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We present a framework for the robust optimization of the heat flux distribution for an anti-ice electro-thermal ice protection system (AI-ETIPS) and iced airfoil performance analysis under uncertain conditions. The considered uncertainty regards a lack of knowledge concerning the characteristics of the cloud i.e. the liquid water content and the median volume diameter of water droplets, and the accuracy of measuring devices i.e., the static temperature probe, uncertain parameters are modeled as uniform random variables. A forward uncertainty propagation analysis is carried out using a Monte Carlo approach. The optimization framework relies on a gradient-free algorithm (Mesh Adaptive Direct Search) and three different problem formulations are considered in this work. Two bi-objective deterministic optimizations aim to minimize power consumption and either minimize ice formations or the iced airfoil drag coefficient.