AI 中文总结
针对低自相关二进制序列问题，提出结合汤普森采样与并行自回避游走的混合搜索框架，经GPU加速等优化，通过两阶段策略改进搜索。实验表明其在多序列长度上改进结果，获新最长序列，有效划分优先级，提供高性能优值因子最大化策略。
AI 中文摘要
低自相关二进制序列问题（LABS）是一个艰难的组合优化挑战，在通信、信号处理和卫星导航中有重要应用。本文提出一种混合搜索框架，将汤普森采样与并行自回避游走相结合，以在LABS搜索空间的限制类别中自适应分配计算资源。通过将分区建模为多臂老虎机设置中的臂，该方法动态地将搜索资源转向经验上产生更高优值因子的分区，同时保持对较少采样区域的探索。该方法通过GPU并行执行、共享后验更新、高效邻域评估和用于防止循环的布隆过滤器进一步加速。此外，使用两阶段优化策略，先搜索受限的分区斜对称空间，然后在无限制空间中优化最佳候选。实验表明，该方法在35个序列长度上改进了之前的最佳结果，还得到了新的最长序列，优值因子超过8.0。结果表明汤普森采样有效地对具有更好观察性能的分区进行了优先级划分，证实了在线、数据驱动的资源分配在LABS优化中的价值。总体而言，该框架为高性能优值因子最大化提供了可扩展且有效的策略。
英文摘要
Low autocorrelation binary sequences problem (LABS) is a hard combinatorial optimization challenge with important applications in communications, signal processing, and satellite navigation. This paper proposes a hybrid search framework that combines Thompson sampling with parallel self-avoiding walks to adaptively allocate computational effort across restriction classes of the LABS search space. By modeling partitions as arms in a multi-armed bandit setting, the proposed method dynamically shifts search resources toward partitions that empirically produce higher merit factors while maintaining exploration of less-sampled regions. The approach is further accelerated through GPU-parallel execution, shared posterior updates, efficient neighborhood evaluation, and a Bloom filter for cycle prevention. In addition, we use a two-stage optimization strategy that first searches constrained partitioned skew-symmetric spaces and then refines the best candidates in the unrestricted space. Experiments on long binary sequences show that the proposed method improves the previously best-known results for 35 sequence lengths in the range $450 \le L \le 527$ and for $L=573$. In particular, we report a new longest sequence with merit factor exceeding $8.0$, obtained for $L=451$. The results also show that Thompson sampling effectively prioritizes partitions with better observed performance, confirming the value of online, data-driven resource allocation in LABS optimization. Overall, the proposed framework provides a scalable and effective strategy for high-performance merit factor maximization.
