Proposed modified computational model for the amoeba-inspired combinatorial optimization machine

TL;DR

The paper addresses efficient solution-search for the traveling salesman problem (TSP) using amoeba-inspired, domain-specific computation. It analyzes the Amoeba TSP model by isolating three core elements (A,B,C), tests their modifications, and demonstrates that fluctuations are essential while the volume-conservation constraint can be relaxed. By combining the effective modifications into the Improved Amoeba TSP model, the authors achieve near-sure approximate solutions with iteration counts that scale as $O(\sqrt{n})$, a significant improvement over prior linear scaling, suggesting practical potential for physical implementations. These results guide the design of high-performance, amoeba-inspired optimization hardware for large-scale combinatorial problems.

Abstract

A single-celled amoeba can solve the traveling salesman problem through its shape-changing dynamics. In this paper, we examine roles of several elements in a previously proposed computational model of the solution-search process of amoeba and three modifications towards enhancing the solution-search preformance. We find that appropriate modifications can indeed significantly improve the quality of solutions. It is also found that a condition associated with the volume conservation can also be modified in contrast to the naive belief that it is indispensable for the solution-search ability of amoeba. A proposed modified model shows much better performance.

Figures (2)

• Figure 1: (a) Experimental setup of the amoeba-based combinatorial optimization machine. (b) Example of a map of the 4-city TSP. In this experiment, the cities are labeled by alphabets, A, B, C and D. (c), (d) Initial and final states of the amoeba-based device in the experiment. The final state shown in (d) represents a solution corresponding to a traveling route in order of B $\rightarrow$ C $\rightarrow$ D $\rightarrow$ A. The red lines and the red numbers in (b) represent the traveling route and the visiting order, respectively.
• Figure 2: (a) City-number dependence of the average number of iterations required to obtain an approximate solution using the Improved Amoeba TSP algorithm, which turns out to scale with $\sqrt{n}$. Inset shows the comparison with results of the original Amoeba TSP algorithm Zhu18, which scales linearly with $n$. (b) City-number dependence of the average of normalized route length $R_{\rm calc}/R_{\rm est}$ obtained by the Improved Amoeba TSP algorithm. The dashed lines represents $R_{\rm calc}/R_{\rm est}=0.9$ as a universal result of the original Amoeba TSP algorithm.