A high-performance, production-ready Multi-Objective Bayesian Optimization implementation with advanced features and comprehensive visualization capabilities.
Real-time heatmap updates during optimization, showing mean predictions, uncertainty, and acquisition function.
- 🎯 Multi-Objective Optimization: Optimize multiple competing objectives simultaneously
- ⚡ High Performance: Numba JIT compilation for 10x+ speed improvements
- 📊 Rich Visualization: Interactive heatmaps and Pareto front analysis
- 🔧 Production Ready: Robust error handling and comprehensive testing
- 📈 Batch Optimization: Evaluate multiple points per iteration for efficiency
- 🔍 Hyperparameter Optimization: Automatic tuning via marginal likelihood maximization
- 🌟 Pareto Analysis: Intelligent trade-off identification and ranking
- Python 3.8+
- NumPy >= 1.19.0
- SciPy >= 1.6.0
- Numba >= 0.53.0 (for performance acceleration)
- Matplotlib >= 3.3.0 (for visualization)
pip install numpy scipy numba matplotlibSee the comprehensive Jupyter Tutorial for detailed examples and explanations.
from bayesian_optimization import BayesianOptimization, toy_function
# Create optimizer
optimizer = BayesianOptimization(
function=toy_function,
bounds=[(0, 30), (0, 30)],
n_objectives=2,
initial_samples=8,
n_iterations=5
)
# Run optimization
optimizer.optimize()
# Analyze results
pareto_points = optimizer.pareto_analysis()| Parameter | Type | Default | Description |
|---|---|---|---|
function |
callable | Required | Multi-objective function returning np.array |
bounds |
list of tuples | Required | [(min, max), ...] for each dimension |
n_objectives |
int | 3 |
Number of objective functions |
n_iterations |
int | 10 |
Number of optimization iterations |
initial_samples |
int | 3 |
Initial Latin Hypercube samples |
batch_size |
int | 1 |
Points to evaluate per iteration |
| Parameter | Type | Default | Description |
|---|---|---|---|
prior_mean |
list/array | [0.0, ...] |
Prior mean for each objective |
prior_variance |
list/array | [1.0, ...] |
Prior variance for each objective |
length_scales |
list/array | [1.0, ...] |
RBF kernel length scales |
betas |
list/array | [2.0, ...] |
Exploration-exploitation trade-off |
A comprehensive tutorial is included: BayesianOptimization_Tutorial.ipynb
Tutorial Contents:
- ✅ Theory: Gaussian Processes and multi-objective optimization
- ✅ Implementation: Understanding the codebase architecture
- ✅ Usage: From basic to advanced configurations
- ✅ Visualization: Heatmap interpretation and Pareto analysis
- ✅ Performance: Parameter tuning and optimization tips
- ✅ Examples: Real-world optimization scenarios
Launch Tutorial:
# Open in VS Code with Jupyter extension
code BayesianOptimization_Tutorial.ipynb
# Or use Jupyter Lab/Notebook
jupyter lab BayesianOptimization_Tutorial.ipynb- 10-50x faster than pure Python with Numba JIT compilation
- Memory-efficient with O(n² × m) complexity (n=evaluations, m=objectives)
- Production mode (default): Full acceleration
- Debug mode: Set
BAYESIAN_DEBUG=truefor debugging
| Problem Size | Evaluations | Time (Production) |
|---|---|---|
| 2D, 2 obj | 50 evals | ~2-5 seconds |
| 2D, 3 obj | 100 evals | ~5-15 seconds |
| 3D, 2 obj | 200 evals | ~15-45 seconds |
- Gaussian Process Regression: Individual GP for each objective
- RBF Kernel: Configurable length scales and prior variance
- Latin Hypercube Sampling: Efficient initial exploration
- Upper Confidence Bound: Balanced exploration-exploitation
- Pareto Analysis: Multi-objective solution ranking
- GP Prior: f(x) ~ GP(μ(x), k(x,x'))
- RBF Kernel: k(x,x') = σ² exp(-||x-x'||²/(2ℓ²))
- UCB Acquisition: UCB(x) = μ(x) + β×σ(x)
- Rasmussen & Williams, "Gaussian Processes for Machine Learning"
- Knowles, "ParEGO: A Hybrid Algorithm"
- Srinivas et al., "Gaussian Process Optimization in the Bandit Setting"
MIT License - Copyright (c) 2025
Happy Optimizing! 🚀🎯📊