We present an algorithm that computes a minimal-cost pursuer trajectory for a single pursuer to solve the visibility-based pursuit-evasion problem in a simply-connected two dimensional environment. This algorithm improves upon the known algorithm of Guibas, Latombe, LaValle, Lin, and Motwani, which is complete but not optimal. Our algorithm uses a Tour of Segments (ToS) subroutine to construct a pursuer path that minimizes the distance traveled by the pursuer while guaranteeing that all evaders in the environment will be captured. We have implemented our algorithm in simulation and provide results.