optimax: Comprehensive Optimization Toolkit

optimax is a comprehensive optimization toolkit designed for the SF2812 Applied Linear Optimization course at KTH. It provides a web-based interface to visualize and solve problems covering the core syllabus topics, including Linear Programming, Integer Programming, Column Generation, Lagrangian Relaxation, and Stochastic Programming.

Syllabus Coverage

This project implements solvers and visualizations for the following course modules:

1. Linear Programming (Simplex/Interior Point)

• Module: api/solvers/lp.py

• Features: Solves LP problems using scipy.optimize.linprog (Highs method, which includes Simplex/Interior Point). Visualizes 2D feasible regions and objective functions.

  

2. Integer Programming (Branch-and-Bound)

• Module: api/solvers/ip.py

• Features: Custom Branch-and-Bound implementation for integer programming. Visualizes the search tree, showing branching decisions, bounds, and pruning.

  

3. Decomposition & Column Generation

• Module: api/solvers/colgen.py
• Features: Solves the Cutting Stock Problem using Column Generation. Iteratively solves the Master Problem (LP) and Subproblem (Knapsack) to generate improving patterns.

4. Lagrangian Relaxation

• Module: api/solvers/lagrangian.py

• Features: Solves the Generalized Assignment Problem (GAP) using Lagrangian Relaxation. Visualizes the convergence of the Lower Bound using subgradient optimization.

  

5. Stochastic Programming

• Module: api/solvers/stochastic.py

• Features: Solves the Two-Stage Stochastic Farmer's Problem (Deterministic Equivalent). Visualizes the optimal first-stage decision (planting) and second-stage profit distribution across scenarios.

  

Tech Stack

• Backend: Python (FastAPI, Scipy, Numpy, Pulp, NetworkX, Matplotlib)
• Frontend: React (Vite)
• Deployment: Vercel (Serverless Python Functions)

Installation & Running Locally

1. Clone the repository:

   git clone https://github.com/dhruvhaldar/optimax.git
   cd optimax

2. Create and Activate Virtual Environment:

   • Windows:

     python -m venv venv
     .\venv\Scripts\activate

   • macOS/Linux:

     python -m venv venv
     source venv/bin/activate

3. Install Backend Dependencies:

   pip install -r requirements.txt

4. Run the API Server:

   python -m uvicorn api.index:app --reload

   The API will be available at http://localhost:8000/api.

5. Run the Frontend:

   cd frontend
   npm install
   npm run dev

   The frontend will run at http://localhost:5173.

Deployment

This project is configured for deployment on Vercel. The vercel.json file handles routing for the FastAPI backend (api/index.py) and the static React frontend.

License

MIT License. See LICENSE for details.