In this paper we assess and compare the effectiveness of four classes of non-nuclear asteroid deflection methods applied to a wide range of virtual collision scenarios. We consider the kinetic impactor, laser ablation, the ion beaming technique and two variants of the gravity tractor. A simple but realistic model of each deflection method was integrated within a systematic approach to size the spacecraft and predict the achievable deflection for a given mission and a given maximum mass at launch. A sample of 100 synthetic asteroids was then created from the current distribution of NEAs and global optimisation methods were used to identify the optimal solution in each case according to two criteria: the minimum duration between the departure date and the time of virtual impact required to deflect the NEA by more than two Earth radii and the maximum miss-distance achieved within a total duration of 10 years. Our results provide an interesting insight into the range of applicability of individual deflection methods and argue the need to develop multiple methods in parallel for a global mitigation of all possible threats.