发表机构
National Tsing Hua University（国立清华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多次灌注底部填充顺序，提出三目标多重集排列模型和二元加法树算法，优化时间与可靠性，量化排序权衡及启发式决策遗憾。
AI 中文摘要
多次灌注底部填充将循环时间与工艺可靠性耦合，因为顺序决定了灌注间的流动时间。本文构建了一个三目标多重集排列路由模型，在硬停留和软停留策略下，最小化标称循环时间和加性持续时间方差，同时最大化可靠性；可靠性结合了灌注、调度相关流动和移动项。在独立持续时间和确定性停留阈值下，方差度量在软停留下等于循环时间方差，在硬停留下为其上界。一种多重集排列二元加法树算法无重复地枚举可行路由，并通过支配性剪枝前缀。六个实例，包括三个BeagleBone Black基准，产生了参考帕累托前沿，最大的搜索空间为$1.47 \ imes 10^{12}$条路由，在20个CPU核心上耗时38分钟。在模拟候选中，标称成本选择的路由在建模的持续时间变异性下每块板的最大估计额外成本为0.0014美元，当变异性加倍时为0.0035美元。循环调度在测试成本下与参考最优值相差在3.7%以内；NSGA-II和简化群优化显示出至多0.53%的观测成本遗憾，同时恢复了最大硬停留前沿的约30%。该框架量化了排序权衡和启发式决策遗憾；物理可靠性预测需要基于检查的校准。
英文摘要
Multi-pass underfill dispensing couples cycle time with process reliability because the sequence determines the inter-pass flow times. This paper formulates a tri-objective multiset-permutation routing model that minimises nominal cycle time and additive duration variance while maximising reliability under hard- and soft-dwell policies; reliability combines pass, schedule-dependent flow and travel terms. Under independent durations and deterministic dwell thresholds, the variance measure equals the cycle-time variance under soft dwell and bounds it from above under hard dwell. A multiset-permutation binary-addition-tree algorithm enumerates the feasible routes without duplication and prunes prefixes by dominance. Six instances, including three BeagleBone Black benchmarks, yield reference Pareto fronts, the largest search space of $1.47 \times 10^{12}$ routes in 38 minutes on 20 CPU cores. Among simulated candidates, the nominally cost-selected routes incur maximum estimated excess costs of USD 0.0014 per board at the modelled duration variability and USD 0.0035 with it doubled. Round-robin dispatch is within 3.7 % of the reference optimum at the tested costs; NSGA-II and simplified swarm optimisation show at most 0.53 % observed cost regret while recovering about 30 % of the largest hard-dwell front. The framework quantifies sequencing trade-offs and heuristic decision regret; physical reliability prediction requires inspection-based calibration.
Comments30 pages, 4 figures, 18 tables. Submitted to Reliability Engineering & System Safety. Supplementary code and data (solvers, instances, reference fronts, heuristic archives, validation outputs, one-command test suite) accompany the journal submission and are available from the author
