Evolutionary algorithms are one of the most popular forms of optimization algorithms. They are comparatively easy to use and were successfully employed for a wide variety of practical applications. However, frequently, it is necessary to execute them in parallel in order to reduce the runtime. There are a number of different approaches for the parallelization of evolutionary algorithms, and various hardware platforms can be used for the parallel execution. However, not every platform is equally suitable for any kind of parallelization of evolutionary algorithms. In addition, it also depends on properties of the concrete optimization problem to be solved and on the used evolutionary algorithm, which platform is best suited for the execution. The present work observes this in detail for two common forms of parallelization of evolutionary algorithms - the island model and the global parallelization - and for four widely used parallel computing platforms - multi-core CPUs, clusters, graphics cards, and grids. Based on empirical and analytical investigations, it is determined, under which circumstances an architecture is better suited for the execution of a parallel evolutionary algorithm than another (and vice versa). Guidelines are derived that support users of parallel evolutionary algorithms with the choice of an appropriate platform. Copyright (c) 2016 John Wiley & Sons, Ltd.