MultiBgolearn: Multi-Objective Bayesian Global Optimization for Materials Design

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Note: Sometimes, the installation of a dependent package, pygmo, may fail when using pip. To resolve this issue, it is recommended to install pygmo via conda by running the following command:

conda install -c conda-forge pygmo

Overview

MultiBgolearn is a Python package designed for multi-objective Bayesian global optimization (MOBO), specifically tailored for materials design. It extends the functionalities of the Bgolearn package, which focuses on single-objective optimization, by enabling the simultaneous optimization of multiple material properties. This makes MultiBgolearn highly suitable for real-world applications where trade-offs between competing objectives are common.

The repository provides the source code of the MultiBgolearn package along with several multi-objective Bayesian global optimization (MOBO) algorithms.

Features

• Implements multiple MOBO algorithms such as Expected Hypervolume Improvement (EHVI), Probability of Improvement (PI), and Upper Confidence Bound (UCB).
• Supports the optimization of multiple objectives simultaneously, making it ideal for materials with competing property targets.
• Flexible surrogate model selection, allowing the user to choose from a range of models such as RandomForest, GradientBoosting, SVR, GaussianProcess, and more.
• Automatic or user-defined selection of surrogate models for optimization.
• Bootstrap iterations for uncertainty quantification in model predictions.

Installation

To install MultiBgolearn, clone the repository and install the dependencies:

pip install MultiBgolearn

Usage

The MultiBgolearn package is designed for ease of use in materials design projects. Below is an example of how to use it:

Example

from MultiBgolearn import bgo

# Define your dataset and virtual space paths
dataset_path = './data/dataset.csv'
VSdataset = 'virtual_sample.xlsx'

# Set the number of objectives (e.g., 3 for three-objective optimization)
object_num = 3

# Apply Multi-Objective Bayesian Global Optimization
VS_recommended, improvements, index = bgo.fit(dataset_path, VSdataset, object_num, 
                                                        max_search=True, method='EHVI', 
                                                        assign_model='GaussianProcess', 
                                                        bootstrap=5)

Parameters

• dataset (str): The path to the dataset containing both features and response variables.
• VSdataset (str): The path to the virtual space where candidate data for optimization is stored.
• object_num (int): The number of objectives (target properties) to optimize.
• max_search (bool, optional, default=True): Whether to maximize (True) or minimize (False) the objectives.
• method (str, optional, default=EHVI): The optimization method. Supported methods:
  • 'EHVI': Expected Hypervolume Improvement
  • 'PI': Probability of Improvement
  • 'UCB': Upper Confidence Bound
• assign_model (bool or str, optional, default=False): Specify the surrogate model:
  • 'RandomForest'
  • 'GradientBoosting'
  • 'LinearRegression'
  • 'Lasso'
  • 'Ridge'
  • 'SVR'
  • 'GaussianProcess'
  • False: The surrogate model is chosen automatically.
• bootstrap (int, optional, default=5): Number of bootstrap iterations for uncertainty quantification.

Return

The fit method returns a tuple:

• VS[res_index]: The recommended data point from the virtual space.
• improvements: The calculated improvements based on the chosen optimization method.
• res_index: The index of the recommended data point in the virtual space.

Notes

The selected method will influence how the algorithm balances different objectives during optimization.

Algorithms

MultiBgolearn includes several optimization strategies, including:

1. Expected Hypervolume Improvement (EHVI): Focuses on maximizing the volume of the objective space dominated by the solutions.
2. Probability of Improvement (PI): Selects points with the highest probability of improving over the best known solution.
3. Upper Confidence Bound (UCB): Explores points with the highest upper confidence bound, balancing exploration and exploitation.

Contributions

We welcome contributions from the community! Please feel free to open issues or submit pull requests.

• Issues: GitHub Issues
• Pull Requests: GitHub Pull Requests

For questions or suggestions, feel free to contact:

• Bin Cao: [email protected]
• GitHub: https://github.com/Bin-Cao/MultiBgolearn

License

This project is licensed under the MIT License. See the LICENSE file for more details.

Architecture

The system architecture diagram shows the key modules of the MultiBgolearn algorithm and their connections.

graph TB
    subgraph MultiBgolearn[MultiBgolearn]
    DataPreprocessing[Data Preprocessing]
    ModelBuilding[Model Building]
    Prediction[Prediction]
    Optimization[Optimization]
    End[End and Output Results]
    end
    
    DataPreprocessing -->|Standardize Data| ModelBuilding
    ModelBuilding -->|Select Best Model| Prediction
    Prediction -->|Predict Virtual Space| Optimization
    Optimization --> End

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Data Preprocessing Flowchart

The data preprocessing flowchart outlines the steps involved in the data preprocessing module.

flowchart TB
    A[Start] --> B[Load Dataset]
    B --> C{Is the file CSV or Excel?}
    C -- Yes --> D[Split Data]
    C -- No --> E[Raise Error]
    D --> F[Standardize Features and Target]
    F --> G[Return Standardized Data]
    G --> H[End]

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Model Building Flowchart

The model building flowchart illustrates how to construct and select the optimal surrogate model.

flowchart TB
    A[Start] --> B[Load Training Data]
    B --> C[Select Model List]
    C --> D{For Each Model}
    D -- Leave-One-Out Cross-Validation --> E[Evaluate Model Performance]
    E --> F[Record R2 Score]
    F --> G[Select Model with Highest R2 Score]
    G --> H[End and Output Best Model]

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Prediction Flowchart

The prediction flowchart details the process of predicting the virtual space data using the selected model.

flowchart TB
    A[Start] --> B[Load Virtual Space Data]
    B --> C[Select Prediction Model]
    C --> D{Is the Model Gaussian Process?}
    D -- Yes --> E[Directly Predict Mean and Variance]
    D -- No --> F[Use Bootstrap to Predict Mean and Variance]
    E --> G[Return Prediction Results]
    F --> G
    G --> H[End]

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Optimization Flowchart

The optimization flowchart demonstrates how to apply the multi-objective Bayesian global optimization algorithm to recommend the optimal data points.

flowchart TB
    A[Start] --> B[Load Prediction Results]
    B --> C[Select Optimization Algorithm]
    C --> D{Execute Optimization}
    D --> E[Recommend Optimal Data Points]
    E --> F[Calculate Improvement Value]
    F --> G[Return Optimal Data Points and Improvement Value]
    G --> H[End]

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Logic Flowchart

The logic flowchart illustrates the overall logic flow of the MultiBgolearn algorithm.

flowchart TB
    A[Start] --> B[Data Preprocessing]
    B --> C[Model Building]
    C --> D[Prediction]
    D --> E[Optimization]
    E --> F[Output Recommended Data Points]
    F --> G[Output Improvement Value]
    G --> H[End]

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