I would not expect to win without a method that I could see to approximate or to exceed linear-programming formulations of multi-agent path planning, for example here (2005/2008) or here (2001). Those methods don't fully cover the stochasticity of resource gathering or the adversariality of combat, but they partly cover resource-finding and patrolling (when up-to-date visual information about unknowns is an objective) and deployment, and they provide a framework into which to fit tradeoffs among options evaluated by more specialized models, such as for combat, exploration, or gathering.

One approximation would be a relaxation of the ant indicator function to a basis of wavelet-like vectors (for example diffusion kernels) on the graph of connected land squares. (The basis vectors should overlap smoothly, because under a rigorous relaxation, non-overlapping basis vectors would allow approximated ants to teleport across the support of basis elements.)