Efficient Bit Labeling in Factorization Machines with Annealing for Traveling Salesman Problem
This work addresses an incremental improvement in binary labeling for machine learning applications in combinatorial optimization, specifically for researchers and practitioners using factorization machines with annealing.
The paper tackled the problem of optimizing binary labeling in factorization machines with annealing for the traveling salesman problem, finding that Gray labeling reduces local minima percentages and yields shorter traveling distances compared to natural labeling in simulations with up to 15 cities.
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.