In this paper, we present a multiobjective ant colony optimization (MOACO) algorithm, called CHAC, designed to solve the problem of finding the path for a military unit that minimizes the cost in resources while maximizing safety. Unlike previous MOACO algorithms, CHAC uses a single colony and two different state transition rules: One that combines the heuristic and pheromone information of both objectives and another based on the dominance concept of multiobjective optimization problems. These rules have been evaluated in different scenarios (maps with different degrees of difficulty), outperforming a greedy algorithm (taken as baseline), and yielding a good military behavior in the tactical sense. In comparison, the combined rule is slightly better than the rule based on dominance.