This project explores and implements advanced optimization techniques to solve complex real-world problems. The repository includes a suite of algorithms, methodologies, and experiments focused on achieving efficient and robust solutions. The main code and experiments are documented in final_project.ipynb.

• Mathematical Modeling: Problems are formulated using mathematical models to define constraints and objectives precisely.
• Linear Programming (LP): Techniques such as the Simplex method are applied to solve problems with linear constraints and objectives.
• Nonlinear Programming (NLP): Algorithms for handling nonlinear relationships are implemented for more complex scenarios.
• Metaheuristics: Genetic Algorithms and Simulated Annealing are used for optimization problems where classical methods are insufficient or impractical.
• Gradient-Based Optimization: Methods like Gradient Descent are employed for continuous optimization tasks.
• Constraint Handling: Specialized approaches are used to manage equality and inequality constraints within optimization problems.
• Data Preprocessing and Analysis: Input data is cleaned, normalized, and analyzed to ensure high-quality results.
• Simulation and Validation: Solutions are validated through simulation to assess their performance under various scenarios.
• Visualization: Results are visualized using plots and charts to facilitate analysis and interpretation.

• Modular codebase for easy extension and experimentation
• Well-documented code and notebooks for clarity
• Visualization tools for analyzing optimization results
• Benchmarking against standard datasets and test cases

1. Clone the repository.
2. Install required dependencies from requirements.txt.
3. Open and run final_project.ipynb to explore the implemented methodologies and experiments.

The project demonstrates improvements in solution quality and computational efficiency across multiple test cases. Comparative analyses in the notebook highlight the strengths and limitations of each methodology.

Contributions are welcome! Please open issues or submit pull requests for enhancements or bug fixes.

This project is licensed under the MIT License.