This paper deals with an industrial problem of machining line design, which consists in partitioning a given set of operations into several subsets corresponding to workstations and sequencing the operations to satisfy the technical requirements and achieve the best performance of the line. The problem has a complex set of constraints that include partial order on operations, part positioning, inclusion, exclusion, cycle time, and installation of parallel machines on a workstation. The problem is NP-hard and even finding a feasible solution can be a difficult task from the practical point of view. A parallel evolutionary algorithm (EA) is proposed and implemented for execution on a Graphics Processing Unit (GPU). The parallelization in the EA is done by working on several parents in one iteration and in multiple application of mutation operator to the same parent to produce the best offspring. The proposed approach is evaluated on large scale instances and demonstrated superior performance compared to the algorithms from the literature in terms of running time and ability to obtain feasible solutions. It is shown that in comparison to the traditional populational EA scheme the newly proposed algorithm is more suitable for advanced GPUs with a large number of cores.