The next decade will see an unprecedented growth in space activity and usher in a new era in space. Together commercial parties, the so-called NewSpace operators, have announced large constellations that will increase the number of satellites in Low Earth Orbit from almost 2,000 satellites to 20,000. Simultaneously, enhanced space object tracking capabilities are expected to increase the number of tracked objects from 23,000 to 100,000. These developments will lead to a strong increase in dangerous conjunction events and the required number of collision avoidance maneuvers as well as more complex conjunction geometries for satellites in Low Earth Orbit. This research proposes a new approach to collision avoidance maneuver planning that produces a set of maneuvers to reduce the collision probability to an acceptable level for complex conjunction geometries without requiring human interpretation beforehand. The approach combines an accurate numerical propagation procedure to take advantage of the small position uncertainties of the Conjunction Data Messages published by the Combined Space Operations Center with a multi-objective optimisation procedure to avoid having to assign relative importance to optimisation objectives beforehand. The approach is tested against four different conjunction scenarios ranging from two objects to involving four objects proving that it efficiently finds solutions for future complex conjunction geometries. It is shown that the new approach finds the global optima in the objective space spawned by collision probability. Applying an intrack maneuver is the most propellant-efficient method for reducing collision probability. In contrast to most contemporary research, this research finds that additional radial and crosstrack maneuver components can offer a significant decrease in collision probability. The quality of the product of many NewSpace operators depends on the service level that is offered: the maximum interval between two satellite visits. Intrack maneuvers significantly change the orbital period and negatively impact the service level. This research investigates extending the problem definition by introducing constellation performance loss as a third optimisation objective. Extending the objective space by an additional dimension increases the required computational effort, but provides an interesting new perspective on the true optimality of maneuvers. The approach uncovers the three-dimensional Pareto front at the expense of 7,875 function evaluations showing both a set of solutions that are propellant-efficient, which were mentioned earlier, as well as a set of solutions that inflict little constellation performance loss. The latter set of solutions has a large radial or crosstrack component and almost no intrack component. It affirms the finding that large radial and crosstrack maneuver components can offer promising solutions for collision avoidance maneuvers. As an alternative for reducing constellation performance loss, this work investigated the application of a second maneuver after the dangerous conjunction situation had passed to restore the original orbit. This concept can offer benefits for simple conjunction geometries, but is infeasible for complex geometries where a large amount of propellant is required to reduce the collision probability. It was also proven that errors in the actuators can cause significant deterioration in the resulting collision probability and constellation performance loss.