Effective logistics distribution paths are crucial in enhancing the fundamental competitiveness of an enterprise. This research introduces the genetic algorithm for logistics routing to address pertinent research issues, such as suboptimal scheduling of time-sensitive orders and reverse distribution of goods. It proposes an enhanced scheme integrating the Metropolis criterion. To address the limited local search ability of the genetic algorithm, this study combines the simulated annealing algorithm’s powerful local optimization capability with the genetic algorithm, thereby developing a genetic algorithm with the Metropolis criterion. The proposed method preserves the optimal chromosome in each generation population and accepts inferior chromosomes with a certain probability, thereby enhancing the likelihood of finding an optimal local solution and achieving global optimization. A comparative study is conducted with the Ant Colony Optimization, Artificial Bee Colony, and Particle Swarm Optimization algorithms, and empirical findings demonstrate that the proposed genetic algorithm effectively achieves excellent results over these algorithms.