In this paper we address scheduling of the permutation flow shop with minimization of makespan and total flow time as the objectives. We propose a memetic algorithm (MA) to search for the set of non-dominated solutions (the Pareto optimal solutions). The proposed MA adopts the permutation-based encoding and the fitness assignment mechanism of NSGA-II. The main feature is the introduction of an NEH-based neighborhood function into the local search procedure. We also adjust the size of the neighborhood dynamically during the execution of the MA to strike a balance between exploration and exploitation. Forty public benchmark problem instances are used to compare the performance of our MA with that of twenty-seven existing algorithms. Our MA provides close performance for small-scale instances and much better performance for large-scale instances. It also updates more than 90% of the net set of non-dominated solutions for the large-scale instances.