A straightforward local-search optimization algorithm on the symmetric group

TL;DR

This paper introduces a simple local-search optimization algorithm tailored for the symmetric group, analyzing its complexity and application to permutation isometries on vectors within cones of specified angles.

Contribution

It presents a novel straightforward local-search algorithm for the symmetric group with complexity analysis and specific application to permutation isometries.

Findings

Algorithm effectively finds permutation isometries within cones

Complexity estimates demonstrate efficiency for high-dimensional cases

Applicable to optimization problems involving symmetric group actions

Abstract

Given a real objective function defined over the symmetric group, a direct local-search algorithm is proposed, and its complexity is estimated. In particular for an $n$-dimensional unit vector we are interested in the permutation isometry that acts on this vector by mapping it into a cone of a given angle.