spotoptim 0.0.40

Sequential Parameter Optimization Toolbox

SpotOptim

Sequential Parameter Optimization

Features

• Surrogate Model Based Optimization: Uses surrogate models to efficiently optimize expensive black-box functions
• Multiple Acquisition Functions: Expected Improvement (EI), Predicted Mean (y), Probability of Improvement (PI)
• Flexible Surrogates: Default Gaussian Process or custom Kriging surrogate
• Variable Types: Support for continuous, integer, and mixed variable types
• scipy-compatible: Returns OptimizeResult objects compatible with scipy.optimize

Installation

pip install spotoptim

Quick Start

import numpy as np
from spotoptim import SpotOptim

# Define objective function
def rosenbrock(X):
    X = np.atleast_2d(X)
    x, y = X[:, 0], X[:, 1]
    return (1 - x)**2 + 100 * (y - x**2)**2

# Set up optimization
bounds = [(-2, 2), (-2, 2)]

optimizer = SpotOptim(
    fun=rosenbrock,
    bounds=bounds,
    max_iter=50,
    n_initial=10,
    seed=42
)

# Run optimization
result = optimizer.optimize()

print(f"Best point: {result.x}")
print(f"Best value: {result.fun}")

Using Kriging Surrogate

SpotOptim includes a simplified Kriging (Gaussian Process) surrogate as an alternative to scikit-learn's GaussianProcessRegressor:

from spotoptim import SpotOptim, Kriging

# Create Kriging surrogate
kriging = Kriging(
    noise=1e-6,
    min_theta=-3.0,
    max_theta=2.0,
    seed=42
)

# Use with SpotOptim
optimizer = SpotOptim(
    fun=rosenbrock,
    bounds=bounds,
    surrogate=kriging,  # Use Kriging instead of default GP
    seed=42
)

result = optimizer.optimize()

API Reference

SpotOptim

Parameters:

• fun (callable): Objective function to minimize
• bounds (list of tuples): Bounds for each dimension as [(low, high), ...]
• max_iter (int, default=20): Maximum number of optimization iterations
• n_initial (int, default=10): Number of initial design points
• surrogate (object, optional): Surrogate model (default: GaussianProcessRegressor)
• acquisition (str, default='ei'): Acquisition function ('ei', 'y', 'pi')
• var_type (list of str, optional): Variable types for each dimension
• tolerance_x (float, optional): Minimum distance between points
• seed (int, optional): Random seed for reproducibility
• verbose (bool, default=False): Print progress information
• max_surrogate_points (int, optional): Maximum number of points for surrogate fitting (default: None, use all points)
• selection_method (str, default='distant'): Point selection method ('distant' or 'best')

Methods:

• optimize(X0=None): Run optimization, optionally with initial design points
• plot_surrogate(i=0, j=1, show=True, **kwargs): Visualize the fitted surrogate model

Point Selection for Surrogate Training

When optimizing expensive functions with many iterations, the number of evaluated points can become large, making surrogate model training computationally expensive. SpotOptim implements an automatic point selection mechanism to address this:

Usage

optimizer = SpotOptim(
    fun=expensive_function,
    bounds=bounds,
    max_iter=100,
    n_initial=20,
    max_surrogate_points=50,  # Use only 50 points for surrogate training
    selection_method='distant',  # or 'best'
    verbose=True
)

Selection Methods

1. 'distant' (default): Uses K-means clustering to select points that are maximally distant from each other, ensuring good space-filling properties.

2. 'best': Clusters points and selects all points from the cluster with the best (lowest) mean objective function value, focusing on promising regions.

Benefits

• Reduced computational cost: Surrogate training scales with the number of points
• Maintained accuracy: Carefully selected points preserve model quality
• Scalability: Enables optimization with hundreds or thousands of function evaluations

See examples/point_selection_example.py for a complete demonstration.

Kriging

Parameters:

• noise (float, optional): Regularization parameter
• kernel (str, default='gauss'): Kernel type
• n_theta (int, optional): Number of theta parameters
• min_theta (float, default=-3.0): Minimum log10(theta) bound
• max_theta (float, default=2.0): Maximum log10(theta) bound
• seed (int, optional): Random seed

Methods:

• fit(X, y): Fit the model to training data
• predict(X, return_std=False): Predict at new points

Visualizing Results

SpotOptim includes a plot_surrogate() method to visualize the fitted surrogate model:

# After running optimization
optimizer.plot_surrogate(
    i=0, j=1,                    # Dimensions to plot
    var_name=['x1', 'x2'],       # Variable names
    add_points=True,             # Show evaluated points
    cmap='viridis',              # Colormap
    show=True
)

The plot shows:

• Top left: 3D surface of predictions
• Top right: 3D surface of prediction uncertainty
• Bottom left: Contour plot of predictions with evaluated points
• Bottom right: Contour plot of prediction uncertainty

For higher-dimensional problems, the method visualizes a 2D slice by fixing other dimensions at their mean values.

Examples

Notebooks

See notebooks/demos.ipynb for interactive examples:

1. 2D Rosenbrock function optimization
2. 6D Rosenbrock with budget constraints
3. Using Kriging surrogate vs default GP
4. Visualizing surrogate models with plot_surrogate()

Real-World Applications

The examples/ directory contains detailed tutorials:

Aircraft Wing Weight Optimization (AWWE)

• awwe.qmd - Comprehensive Quarto tutorial teaching surrogate-based optimization
• awwe_optimization.py - Standalone Python script demonstrating complete workflow
• 9-dimensional optimization problem from engineering design
• Includes homework exercise for 10-dimensional extension

Run the example:

cd examples
python awwe_optimization.py

See examples/README.md for more details and additional examples.

Development

# Clone repository
git clone https://github.com/sequential-parameter-optimization/spotoptim.git
cd spotoptim

# Install with uv
uv pip install -e .

# Run tests
uv run pytest tests/

# Build package
uv build

License

See LICENSE file.

References

Based on the SPOT (Sequential Parameter Optimization Toolbox) methodology.