We present in this work a wide spectrum of results on analyzing the behavior of parallel heuristics for solving optimization problems. We focus on evolutionary algorithms as well as on simulated annealing. Our goal is to offer a first study on the possible changes in the search mechanics when shifting from a LAN distributed algorithm to a WAN environment. We will address six optimization tasks of considerable complexity. The results show that, despite the expected slower execution time, the WAN versions of our algorithms consistently solve the problems. We even report some interesting results in which WAN algorithms outperform LAN ones. We also extend the study to include hybrid versions to check the scope of our conclusions.