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README.md

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----
-license: mit
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+---
+license: mit
+---
+Here's a comprehensive Hugging Face model card for your Particle Swarm Optimization PyQt5 application:
+
+```markdown
+---
+language:
+- en
+tags:
+- optimization
+- particle-swarm
+- pso
+- mathematical-optimization
+- benchmark-functions
+- pyqt5
+- gui
+- visualization
+- metaheuristics
+- evolutionary-computation
+library_name: pyqt5
+pipeline_tag: visualization
+---
+
+# Particle Swarm Optimization Visualizer
+
+## Model Overview
+
+A comprehensive PyQt5 application that implements Particle Swarm Optimization (PSO) to solve 20 different mathematical optimization problems with real-time 2D and 3D visualizations. Watch particles oscillate and converge towards optimal solutions across various benchmark functions.
+
+![PSO Visualization](https://img.shields.io/badge/PSO-Visualization-blue)
+![PyQt5](https://img.shields.io/badge/GUI-PyQt5-green)
+![Optimization](https://img.shields.io/badge/Metaheuristic-Optimization-orange)
+
+## Features
+
+### 🎯 20 Optimization Problems
+- **10 2D Benchmark Functions**: Sphere, Rosenbrock, Rastrigin, Ackley, Matyas, Himmelblau, Three-Hump Camel, Easom, Cross-in-Tray, Holder Table
+- **10 3D Benchmark Functions**: Sphere 3D, Rosenbrock 3D, Rastrigin 3D, Ackley 3D, Sum of Different Powers, Rotated Hyper-Ellipsoid, Zakharov 3D, Dixon-Price, Levy 3D, Michalewicz 3D
+
+### 📊 Real-time Visualizations
+- **2D Contour Plots**: Particle movement over function landscapes
+- **3D Surface Plots**: Interactive 3D optimization landscapes
+- **Live Particle Tracking**: Watch particles oscillate and converge
+- **Progress Monitoring**: Real-time optimization progress
+
+### ⚙️ Customizable PSO Parameters
+- Particle count (10-100)
+- Iterations (10-500)
+- Inertia weight (0.1-1.0)
+- Cognitive parameter (0.1-2.0)
+- Social parameter (0.1-2.0)
+
+## Quick Start
+
+### Installation
+
+```bash
+# Clone repository
+git clone https://huggingface.co/TroglodyteDerivations/pso-pyqt5-visualizer
+cd pso-pyqt5-visualizer
+
+# Install dependencies
+pip install -r requirements.txt
+
+# Run the application
+python app.py
+```
+
+### Requirements
+
+```txt
+numpy>=1.21.0
+matplotlib>=3.5.0
+PyQt5>=5.15.0
+```
+
+## Usage
+
+1. **Select Equation**: Choose from 20 benchmark functions
+2. **Configure Parameters**: Adjust PSO parameters as needed
+3. **Run Optimization**: Click "Run PSO" to start
+4. **Visualize**: Watch real-time particle movement
+5. **Analyze**: Review optimization results
+
+## Application Interface
+
+### Control Panel
+- Equation selection with detailed descriptions
+- PSO parameter configuration
+- Interactive controls (Run, Pause, Step, Reset)
+- Real-time progress tracking
+- Results display
+
+### Visualization Panel
+- **Top**: 2D contour plots with particle trajectories
+- **Bottom**: 3D surface plots showing optimization landscape
+- Real-time updates during optimization
+
+## Benchmark Functions
+
+### 2D Functions
+| Function | Description | Global Minimum |
+|----------|-------------|----------------|
+| Sphere | f(x,y) = x² + y² | (0,0) |
+| Rosenbrock | f(x,y) = 100(y-x²)² + (1-x)² | (1,1) |
+| Rastrigin | Multi-modal function | (0,0) |
+| Ackley | Many local minima | (0,0) |
+| Himmelblau | Four equal minima | Multiple |
+
+### 3D Functions
+| Function | Dimensions | Complexity |
+|----------|------------|------------|
+| Sphere 3D | 3 | Unimodal |
+| Rastrigin 3D | 3 | Multi-modal |
+| Michalewicz | 3 | Many local minima |
+| Levy 3D | 3 | Complex landscape |
+
+## PSO Algorithm
+
+### Mathematical Formulation
+Particle velocity and position updates:
+
+```
+v_i(t+1) = w * v_i(t) + c1 * r1 * (pbest_i - x_i(t)) + c2 * r2 * (gbest - x_i(t))
+x_i(t+1) = x_i(t) + v_i(t+1)
+```
+
+Where:
+- `w`: Inertia weight
+- `c1`, `c2`: Cognitive and social parameters
+- `r1`, `r2`: Random numbers
+- `pbest_i`: Particle's best position
+- `gbest`: Global best position
+
+### Key Features
+- **Boundary Handling**: Particles bounce off boundaries
+- **Velocity Clamping**: Prevents explosion
+- **History Tracking**: Complete optimization history
+- **Convergence Monitoring**: Real-time best value tracking
+
+## Educational Value
+
+This application serves as an excellent educational tool for:
+- Understanding PSO algorithm behavior
+- Visualizing optimization landscapes
+- Comparing benchmark function characteristics
+- Studying metaheuristic optimization
+- Learning about multi-modal optimization
+
+## Performance
+
+### Optimization Capabilities
+- **Convergence**: Rapid convergence on unimodal functions
+- **Exploration**: Effective global search on multi-modal functions
+- **Stability**: Robust performance across different landscapes
+- **Scalability**: Handles 2D and 3D problems efficiently
+
+### Visualization Performance
+- **Smooth Animation**: 30+ FPS particle movement
+- **Interactive Plots**: Zoom, pan, and rotate 3D views
+- **Real-time Updates**: Instant parameter feedback
+- **Memory Efficient**: Optimized for long runs
+
+## Use Cases
+
+### 🎓 Education
+- Optimization algorithm courses
+- Metaheuristic visualization
+- Mathematical modeling classes
+
+### 🔬 Research
+- Algorithm benchmarking
+- Parameter sensitivity analysis
+- Optimization landscape study
+
+### 💼 Industry
+- Engineering optimization problems
+- Machine learning hyperparameter tuning
+- Financial modeling optimization
+
+## Contributing
+
+We welcome contributions! Areas for improvement:
+- Additional benchmark functions
+- Advanced PSO variants
+- Export functionality
+- Performance optimizations
+- Additional visualization types
+
+## Citation
+
+If you use this application in your research or teaching, please cite:
+
+```bibtex
+@software{pso_pyqt5_visualizer,
+  title = {Particle Swarm Optimization PyQt5 Visualizer},
+  author = {Martin Rivera},
+  year = {2025},
+  url = {https://huggingface.co/TroglodyteDerivations/pso-pyqt5-visualizer}
+}
+```
+
+## License
+
+This project is licensed under the MIT License - see the LICENSE file for details.
+
+## Support
+
+For issues and questions:
+- Open an issue on Hugging Face
+- Check the documentation
+- Review example configurations
+
+## Model Card Authors
+
+[TroglodyteDerivations]
+
+## Model Card Contact
+
+[https://huggingface.co/TroglodyteDerivations/Particle_Swarm_Optimization_Visualizer_PyQt5/edit/main/README.md]
+
+---
+
+<div align="center">
+
+**✨ Watch particles find optimal solutions in beautiful visualizations! ✨**
+
+</div>
+```
+
+## Additional Files for Hugging Face
+
+You should also create these files for your Hugging Face repository:
+
+### `README.md` (same as above)
+
+### `requirements.txt`
+```txt
+numpy>=1.21.0
+matplotlib>=3.5.0
+PyQt5>=5.15.0
+```
+
+### `app.py` 
+
+### `LICENSE`
+```txt
+MIT License
+
+Copyright (c) 2025 [Martin Rivera]
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+```
+
+### `.gitattributes`
+```gitattributes
+*.py filter=lfs diff=lfs merge=lfs -text
+*.png filter=lfs diff=lfs merge=lfs -text
+*.jpg filter=lfs diff=lfs merge=lfs -text
+```
+
+This model card provides comprehensive documentation for your PSO PyQt5 application and makes it ready for sharing on Hugging Face Hub!