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Physarum-based approach to distributed optimal transport on graphs
Koshi Oishi1, Tomohiko Jimbo2, Satoshi Kikuchi3
1Toyota Central R&D Labs, Inc., 41-1, Yokomichi, Nagakute, Aichi, Japan. e1616@mosk.tytlabs.co.jp.
Scientific Reports
|July 14, 2026
Summary
We introduce distributed Physarum-OT, a novel model inspired by slime mold behavior for efficient, adaptive transport networks. This approach enables local, distributed execution, overcoming limitations of traditional optimal transport (OT) methods.
Area of Science:
- Complex Systems
- Computational Biology
- Operations Research
Background:
- Biological transport networks, like the slime mold Physarum polycephalum, exhibit adaptive reorganization via local interactions.
- The Physarum model is mathematically equivalent to optimal transport (OT), a powerful tool for network optimization.
- Current OT implementations require centralized computation, hindering distributed applications and limiting adaptability.
Purpose of the Study:
- To develop a distributed model of Physarum-based optimal transport (Physarum-OT) that mimics slime mold's local interaction principles.
- To enable decentralized execution for artificial transport networks, enhancing robustness and adaptability.
- To address the limitations of centralized OT methods in dynamic environments.
Main Methods:
- Formulated distributed Physarum-OT as a bilevel optimization problem, separating network development (outer) and linear system solution (inner).
- Developed a computational relaxation method with proven convergence guarantees for the bilevel optimization.
- Validated the model through numerical experiments on a logistics network.
Main Results:
- The proposed distributed Physarum-OT method converges to optimal transport solutions.
- Demonstrated locally distributed computation, mirroring slime mold's decentralized behavior.
- Showcased smooth adaptation to changing network costs, akin to slime mold's resilience.
Conclusions:
- Distributed Physarum-OT successfully replicates slime mold's adaptive network formation in a computationally feasible, decentralized manner.
- The model offers a promising alternative for designing robust and adaptable artificial transport systems, particularly in logistics.
- This work bridges biological inspiration with computational optimization for advanced network solutions.
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