Visual Optimization System 📊

About the Project

The Visual Optimization System (Solver LP) is an interactive and didactic platform developed to assist in teaching and learning Operations Research. It focuses on the resolution and visualization of Linear Programming (LP) and Integer Programming (IP) problems.

Built with Python and Streamlit, the system offers rich visualizations (2D/3D charts, decision trees, step-by-step tableaux) to turn abstract mathematical concepts into tangible experiences.

---

🚀 Key Features

📐 Simplex

• Step-by-Step Resolution: Follow each iteration of the Simplex algorithm.
• 3D/2D Visualization: Interactive charts of the feasible region identifying vertices and the solution path.
• Interactive Tableau: Detailed display of basic and non-basic variables and pivoting operations.
• Case Identification: Detects optimal solutions, multiple solutions, unbounded problems, and infeasible cases.

🌐 Internationalization (Multi-Language)

The project supports multiple languages via JSON files.

• Supported Languages: Portuguese (pt), English (en), Spanish (es).
• Contribution: To add a new language, simply create a .json file in ui/locales/ (e.g., fr.json) mirroring the structure of en.json and submit a Pull Request. The system will automatically detect it.

🌳 Branch & Bound

• Integer Programming: Complete algorithm for solving IP problems.
• Visual Decision Tree: Real-time interactive graph showing nodes, prunings (bound, integrality, infeasibility), and branches.
• Search Strategies: Support for BFS, DFS, and Best-Bound.

🛠️ Analysis Tools

• 🔄 Primal-Dual Converter: Instantly transform problems and solve the Dual.
• 📊 Sensitivity Analysis: Calculate Shadow Prices and stability intervals for objective function coefficients ($c_j$) and constraints ($b_i$).
• 📝 Standard Form: Automatic converter to canonical form (Maximization, Equalities, RHS $\ge$ 0) with didactic step-by-step explanation.

📚 Additional Resources

• Problem Library: Collection of classic problems (Diet, Knapsack, Production Mix) ready for testing.
• Session History: Your solved problems are automatically saved for comparison and review.

📖 Detailed Documentation

• Features Documentation - Detailed breakdown of functional and non-functional requirements.
• Architecture Documentation - Technical decisions, structure, and diagrams (C4 Model).

---

🛠️ Technologies

• Frontend: Streamlit
• Numerical Calculation: NumPy and Pandas
• Visualization: Plotly (Charts) and St-Link-Analysis (Graphs/Trees)

---

⚡ How to Run

Prerequisites

• Python 3.8+

Step-by-Step

1. Clone the repository

   git clone <repository-url>
   cd solver_pl

2. Create a virtual environment

   # MacOS/Linux
   python3 -m venv .venv
   source .venv/bin/activate
   
   # Windows
   python -m venv .venv
   .venv\Scripts\activate

3. Install dependencies

   pip install -r requirements.txt

4. Run the application

   streamlit run app.py

---

📂 Project Structure

solver_pl/
├── app.py                  # Main Entrypoint (Navigation)
├── core/                   # Mathematical Logic (Solvers)
│   ├── simplex_solver.py       # Primal Simplex
│   ├── branch_bound_solver.py  # Branch & Bound
├── ui/                     # User Interface (Pages)
│   ├── home_page.py            # Main Dashboard
│   ├── simplex_page.py         # Simplex UI
│   ├── branch_and_bound_page.py# Branch & Bound UI
│   ├── sensitivity_page.py     # Sensitivity Analysis
│   ├── Standard_form_page.py   # Standard Form Converter
│   ├── duality_page.py         # Dual Converter
│   ├── library_page.py         # Problem Library
│   └── plots.py                # 2D/3D Chart Generation

---

Developed with ❤️ for educational purposes - v0.5 (January 2026)