Ant Colony Optimisation applied to the Travelling Santa Problem

TL;DR

This paper introduces TSaP-ACO, a novel ant colony optimization framework for planning Santa Claus's global delivery route, optimizing for energy efficiency and daylight constraints, outperforming traditional methods in complex scenarios.

Contribution

The paper presents a new heuristic framework, TSaP-ACO, that incorporates local darkness feasibility, aerodynamic work minimization, and dynamic speed tuning for efficient route planning.

Findings

Eliminates all daylight violations in benchmark tests.

Reduces total work by up to 10% compared to distance-only ACO.

Cuts energy use by 88% and tour length by 67% in stress tests.

Abstract

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.