The DevOps movement evolved as a natural extension of the Agile methodology.

Agile (Option A): Agile emphasizes iterative development, collaboration, and flexibility. While Agile improved software development speed, it created challenges in integrating development with IT operations. DevOps emerged to address this by bringing operations into the Agile cycle — enabling continuous integration, delivery, and deployment.

Waterfall (Option B): Incorrect. Waterfall is a rigid, sequential methodology, fundamentally opposite to the DevOps philosophy.

Promise-based algorithms (Option C): Not a methodology — irrelevant here.

Test-driven development and model-driven development (Option D): While these practices support DevOps, they are not the origin of the movement.

Thus, the DevOps movement is an outgrowth of Agile methodology.