Submarine search-evasion path planning aims to acquire an evading route for a submarine so as to avoid the detection of hostile anti-submarine searchers such as helicopters, aircraft and surface ships. In this paper, we propose a numerical optimization model of search-evasion path planning for invading submarines. We use the Artificial Bee Colony (ABC) algorithm, which has been confirmed to be competitive compared to many other nature-inspired algorithms, to solve this numerical optimization problem. In this work, several search-evasion cases in the two-dimensional plane have been carefully studied, in which the anti-submarine vehicles are equipped with sensors with circular footprints that allow them to detect invading submarines within certain radii. An invading submarine is assumed to be able to acquire the real-time locations of all the anti-submarine searchers in the combat field. Our simulation results show the efficacy of our proposed dynamic route optimization model for the submarine search-evasion path planning mission.