Multi-bitrate streaming, especially HTTP adaptive streaming (HAS), is becoming popular for video delivery in multimedia network. In this trend, a video is encoded into different versions with different quality levels. Based on the current conditions, a client can adaptively choose the most suitable encoded version. However, the adoption of HAS in managed network (e.g. IPTV) has many challenges because of the purely client-driven approach of current HAS which causes competing behavior, excessive quality oscillations, and thus negatively impacting quality of experience (QoE). Some recent studies have proposed network-based solutions to overcome these problems; however, they just target at constant bitrate (CBR) videos. In this paper, we propose a new method that allows components inside the network to select an adapted version for each HAS client. To the best of our knowledge, this is the first study on the quality optimization when streaming multiple variable bitrate (VBR) videos. The experimental result show that our method can provide in real-time the optimal version for each client with the best possible quality while meeting the constraints of overall bandwidth and delay.