Efficient Bit Labeling in Factorization Machines with Annealing for Traveling Salesman Problem

TL;DR

This paper introduces Gray labeling, a binary labeling method for factorization machines with annealing, which improves convergence speed and solution quality in solving the Traveling Salesman Problem by reducing local minima.

Contribution

It proposes and evaluates Gray labeling, a novel binary labeling technique that enhances optimization performance in quadratic unconstrained binary problems like TSP.

Findings

Gray labeling reduces local minima percentage.

Gray labeling results in shorter traveling distances.

Gray labeling improves convergence speed.

Abstract

To efficiently find an optimum parameter combination in a large-scale problem, it is a key to convert the parameters into available variables in actual machines. Specifically, quadratic unconstrained binary optimization problems are solved with the help of machine learning, e.g., factorization machines with annealing, which convert a raw parameter to binary variables. This work investigates the dependence of the convergence speed and the accuracy on binary labeling method, which can influence the cost function shape and thus the probability of being captured at a local minimum solution. By exemplifying traveling salesman problem, we propose and evaluate Gray labeling, which correlates the Hamming distance in binary labels with the traveling distance. Through numerical simulation of traveling salesman problem up to 15 cities at a limited number of iterations, the Gray labeling shows less local minima percentages and shorter traveling distances compared with natural labeling.