Evolution of unknotting strategies for knots and braids

TL;DR

This paper investigates the use of evolutionary computation to develop strategies for unknotting knots and braids, demonstrating effectiveness in both specific and generic scenarios.

Contribution

It introduces a novel application of evolutionary algorithms to learn unknotting sequences, advancing computational methods in knot theory.

Findings

Evolutionary methods successfully find unknotting sequences.

Generic move sequences can be evolved for multiple knots.

Approach improves computational knot simplification techniques.

Abstract

This paper explores the problem of unknotting closed braids and classical knots in mathematical knot theory. We apply evolutionary computation methods to learn sequences of moves that simplify knot diagrams, and show that this can be effective both when the evolution is carried out for individual knots and when a generic sequence of moves is evolved for a set of knots.