Effectiveness of Binary Autoencoders for QUBO-Based Optimization Problems

TL;DR

This paper investigates how binary autoencoders improve the efficiency of QUBO-based optimization by providing better latent representations that preserve problem structure, leading to faster convergence and higher quality solutions.

Contribution

It demonstrates that binary autoencoders enhance surrogate modeling in black-box optimization by preserving neighborhood structure and feasibility, with insights from the traveling salesman problem.

Findings

Binary autoencoders accurately reconstruct feasible solutions.

Latent Hamming distances better reflect original solution distances.

Autoencoders lead to fewer local optima and faster approximation ratios.

Abstract

In black-box combinatorial optimization, objective evaluations are often expensive, so high quality solutions must be found under a limited budget. Factorization machine with quantum annealing (FMQA) builds a quadratic surrogate model from evaluated samples and optimizes it on an Ising machine. However, FMQA requires binary decision variables, and for nonbinary structures such as integer permutations, the choice of binary encoding strongly affects search efficiency. If the encoding fails to reflect the original neighborhood structure, small Hamming moves may not correspond to meaningful modifications in the original solution space, and constrained problems can yield many infeasible candidates that waste evaluations. Recent work combines FMQA with a binary autoencoder (bAE) that learns a compact binary latent code from feasible solutions, yet the mechanism behind its performance gains is unclear. Using a small traveling salesman problem as an interpretable testbed, we show that the bAE reconstructs feasible tours accurately and, compared with manually designed encodings at similar compression, better aligns tour distances with latent Hamming distances, yields smoother neighborhoods under small bit flips, and produces fewer local optima. These geometric properties explain why bAE+FMQA improves the approximation ratio faster while maintaining feasibility throughout optimization, and they provide guidance for designing latent representations for black-box optimization.