Ant Colony Optimization applied to the Travelling Santa Problem

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. Given the vast number of permutations of city-to-city legs, different payload drop-offs at each location, and the necessity of delivering gifts during the hours of darkness, to minimize energy expenditure, a heuristic-based optimization was applied. To design this schedule, the Traveling-Santa Ant-Colony Optimization (TSaP–ACO) framework 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 minimize aerodynamic work via a shrinking sleigh cross-sectional area depending on current payload, (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 Ant-Colony Optimization (ACO). In a 40-capital-city stress test, it cuts energy use by 89% and shortens tour length by 60%. Population-first routing emerges naturally from work minimization (50% served by leg 11 of 40). These results demonstrate that rolling-window, energy-aware ACO has potential applications in more realistic global delivery scenarios.