This project estimates an Origin-Destination (OD) matrix from observed traffic link counts using a Non-Negative Least Squares (NNLS) approach.

The project is divided into two independent modules:

• Generator: Creates synthetic transportation network data, including the true OD matrix, assignment matrix, and observed link counts.
• Estimator: Estimates the OD matrix using the assignment matrix and observed link counts.

OD/
│
├── generator.py
├── estimator.py
├── main.py
├── README.md
└── requirements.txt

• Python 3.10+
• NumPy
• SciPy
• NetworkX

Install dependencies:

pip install -r requirements.txt

or

pip install numpy scipy networkx

Responsible for generating synthetic traffic data.

Functions include:

• Generate transportation network
• Generate true OD matrix
• Compute shortest paths
• Build assignment matrix (P)
• Compute observed link counts

Outputs:

• Assignment Matrix (P)
• True OD Matrix
• Link Counts

Implements the OD estimation algorithm.

Input:

• Assignment Matrix (P)
• Observed Link Counts

Method:

• Non-Negative Least Squares (NNLS)

Output:

• Estimated OD Matrix
• Reconstructed Link Counts
• RMSE
• Residual Error

Runs the complete workflow:

1. Generate synthetic data.
2. Estimate the OD matrix.
3. Display the results.

The estimation problem is formulated as

P × x ≈ y

where

• P : Assignment Matrix
• x : Unknown OD demand vector
• y : Observed link counts

The optimization problem is

min ||P x - y||²

subject to

x ≥ 0

which is solved using the Non-Negative Least Squares (NNLS) algorithm provided by SciPy.

Transportation Network
        │
        ▼
Generate True OD Matrix
        │
        ▼
Compute Shortest Paths
        │
        ▼
Build Assignment Matrix (P)
        │
        ▼
Generate Link Counts
        │
        ▼
Estimate OD Matrix (NNLS)
        │
        ▼
Evaluation

The program prints:

• True OD Matrix
• Estimated OD Matrix
• Observed Link Counts
• Reconstructed Link Counts
• RMSE
• Residual Error

Origin-Destination Matrix Estimation using NNLS