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The paper addresses the issue of incomplete marginal bit coverage in FMQA when applied to integer/discretized variables via one-hot encoding, which leads to some FM parameters not being updated during initial training. They propose using Latin hypercube sampling (LHS) and Sobol' sequence to design initial training data that ensures every binary variable takes the value one at least once. Experiments on a human-powered aircraft wing-shape optimization benchmark show that LHS-FMQA and Sobol'-FMQA achieve higher mean final cruising speeds compared to the baseline FMQA, especially for higher-dimensional problems.
Incomplete one-hot encoding during FMQA's initial training phase can be overcome with space-filling sampling methods, leading to improved optimization performance.
Factorization machine with quadratic-optimization annealing (FMQA) is a black-box optimization method that combines a factorization machine (FM) surrogate with QUBO-based search by an Ising machine. When FMQA is applied to integer or discretized continuous variables via one-hot encoding, uniform random initial sampling can leave many binary variables never active in the initial training data, and the corresponding FM parameters receive no direct gradient updates from the observed responses. We address this by designing the initial training data to achieve complete marginal bit coverage, namely, ensuring that every binary variable obtained by one-hot encoding takes the value one at least once. We use two space-filling sampling methods, Latin hypercube sampling (LHS) and the Sobol'sequence, yielding LHS-FMQA and Sobol'-FMQA. On the human-powered aircraft wing-shape optimization benchmark with 17 and 32 design variables, both proposed methods achieved numerically higher mean final cruising speeds than the baseline FMQA, with the advantage more pronounced on the 32-variable problem.
