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A computational method for implementation of evolution strategies (ES) in grid computing environments is discussed. In this paper, list scheduling with round-robin order replication (RR) is adopted to reduce waiting times due to synchronization in ES. However, RR is suitable for coarsegrained tasks. For ES as medium-grained tasks, we propose a new technique to reduce the communication overhead, called the remote work queue (RWQ) method. We then define round- robin replication remote work queue (R3Q) as RWQ with RR. Our results show that R3Q can reduce both the synchronous waiting time and communication time, and provides efficient forced termination of tasks compared to other methods.