From Mixing to Tearing: Graph Decomposition in Decentralized Optimization via Message Passing

This project gives research direction and simulation help for testing decentralized optimization algorithms on complex networks. It focuses on distributed bioprocess systems such as multi‑stage fermentation networks or parallel bioreactor media optimization. Traditional methods use gossip or spanning‑tree routing to share local data, but they usually lack a single framework that designs both the optimization subproblems and the communication together. To fix that, we explore the Graph‑Tearing message passing (GATE) framework. GATE breaks the graph into tree blocks and assigns dedicated edge variables to each block. Agents then minimize the total of endpoint cost‑to‑go messages and relax the solution, letting them solve small local subproblems cooperatively. Our methodology simulates this

decentralized framework to optimize convex cost functions that represent resource allocation, nutrient‑feeding schedules, or metabolic‑flux constraints across the distributed nodes. The project also provides guidance on setting up simulations and measuring convergence speed, communication load, and computational efficiency, comparing these results to standard consensus‑based ADMM or gossip algorithms. Detailed modeling shows that graph‑tearing strategies can improve coordination and overall optimization in decentralized bioprocess networks.

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