = x_i$

Constraints:

• $g_1(x) = -x_1^2 -x_2^2 + 1 + 0.1 \cos\left(16 \arctan \frac{x_1}{x_2}\right) \le 0$
• $g_2(x) = (x_1 - 1/2)^2 + (x_2-1/2)^2 \le 0.5$

In [1]:

# set values if testing
import os

from copy import deepcopy

import pandas as pd
import numpy as np

from xopt import Xopt, Evaluator
from xopt.generators.bayesian.mggpo import MGGPOGenerator
from xopt.resources.test_functions.tnk import evaluate_TNK, tnk_vocs
from xopt.vocs import get_feasibility_data

from matplotlib import pyplot as plt

# Ignore all warnings
import warnings

warnings.filterwarnings("ignore")

SMOKE_TEST = os.environ.get("SMOKE_TEST")
N_MC_SAMPLES = 1 if SMOKE_TEST else 128
NUM_RESTARTS = 1 if SMOKE_TEST else 20

evaluator = Evaluator(function=evaluate_TNK)
evaluator.max_workers = 10

# test check options
vocs = deepcopy(tnk_vocs)
gen = MGGPOGenerator(vocs=vocs, reference_point={"y1": 1.5, "y2": 1.5})
gen.n_monte_carlo_samples = N_MC_SAMPLES
gen.numerical_optimizer.n_restarts = NUM_RESTARTS
gen.gp_constructor.use_low_noise_prior = True
X = Xopt(evaluator=evaluator, generator=gen)
X.evaluate_data(pd.DataFrame({"x1": [1.0, 0.75], "x2": [0.75, 1.0]}))

X

# set values if testing import os from copy import deepcopy import pandas as pd import numpy as np from xopt import Xopt, Evaluator from xopt.generators.bayesian.mggpo import MGGPOGenerator from xopt.resources.test_functions.tnk import evaluate_TNK, tnk_vocs from xopt.vocs import get_feasibility_data from matplotlib import pyplot as plt # Ignore all warnings import warnings warnings.filterwarnings("ignore") SMOKE_TEST = os.environ.get("SMOKE_TEST") N_MC_SAMPLES = 1 if SMOKE_TEST else 128 NUM_RESTARTS = 1 if SMOKE_TEST else 20 evaluator = Evaluator(function=evaluate_TNK) evaluator.max_workers = 10 # test check options vocs = deepcopy(tnk_vocs) gen = MGGPOGenerator(vocs=vocs, reference_point={"y1": 1.5, "y2": 1.5}) gen.n_monte_carlo_samples = N_MC_SAMPLES gen.numerical_optimizer.n_restarts = NUM_RESTARTS gen.gp_constructor.use_low_noise_prior = True X = Xopt(evaluator=evaluator, generator=gen) X.evaluate_data(pd.DataFrame({"x1": [1.0, 0.75], "x2": [0.75, 1.0]})) X

/home/runner/work/Xopt/Xopt/.venv/lib/python3.12/site-packages/pyro/ops/stats.py:527: SyntaxWarning: invalid escape sequence '\g'
  we have :math:`ES^{*}(P,Q) \ge ES^{*}(Q,Q)` with equality holding if and only if :math:`P=Q`, i.e.

Out[1]:

            Xopt
________________________________
Version: 0.1.dev1+gb834d2348
Data size: 2
Config as YAML:
dump_file: null
evaluator:
  function: xopt.resources.test_functions.tnk.evaluate_TNK
  function_kwargs:
    raise_probability: 0
    random_sleep: 0
    sleep: 0
  max_workers: 10
  vectorized: false
generator:
  computation_time: null
  custom_objective: null
  fixed_features: null
  ga_generator:
    crossover_probability: 0.9
    mutation_probability: 1.0
    output_path: null
    population: null
    population_file: null
    population_size: 64
    returns_id: false
    supports_constraints: true
    supports_multi_objective: true
    supports_single_objective: true
    vocs:
      constants:
        a:
          dtype: null
          type: Constant
          value: dummy_constant
      constraints:
        c1:
          dtype: null
          type: GreaterThanConstraint
          value: 0.0
        c2:
          dtype: null
          type: LessThanConstraint
          value: 0.5
      objectives:
        y1:
          dtype: null
          type: MinimizeObjective
        y2:
          dtype: null
          type: MinimizeObjective
      observables: {}
      variables:
        x1:
          default_value: null
          domain:
          - 0.0
          - 3.14159
          dtype: null
          type: ContinuousVariable
        x2:
          default_value: null
          domain:
          - 0.0
          - 3.14159
          dtype: null
          type: ContinuousVariable
  gp_constructor:
    covar_modules: {}
    custom_noise_prior: null
    mean_modules: {}
    name: standard
    train_config: null
    train_kwargs: null
    train_method: lbfgs
    train_model: true
    trainable_mean_keys: []
    transform_inputs: true
    use_cached_hyperparameters: false
    use_low_noise_prior: true
  max_travel_distances: null
  model: null
  n_candidates: 1
  n_interpolate_points: null
  n_monte_carlo_samples: 128
  name: mggpo
  numerical_optimizer:
    max_iter: 2000
    max_time: 5.0
    n_restarts: 20
    name: LBFGS
  population_size: 64
  reference_point:
    y1: 1.5
    y2: 1.5
  returns_id: false
  supports_batch_generation: true
  supports_constraints: true
  supports_multi_objective: true
  turbo_controller: null
  use_cuda: false
  vocs:
    constants:
      a:
        dtype: null
        type: Constant
        value: dummy_constant
    constraints:
      c1:
        dtype: null
        type: GreaterThanConstraint
        value: 0.0
      c2:
        dtype: null
        type: LessThanConstraint
        value: 0.5
    objectives:
      y1:
        dtype: null
        type: MinimizeObjective
      y2:
        dtype: null
        type: MinimizeObjective
    observables: {}
    variables:
      x1:
        default_value: null
        domain:
        - 0.0
        - 3.14159
        dtype: null
        type: ContinuousVariable
      x2:
        default_value: null
        domain:
        - 0.0
        - 3.14159
        dtype: null
        type: ContinuousVariable
serialize_inline: false
serialize_torch: false
stopping_condition: null
strict: true

In [2]:

for i in range(10):
    print(i)
    X.step()

for i in range(10): print(i) X.step()

0

1

2

3

4

5

6

7

8

9

In [3]:

X.generator.data

X.generator.data

Out[3]:

	x1	x2	a	y1	y2	c1	c2	xopt_runtime	xopt_error
0	1.000000	0.750000	dummy_constant	1.000000	0.750000	0.626888	0.312500	0.002941	False
1	0.750000	1.000000	dummy_constant	0.750000	1.000000	0.626888	0.312500	0.002924	False
2	1.640872	0.192596	dummy_constant	1.640872	0.192596	1.758974	1.396085	0.006122	False
3	0.140275	1.541810	dummy_constant	0.140275	1.541810	1.384973	1.214771	0.005999	False
4	0.015958	1.556060	dummy_constant	0.015958	1.556060	1.322921	1.349560	0.000142	False
...	...	...	...	...	...	...	...	...	...
97	0.046599	0.997898	dummy_constant	0.046599	0.997898	-0.075428	0.453475	0.000139	False
98	0.882588	0.510810	dummy_constant	0.882588	0.510810	0.091351	0.146491	0.000137	False
99	0.043506	1.008173	dummy_constant	0.043506	1.008173	-0.058817	0.466627	0.000110	False
100	0.982345	0.213217	dummy_constant	0.982345	0.213217	0.106619	0.314901	0.000141	False
101	0.966685	0.350944	dummy_constant	0.966685	0.350944	-0.018110	0.240013	0.000142	False

102 rows × 9 columns

plot results¶

In [4]:

fig, ax = plt.subplots()

theta = np.linspace(0, np.pi / 2)
r = np.sqrt(1 + 0.1 * np.cos(16 * theta))
x_1 = r * np.sin(theta)
x_2_lower = r * np.cos(theta)
x_2_upper = (0.5 - (x_1 - 0.5) ** 2) ** 0.5 + 0.5

z = np.zeros_like(x_1)

# ax2.plot(x_1, x_2_lower,'r')
ax.fill_between(x_1, z, x_2_lower, fc="white")
circle = plt.Circle(
    (0.5, 0.5), 0.5**0.5, color="r", alpha=0.25, zorder=0, label="Valid Region"
)
ax.add_patch(circle)
history = pd.concat(
    [X.data, get_feasibility_data(tnk_vocs, X.data)], axis=1, ignore_index=False
)

ax.plot(*history[["x1", "x2"]][history["feasible"]].to_numpy().T, ".C1")
ax.plot(*history[["x1", "x2"]][~history["feasible"]].to_numpy().T, ".C2")

ax.set_xlim(0, 3.14)
ax.set_ylim(0, 3.14)
ax.set_xlabel("x1")
ax.set_ylabel("x2")
ax.set_aspect("equal")

fig, ax = plt.subplots() theta = np.linspace(0, np.pi / 2) r = np.sqrt(1 + 0.1 * np.cos(16 * theta)) x_1 = r * np.sin(theta) x_2_lower = r * np.cos(theta) x_2_upper = (0.5 - (x_1 - 0.5) ** 2) ** 0.5 + 0.5 z = np.zeros_like(x_1) # ax2.plot(x_1, x_2_lower,'r') ax.fill_between(x_1, z, x_2_lower, fc="white") circle = plt.Circle( (0.5, 0.5), 0.5**0.5, color="r", alpha=0.25, zorder=0, label="Valid Region" ) ax.add_patch(circle) history = pd.concat( [X.data, get_feasibility_data(tnk_vocs, X.data)], axis=1, ignore_index=False ) ax.plot(*history[["x1", "x2"]][history["feasible"]].to_numpy().T, ".C1") ax.plot(*history[["x1", "x2"]][~history["feasible"]].to_numpy().T, ".C2") ax.set_xlim(0, 3.14) ax.set_ylim(0, 3.14) ax.set_xlabel("x1") ax.set_ylabel("x2") ax.set_aspect("equal")

In [5]:

X.generator.visualize_model(show_feasibility=True)

X.generator.visualize_model(show_feasibility=True)

Out[5]:

(<Figure size 800x1980 with 22 Axes>,
 array([[<Axes: title={'center': 'Posterior Mean [y1]'}, xlabel='x1', ylabel='x2'>,
         <Axes: title={'center': 'Posterior SD [y1]'}, xlabel='x1', ylabel='x2'>],
        [<Axes: title={'center': 'Posterior Mean [y2]'}, xlabel='x1', ylabel='x2'>,
         <Axes: title={'center': 'Posterior SD [y2]'}, xlabel='x1', ylabel='x2'>],
        [<Axes: title={'center': 'Posterior Mean [c1]'}, xlabel='x1', ylabel='x2'>,
         <Axes: title={'center': 'Posterior SD [c1]'}, xlabel='x1', ylabel='x2'>],
        [<Axes: title={'center': 'Posterior Mean [c2]'}, xlabel='x1', ylabel='x2'>,
         <Axes: title={'center': 'Posterior SD [c2]'}, xlabel='x1', ylabel='x2'>],
        [<Axes: title={'center': 'Acq. Function'}, xlabel='x1', ylabel='x2'>,
         <Axes: >],
        [<Axes: title={'center': 'Feasibility'}, xlabel='x1', ylabel='x2'>,
         <Axes: >]], dtype=object))

In [6]:

X.generator.update_pareto_front_history()
X.generator.pareto_front_history.plot(y="hypervolume", label="Hypervolume")
X.generator.pareto_front_history.plot(y="n_non_dominated", label="n_non_dominated")

X.generator.update_pareto_front_history() X.generator.pareto_front_history.plot(y="hypervolume", label="Hypervolume") X.generator.pareto_front_history.plot(y="n_non_dominated", label="n_non_dominated")

Out[6]:

<Axes: >

In [ ]: