AI 中文总结
PrecPack是一个开源精确求解器，通过扩展分支-边界-记忆算法并引入广义状态和根列生成，高效求解具有广义优先约束的装箱问题，在基准测试中优于现有实现。
AI 中文摘要
在包装和装配线应用中，高效利用资源需要同时考虑容量和优先约束的决策。具有广义优先约束的装箱问题（BPP-GP）是强NP难的，它通过最小化所需的有序、有容量限制的箱子的数量来建模此类决策，即使优先需求跨越多个箱子。现有的精确算法主要关注经典特例，而一般的BPP-GP仅通过紧凑整数模型和启发式方法解决，没有高效的开源精确求解器。我们提出了PrecPack，一个统一的精确求解器，它将分支-边界-记忆（BBR）扩展到任意非负优先权重，并自然地特化到经典情况。广义状态捕获了在未来箱子中仍然有效的限制，这些限制通过分支、支配和冲突感知下界来处理。根列生成使用定点算术来计算数值上有效的对偶界以用于剪枝或证明最优性。为了支持重用和验证，我们提供了通用的编程和命令行接口、独立的分配检查、明确的终止状态和可重复的批处理执行；核心过程不需要商业软件。在相同机器、单线程的经典装配线基准比较中，更多的实例被证明是最优的，并且相对于领先的源代码可用的BBR实现，平均计算时间大幅减少。与已发表的装箱问题（带优先约束）和BPP-GP基准结果的进一步比较也显示，在大多数基准集上，更多的实例被证明是最优的，并且报告的平均差距更小。PrecPack在MIT许可证下发布，网址为https://this https URL。
英文摘要
Efficient resource use in packing and assembly-line applications requires decisions that jointly account for capacity and precedence constraints. The strongly NP-hard bin packing problem with generalized precedence constraints (BPP-GP) models such decisions by minimizing the number of ordered, capacitated bins required to pack weighted items, even when precedence requirements span multiple bins. Existing exact algorithms primarily focus on classical special cases, whereas general BPP-GP has been addressed only via compact integer models and heuristics, with no efficient open-source exact solver. We present PrecPack, a unified exact solver that extends branch-bound-and-remember (BBR) to arbitrary nonnegative precedence weights and naturally specializes to the classical cases. Generalized states capture restrictions that remain active across future bins, which are addressed through branching, dominance, and conflict-aware lower bounds. Root column generation uses fixed-point arithmetic to compute numerically valid dual bounds for pruning or to prove optimality. To support reuse and verification, we provide common programming and command-line interfaces, independent assignment checking, explicit termination statuses, and reproducible batch execution; the core procedures require no commercial software. In same-machine, single-threaded comparisons on classic assembly-line benchmarks, more instances are proven optimal, and average computing times are substantially reduced relative to leading source-available BBR implementations. Further comparisons with published benchmark results for bin packing with precedence constraints and BPP-GP also show that more instances were proved optimal and that reported average gaps were smaller on most benchmark sets. PrecPack is released under the MIT License at https://github.com/Sunkanghong-Wang/PrecPack.
