Effectiveness of Binary Autoencoders for QUBO-Based Optimization Problems
This work addresses the challenge of encoding nonbinary structures for quantum annealing-based optimization, providing insights for designing latent representations in black-box settings, though it is incremental as it builds on existing FMQA methods.
The paper tackled the problem of inefficient binary encodings in black-box combinatorial optimization, showing that a binary autoencoder (bAE) improves search efficiency by better aligning latent Hamming distances with original solution distances, leading to faster improvement in approximation ratios while maintaining feasibility.
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.