This paper considers a non-preemptive open shop scheduling problem (OSSP), in which machines are not available to process jobs on known periodic interval times resulted from periodic service repair, rest period, and so on. Asymmetric transportation time between machines is considered, which can be different from one job to another. The objective is to minimize the weighted mean completion time (WMCT). Since the problem is categorized into NP-hard class, two meta-heuristic algorithms including genetic algorithm (GA) and differential evolution (DE) are proposed. Meanwhile, a new initial population is introduced, which significantly improves the performance of the algorithms. Finally, the performance of the algorithms is validated through some large-sized instances and the results are discussed.