This paper presents a novel approach to the robust design of deflection actions for Near Earth Objects (NEO). In particular, the case of deflection by means of Solar-pumped Laser ablation is studied here in detail. The basic idea behind Laser ablation is that of inducing a sublimation of the NEO surface, which produces a low thrust thereby slowly deviating the asteroid from its initial Earth threatening trajectory. This work investigates the integrated design of the Space-based Laser system and the deflection action generated by laser ablation under uncertainty. The integrated design is formulated as a multi-objective optimisation problem in which the deviation is maximised and the total system mass is minimised. Both the model for the estimation of the thrust produced by surface laser ablation and the spacecraft system model are assumed to be affected by epistemic uncertainties (partial or complete lack of knowledge). Evidence Theory is used to quantify these uncertainties and introduce them in the optimisation process. The propagation of the trajectory of the NEO under the laser-ablation action is performed with a novel approach based on an approximated analytical solution of Gauss' Variational Equations. An example of design of the deflection of asteroid Apophis with a swarm of spacecraft is presented.