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

arXiv: https://arxiv.org/abs/2407.02091 · HTML: https://mlsanity.com/paper/2407.02091/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 32 references that are in the map.
- First posted on arXiv 2 Jul 2024.

## Builds on (most cited first, 5 of 5)

- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Application of QUBO solver using black-box optimization to structural design for resonance avoidance](https://mlsanity.com/paper/2204.04906/) (2022)
- [Black-box optimization for integer-variable problems using Ising machines and factorization machines](https://mlsanity.com/paper/2209.01016/) (2022)
- [Lossy compression of matrices by black-box optimisation of mixed integer nonlinear programming](https://mlsanity.com/paper/2204.10579/) (2022)
- [Black Box Optimization Using QUBO and the Cross Entropy Method](https://mlsanity.com/paper/2206.12510/) (2022)

## Built on by (most cited first, 1 of 1)

- [Factorization Machine with Quadratic-Optimization Annealing for RNA Inverse Folding and Evaluation of Binary-Integer Encoding and Nucleotide Assignment](https://mlsanity.com/paper/2602.16643/) (2026)

## Abstract (arXiv)

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.