Amoeba model handles 180 cities in mathematical tests

In the Waseda University model, an amoeba starts as a blob in a central hub, then sends branches down radial lanes to gather nutrients while light makes some branches contract. Those lanes stand for cities in the traveling-salesman problem, and the branch lengths encode candidate routes. Yusuke Miyajima and Masahito Mochizuki have now simplified the mathematics behind that behavior for physical implementation.

The obstacle was not the idea of using a slime mold as a computer. It was the machinery wrapped around it: earlier versions relied on a volume-conservation law, multiple conditional branches and complex functions. The researchers made five targeted modifications, including replacing sigmoid functions with constants or simpler functions and removing conservation-law constraints, branching and counting operations.

The result is a recurrence formula that produced feasible routes in fewer iterations than both the original Amoeba TSP model and its improved version. In tests, the revised model handled up to 180 cities. The improved model was limited to 100, while the original reached 30. A tunable parameter lets researchers adjust performance rather than accept one fixed behavior.

The mathematical result also links two apparently different ideas. The team showed that the amoeba-inspired process is equivalent to a recurrent neural network with fixed weights: each weight represents either the distance between two cities or a penalty for violating the route's constraints. That suggests a shared computational principle between slime-mold dynamics and a class of neural networks.

So what changes in practice? A simpler model gives engineers more materials to work with, including photonic circuits, spintronic devices, and mechanical or fluidic systems. The researchers describe a spintronic implementation, a class of devices built around electron spin, as stable against heat and radiation and capable of low energy consumption. But this is still a research model and hardware proposal, not a computer already serving logistics or AI users; the study does not report a deployed device or independent real-world benchmark.