Modern web services rely on Content Delivery Networks (CDNs) to efficiently deliver contents to end users. In order to minimize the experienced communication cost, it is necessary to send the end user's requests to the nearest servers. However, it is shown that this naive method causes some servers to get overloaded. Similarly, when distributing the requests to avoid overloading, the communication cost increases. This is a well-known trade-off between communication cost and load balancing in CDNs. In this work, by introducing a new meta-heuristic algorithm, we try to optimize this trade-off, that is, to have less-loaded servers at lower experienced communication cost. This trade-off is even better managed when we optimize the way servers update their information of each others' load. The proposed scheme, which is based on Honeybee algorithm, is an implementation of bees algorithm which is known for solving continuous optimization problems. Our proposed version for CDNs is a combination of a request redirecting method and a server information update algorithm. To evaluate the suggested method in a large-scale network, we leveraged our newly developed CDN simulator which takes into account all the important network parameters in the scope of our problem. The simulation results show that our proposed scheme achieves a better trade-off between the communication cost and load balancing in CDNs, compared to previously proposed schemes.