HiGHS 中的预求解启发式算法：实现与计算研究
Presolve heuristics in HiGHS: implementation and computational study
AI总结：
在开源求解器HiGHS中实现四种混合整数规划原始启发式算法，评估显示原始积分提升23.7%，能更快找到优质解，部分启发式因无效被禁用，实现已开源。
AI中文摘要：
我们在开源求解器 HiGHS（Huangfu 和 Hall, 2018）中提供了四种已发表的混合整数规划原始启发式算法的参考实现：Feasibility Jump（Luteberget 和 Sartor, 2023）、fix-propagate-repair（FPR；Salvagnin, Roberti 和 Fischetti, 2025）及其 LP 引导的潜水变体、LocalMIP（Lin, Zou 和 Cai, 2024）以及一阶 LP 可行性泵 Scylla（Mexi 等人, 2025）。它们共享一个集成接口，具有每个启发式的预算和耐心参数，并且每个都在独立种子的工作进程上并行运行。评估在 mipfeas 基准（Bussieck 和 Dirkse, 2026）上进行，包含 233 个实例，时限为 600 秒，与在同一台机器上单独构建的未修补 HiGHS 进行比较。原始积分在完整集合上提高了 23.7%，在未用于调优的实例上提高了 12.9%：修补后的求解器能更快地达到良好解。在时间限制时，它略微领先。它在 4 个未修补求解器未找到解的实例上找到了解，而反向情况有 1 个，其最终间隙更小，仅在完整集合上显著。Scylla 和 LP 引导的潜水在任何完整运行中均未产生被接受的当前最优解，因此被禁用发布；它们的实现仍然保留。该实现已作为开源发布。
英文摘要：
We present reference implementations of four published primal heuristics for mixed-integer programming inside the open-source solver HiGHS (Huangfu and Hall, 2018): Feasibility Jump (Luteberget and Sartor, 2023), fix-propagate-repair (FPR; Salvagnin, Roberti and Fischetti, 2025) with its LP-guided dive-time variant, LocalMIP (Lin, Zou and Cai, 2024), and the first-order-LP feasibility pump Scylla (Mexi et al., 2025). They share one integration interface with per-heuristic budgets and patiences, and each runs in parallel on independently seeded workers. The evaluation is on the mipfeas benchmark (Bussieck and Dirkse, 2026), 233 instances at 600 s, against a separately built unpatched HiGHS on the same machine. The primal integral improves by 23.7% over the full set and by 12.9% on the instances not used for tuning: the patched solver reaches a good solution sooner. At the time limit it is slightly ahead. It finds a solution on 4 instances where the unpatched solver finds none, against 1 the other way, and its final gap is smaller, significantly so only over the full set. Scylla and the LP-guided dive produced no accepted incumbent in any full-limit run that carried them and ship disabled; their implementations remain. The implementation is released as open source.
