A low-autocorrelation binary sequences problem with a high figure of merit factor represents a formidable computational challenge. An efficient parallel computing algorithm is required to reach the new best-known solutions for this problem. Therefore, we developed the $\mathit{sokol}_{\mathit{skew}}$ solver for the skew-symmetric search space. The developed solver takes the advantage of parallel computing on graphics processing units. The solver organized the search process as a sequence of parallel and contiguous self-avoiding walks and achieved a speedup factor of 387 compared with $\mathit{lssOrel}$, its predecessor. The $\mathit{sokol}_{\mathit{skew}}$ solver belongs to stochastic solvers and can not guarantee the optimality of solutions. To mitigate this problem, we established the predictive model of stopping conditions according to the small instances for which the optimal skew-symmetric solutions are known. With its help and 99% probability, the $\mathit{sokol}_{\mathit{skew}}$ solver found all the known and seven new best-known skew-symmetric sequences for odd instances from $L=121$ to $L=223$. For larger instances, the solver can not reach 99% probability within our limitations, but it still found several new best-known binary sequences. We also analyzed the trend of the best merit factor values, and it shows that as sequence size increases, the value of the merit factor also increases, and this trend is flatter for larger instances.

翻译：高优值因子的低自相关二进制序列问题具有极大的计算挑战性。为解决该问题并获取新的已知最优解，需设计高效的并行计算算法。为此，我们针对斜对称搜索空间开发了$\mathit{sokol}_{\mathit{skew}}$求解器。该求解器利用图形处理单元并行计算优势，将搜索过程组织为一系列并行且连续的自我规避行走，相对于前身$\mathit{lssOrel}$实现了387倍的加速比。作为随机型求解器，$\mathit{sokol}_{\mathit{skew}}$无法保证解的全局最优性。为缓解此问题，我们根据已知最优斜对称解的小规模实例建立了停止条件预测模型。借助该模型，在99%概率条件下，$\mathit{sokol}_{\mathit{skew}}$求解器成功发现了$L=121$至$L=223$奇数实例中全部已知及七个新增最优斜对称序列。对于更大规模实例，受限于现有条件，该求解器无法达到99%概率精度，但仍发现了若干新增最优二进制序列。通过对最优优值因子变化趋势的分析，我们发现该值随序列长度增加而递增，且在大规模实例中增长趋势趋于平缓。