This paper proposes an Integer Linear Programming optimization approach for the allocation of fault-tolerant embedded software applications that are developed using the AUTOSAR standard. The allocation takes into account the timing and reliability requirements of the multi-rate cause-effect chains in these applications and the heterogeneity of their execution platforms. The optimization objective is to minimize the total power consumption of the these applications that are distributed over more than one computing unit. The proposed approach is evaluated using a range of different software applications from the automotive domain, which are generated using the real-world automotive benchmark. The evaluation results indicate that the proposed allocation approach is effective and scalable while meeting the timing, reliability and power requirements in small- and medium-sized automotive software applications.