Evacuation path optimization (EPO) is a crucial problem in crowd and disaster management. With the consideration of dynamic evacuee velocity, the EPO problem becomes nondeterministic polynomial-time hard (NP-Hard). Furthermore, since not only one single evacuation path but multiple mutually restricted paths should be found, the crowd evacuation problem becomes even challenging in both solution spatial encoding and optimal solution searching. To address the above challenges, this article puts forward an ant colony evacuation planner (ACEP) with a novel solution construction strategy and an incremental flow assignment (IFA) method. First, different from the traditional ant algorithms, where each ant builds a complete solution independently, ACEP uses the entire colony of ants to simulate the behavior of the crowd during evacuation. In this way, the colony of ants works cooperatively to find a set of evacuation paths simultaneously and thus multiple evacuation paths can be found effectively. Second, in order to reduce the execution time of ACEP, an IFA method is introduced, in which fractions of evacuees are assigned step by step, to imitate the group-based evacuation process in the real world so that the efficiency of ACEP can be further improved. Numerical experiments are conducted on a set of networks with different sizes. The experimental results demonstrate that ACEP is promising.