The hypothetical global delivery schedule of Santa Claus must follow strict rolling night-time windows that vary with the Earth's rotation and obey an energy budget that depends on payload size and cruising speed. To design this schedule, the Travelling-Santa Ant-Colony Optimisation framework (TSaP-ACO) was developed. This heuristic framework constructs potential routes via a population of artificial ants that iteratively extend partial paths. Ants make their decisions much like they do in nature, following pheromones left by other ants, but with a degree of permitted exploration. This approach: (i) embeds local darkness feasibility directly into the pheromone heuristic, (ii) seeks to minimise aerodynamic work via a shrinking sleigh cross sectional area, (iii) uses a low-cost "rogue-ant" reversal to capture direction-sensitive time-zones, and (iv) tunes leg-specific cruise speeds on the fly. On benchmark sets of 15 and 30 capital cities, the TSaP-ACO eliminates all daylight violations and reduces total work by up to 10% compared to a distance-only ACO. In a 40-capital-city stress test, it cuts energy use by 88%, and shortens tour length by around 67%. Population-first routing emerges naturally from work minimisation (50% served by leg 11 of 40). These results demonstrate that rolling-window, energy-aware ACO has potential applications more realistic global delivery scenarios.

翻译：圣诞老人的假设性全球配送计划必须遵循严格的滚动夜间时间窗口，这些窗口随地球自转而变化，并需遵守取决于有效载荷大小和巡航速度的能量预算。为设计该计划，我们开发了旅行圣诞老人-蚁群优化框架（TSaP-ACO）。该启发式框架通过人工蚂蚁种群构建潜在路径，这些蚂蚁通过迭代扩展局部路径进行搜索。蚂蚁的决策机制高度模拟自然界：遵循其他蚂蚁遗留的信息素轨迹，同时允许一定程度的探索性行为。本方法具有以下特点：（i）将局部黑暗可行性直接嵌入信息素启发函数；（ii）通过动态缩减雪橇横截面积以最小化空气动力做功；（iii）采用低成本的“异常蚂蚁”反向移动机制以捕捉方向敏感时区；（iv）实时调整路段特定的巡航速度。在包含15个和30个首都城市的基准测试集中，TSaP-ACO完全消除了所有日间飞行违规，相较于仅考虑距离的ACO算法，总做功减少达10%。在包含40个首都城市的压力测试中，能耗降低88%，路径总长度缩短约67%。基于做功最小化的目标自然催生了人口优先路径规划策略（第11个配送段即完成50%人口服务）。这些结果表明，滚动时间窗口与能量感知相结合的ACO算法在更现实的全球配送场景中具有应用潜力。