CANTS-GP: A Nature-Inspired Metaheuristic for Graph-Based Genetic Programs

Graph-based genetic programs built from arithmetic primitives (e.g., addition, multiplication, trigonometric functions) offer inherently interpretable models for complex tasks. This work introduces CANTS-GP, an extension on Continuous Ant-Based Neural Topology Search (CANTS), which is a nature-inspired metaheuristic that constructs computational graphs with trainable arithmetic functions rather than opaque neural units. CANTS-GP employs a multi-colony framework: simulated ant agents traverse an unbounded continuous search space guided by pheromone trails, and colonies periodically exchange evolving parameters—pheromone evaporation rates and the number of foraging ants—via a particle swarm optimization-inspired information sharing. Ant-generated paths are consolidated into flexible, acyclic computational graphs through the DBSCAN clustering algorithm and depth-first search-based cycle removal. Key innovations include adaptive colony evaporation control, dynamic movement heuristics, and multi-colony evolutionary strategies. We evaluate CANTS-GP on six benchmark time-series forecasting tasks, demonstrating consistent performance gains over state-of-the-art methods while yielding transparent models whose arithmetic structures provide model interpretability.