Quantum-Inspired Optimization over Permutation Groups

TL;DR

This paper introduces Perm-QIO, a quantum-inspired optimization framework tailored for permutation-based problems, demonstrating its effectiveness on vehicle routing problems with promising results.

Contribution

The paper develops a novel algorithmic framework, Perm-QIO, enabling quantum-inspired optimization techniques to directly address permutation domain problems, expanding their applicability.

Findings

Perm-QIO effectively finds high-quality solutions for vehicle routing problems.

The framework leverages cost-landscape structure to improve optimization results.

Demonstrates polynomial speedup potential over traditional methods.

Abstract

Quantum-inspired optimization (QIO) algorithms are computational techniques that emulate certain quantum mechanical effects on a classical hardware to tackle a class of optimization tasks. QIO methods have so far been employed to solve various binary optimization problems and a significant (polynomial) computational speedup over traditional techniques has also been reported. In this work, we develop an algorithmic framework, called Perm-QIO, to tailor QIO tools to directly solve an arbitrary optimization problem, where the domain of the underlying cost function is defined over a permutation group. Such problems are not naturally recastable to a binary optimization and, therefore, are not necessarily within the scope of direct implementation of traditional QIO tools. We demonstrate the efficacy of Perm-QIO in leveraging the structure of cost-landscape to find high-quality solutions for a class of vehicle routing problems that belong to the category of non-trivial combinatorial optimization over the space of permutations.