In many engineering problems, including those related to robotics, optimization of the control policy for multiple conflicting criteria is required. However, this can be very challenging because of the existence of noise, which may be input dependent or heteroscedastic, and restrictions regarding the number of evaluations owing to the costliness of the experiments in terms of time and/or money. This paper presents a multiobjective optimization algorithm for expensive-to-evaluate noisy functions for robotics. We present a method for model selection between heteroscedastic and standard homoscedastic Gaussian process regression techniques to create suitable surrogate functions from noisy samples, and to find the point to be observed at the next step. This algorithm is compared against an existing multiobjective optimization algorithm, and then used to optimize the speed and head stability of the sidewinding gait of a snake robot.