This paper compares and analyzes four heuristic algorithms for collision avoidance maneuver optimization (CAMO) when multiple space objects threaten a satellite. Classical gradient-based optimization methods are not appropriate for this kind of problem due to their discontinuities. On the other hand, heuristic algorithms can obtain suboptimal solutions due to their robustness and flexibility. In this paper, we develop CAMO planning methods using four heuristic algorithms. Their performance is compared in terms of the Del-V achieved under constraints on the minimum distance between the user satellite and multiple threatening objects, the maximum burn duration, and the boundary conditions for the maneuver start time. To validate the proposed strategy with the heuristic algorithms, two CAMO problems are analyzed. One is a simple problem using two control parameters (the maneuver start time and Del-V along the in-track direction) when a single threatening object is approaching. The second is a more complex CAMO problem that uses four control parameters (the maneuver start time and Del-V in three directions, i.e. radial, in-track, and cross-track) when four threatening objects are approaching from different angles and at different times. As a result, we minimize Del-V for each CAMO problem while satisfying all constraints. The differential evolution heuristic algorithm is found to exhibit the best performance in terms of minimized Del-V.