The Progressive Edge Growth (PEG) algorithm is one of the most widely-used methods for constructing fi nite length LDPC codes. In this paper we consider the PEG algorithm together with a scheduling distribution, which specifi es the order in which edges are established in the graph. The goal is to find a scheduling distribution that yields "the best" performance in terms of decoding overhead, performance metric speci c to erasure codes and widely used for upper-layer forward error correction (UL-FEC). We rigorously formulate this optimization problem, and we show that it can be addressed by using genetic optimization algorithms. We also exhibit PEG codes with optimized scheduling distribution, whose decoding overhead is less than half of the decoding overhead of their classical-PEG counterparts.