Self-organization and solution of shortest-path optimization problems with memristive networks

TL;DR

This paper demonstrates that memristive networks can self-organize to efficiently solve shortest-path problems, with potential applications to complex optimization tasks like the traveling salesman problem, leveraging their memory properties.

Contribution

It introduces a novel approach using memristive networks for solving shortest-path and TSP problems, highlighting self-organization and solution healing capabilities.

Findings

Memristive networks self-organize into shortest paths.

The network entropy characterizes the self-organization process.

An algorithm for the traveling salesman problem is proposed.

Abstract

We show that memristive networks-namely networks of resistors with memory-can efficiently solve shortest-path optimization problems. Indeed, the presence of memory (time non-locality) promotes self organization of the network into the shortest possible path(s). We introduce a network entropy function to characterize the self-organized evolution, show the solution of the shortest-path problem and demonstrate the healing property of the solution path. Finally, we provide an algorithm to solve the traveling salesman problem. Similar considerations apply to networks of memcapacitors and meminductors, and networks with memory in various dimensions.