Finite element-based crashworthiness optimization is extensively used to improve the safety of motor vehicles. However, the responses of crash simulations are characterized by a high level of numerical noise, which can hamper the blind use of surrogate-based design optimization methods. It is therefore essential to account for the noise-induced uncertainty when performing optimization. For this purpose, a surrogate, referred to as non-deterministic kriging (NDK), can be used. It models the noise as a non-stationary stochastic process, which is added to a traditional deterministic kriging surrogate. Based on the NDK surrogate, this study proposes an optimization algorithm tailored to account for both epistemic uncertainty, due to the lack of data, and irreducible aleatory uncertainty, due to the simulation noise. The variances are included within an extension of the well-known expected improvement infill criterion referred to as modified augmented expected improvement (MAEI). Because the proposed optimization scheme requires an estimate of the aleatory variance, it is approximated through a regression kriging, referred to as variance kriging, which is iteratively refined. The proposed algorithm is tested on a set of analytical functions and applied to the optimization of an occupant restraint system (ORS) during a crash.