Portfolio Optimization with Spectral Mixture Gaussian Processes

A professional-grade Python implementation of Multi-Objective Portfolio Optimization. This project combines advanced time-series forecasting (Spectral Mixture Gaussian Processes) with state-of-the-art evolutionary algorithms (MOEA/D) to find optimal asset allocations.

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🚀 Overview

This repository provides a modular framework for:

1. Price Prediction: Using Gaussian Processes with Spectral Mixture (SM) kernels to capture complex periodicity and trends in financial data.
2. Portfolio Modeling: Defining multi-objective problems including Expected Return, Risk (Variance), and Diversification (HHI Index).
3. Pareto Front Discovery: Solving the optimization problem using classical (Weighted Sum, Epsilon-Constrained) and evolutionary (MOEA/D) approaches.

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🛠️ Key Algorithms

1. Classical Optimizers

• Weighted Sum: Aggregates objectives into a single scalar value.
• Epsilon-Constrained (ECM): Maximizes return while keeping other objectives within strict bounds. Used as the ground-truth reference for quality metrics.

2. MOEA/D (Decomposition-based Optimization)

• Standard MOEA/D: Decomposes the problem into subproblems with fixed weight vectors.
• MOEA/D-DRA (Dynamic Resource Allocation): Optimizes computational efficiency by focusing on subproblems that show the most improvement.
• MOEA/D-AWA (Adaptive Weight Adjustment): Dynamically repositions weight vectors during search to ensure a uniform distribution of solutions across the Pareto front.

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📦 Project Structure

├── .github/workflows/  # CI/CD Pipeline (Linting & Formatting)
├── data/               # Historical asset price data (CSV)
├── scripts/            # Experiment entry points
│   ├── experiment_standard.py  # Classical optimization comparison
│   ├── experiment_moead.py     # Basic MOEA/D vs ECM
│   ├── experiment_dra.py       # Performance & efficiency testing
│   └── experiment_awa.py       # Diversity & distribution testing
├── src/
│   ├── portfolio/      # Core optimization logic
│   │   ├── metrics.py  # Quality metrics (IGD, Spacing, Spread)
│   │   ├── moead_base.py # Common evolutionary logic
│   │   └── ...
│   ├── predictors.py   # GP-SM Regression models
│   └── visualization.py # Advanced plotting and 3D animations
└── requirements.txt    # Dependency list

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⚙️ Setup & Installation

1. Clone the repository:

   git clone https://github.com/MichalRedm/portfolio-optimization.git
   cd portfolio-optimization

2. Create and activate a virtual environment:

   python -m venv .venv
   # Windows
   .venv\Scripts\activate
   # Linux/macOS
   source .venv/bin/activate

3. Install dependencies:

   pip install -r requirements.txt

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📈 Running Experiments

The project includes several built-in experiments to evaluate algorithm performance.

Standard Optimization (ECM vs Weighted Sum)

python scripts/experiment_standard.py

MOEA/D vs Standard Comparison

python scripts/experiment_moead.py

Efficiency & Resource Allocation (DRA)

python scripts/experiment_dra.py

Distribution & Adaptive Weights (AWA)

python scripts/experiment_awa.py

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📊 Quality Metrics

We evaluate the quality of the found Pareto fronts using:

• IGD (Inverted Generational Distance): Measures how close the found solutions are to the true Pareto front.
• Spacing: Measures how evenly the solutions are distributed.
• Spread: Measures how well the solutions cover the entire objective space.

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🎨 Visualizations

The framework generates high-quality visualizations, including:

• 2D Comparisons: Scatter plots showing the Pareto front against reference models.
• 3D Animations: Interactive rotation of 3D fronts (Return vs Risk vs Diversification) saved as smooth GIFs (25 FPS).
• Efficiency Plots: Performance over time (IGD vs. Function Evaluations).

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📜 License

This project is licensed under the MIT License - see the LICENSE file for details.