Heterogeneous HPC workflow scheduling under multiple hard constraints poses a challenging combinatorial optimization problem. Classical exact solvers guarantee optimality but face scalability limits, motivating interest in quantum-inspired Quadratic Unconstrained Binary Optimization (QUBO) as an alternative optimization paradigm. This work presents a systematic empirical evaluation of QUBO-based scheduling methods against classical baselines including MILP, CP-SAT, GA, and HEFT. We evaluate three QUBO variants, single-run simulated annealing, multi-attempt annealing, and a layered QAOA-inspired schedule, with hybrid enhancement strategies on validation workflows (3-4 tasks) and synthetic scaling instances (5-20 tasks). All solvers are assessed through a unified pipeline tracking feasibility, makespan, and resource utilization under progressive constraint activation and controlled penalty sweeps. All approaches recover the expected optimal makespan on validation instances, confirming formulation correctness. However, feasibility degradation emerges for specific QUBO variants as constraint interactions intensify, particularly when communication costs are introduced. Penalty analysis reveals a sharp feasibility threshold for QUBO-SA, where insufficient penalties consistently fail and moderate-to-strong penalties restore feasibility. Scaling experiments show that classical solvers remain robust across all tested sizes, while QUBO-SA loses feasibility beyond 15 tasks and the QAOA-inspired variant beyond 10 tasks. The study provides a clear empirical characterization of the reliability boundaries of quantum-inspired QUBO formulations for HPC scheduling and identifies regimes where classical approaches remain preferable under current solver capabilities.

翻译：多重硬约束下的异构高性能计算工作流调度是一个具有挑战性的组合优化问题。经典精确求解器虽能保证最优性，但面临可扩展性限制，这激发了学界对量子启发式二次无约束二元优化（QUBO）这一替代优化范式的兴趣。本文针对基于QUBO的调度方法，与包括MILP、CP-SAT、GA和HEFT在内的经典基线方法进行了系统性实证评估。我们评估了三种QUBO变体——单次运行模拟退火、多次尝试退火及分层QAOA启发式调度——在验证工作流（3-4个任务）和合成规模实例（5-20个任务）上采用混合增强策略的表现。所有求解器均通过统一流程进行评估，在渐进式约束激活和受控罚项扫描下追踪可行性、制造期和资源利用率。所有方法均在验证实例上恢复预期最优制造期，证实了公式的正确性。然而，随着约束交互增强（尤其是引入通信成本时），特定QUBO变体出现可行性退化。罚项分析揭示了QUBO-SA的尖锐可行性阈值：罚项不足时持续失效，而中等至强罚项可恢复可行性。规模实验表明，经典求解器在所有测试规模下保持稳健，而QUBO-SA在超过15个任务时丧失可行性，QAOA启发式变体则在超过10个任务时失效。本研究清晰表征了量子启发式QUBO公式用于HPC调度的可靠性边界，并识别出当前求解器能力下经典方法仍占优的区间。