The most common approach for solving the problem of optimal task scheduling is to use expected values of the variables that the function to be optimized depends on, e.g., execution time or energy consumption, in which case we refer to the problem as the deterministic scheduling. However, the execution time of a task in reality can vary considerably, due to a number of reasons, e.g., unknown memory access time, operating system effects that cannot be known in advance, etc. For this reason, it is more accurate to treat execution time, as well as energy consumption, which is closely related, as a random variable with a corresponding probability density and/or cumulative distribution function. We refer to this group of problems as stochastic scheduling problems. The state of the art results of optimal scheduling for makespan optimization prove that in certain situations the deterministic scheduler provides results that significantly deviate from the optimal ones, and that better results can be obtained using stochastic scheduling. In our work we have proven that this is also the case for energy consumption optimization. Our objective is to optimize the energy consumption through scheduling and allocation of a set of tasks running on multiprocessor/multicore and multithreaded voltage and frequency scalable architectures designed by XMOS. In the work carried out so far we have assumed that the execution time and energy consumption of different tasks are independent. However, in reality these values are usually dependent. For this reason, we are currently studying a particular way to model dependence based on copula theory. In this talk we will present the designed scheduler based on multiobjective evolutionary algorithm and also give a short introduction to copula theory and mention the results obtained so far.