Iterated local search (ILS) is a powerful framework for developing efficient algorithms for the permutation flow-shop problem (PFSP). These algorithms are relatively simple to implement and use very few parameters, which facilitates the associated fine-tuning process. Therefore, they constitute an attractive solution for real-life applications. In this paper, we discuss some parallelization, parametrization, and randomization issues related to ILS-based algorithms for solving the PFSP. In particular, the following research questions are analyzed: (a) Is it possible to simplify even more the parameter setting in an ILS framework without affecting performance? (b) How do parallelized versions of these algorithms behave as we simultaneously vary the number of different runs and the computation time? (c) For a parallelized version of these algorithms, is it worthwhile to randomize the initial solution so that different starting points are considered? (d) Are these algorithms affected by the use of a “good-quality” pseudorandom number generator? In this paper, we introduce the new ILS-ESP (where ESP is efficient, simple, and parallelizable) algorithm that is specifically designed to take advantage of parallel computing, allowing us to obtain competitive results in “real time” for all tested instances. The ILS-ESP also uses “natural” parameters, which simplifies the calibration process. An extensive set of computational experiments has been carried out in order to answer the aforementioned research questions.