HyperText Transfer Protocol (HTTP) Adaptive Streaming (HAS) has become the de facto standard video-streaming technology. The benefits of HAS are manifold: reliable transmission of video data avoiding artifacts caused by packet loss, easy fire wall, and Network Address Translation (NAT) traversal and the seamless reuse of existing HTTP caching infrastructure. However, introducing transparent, intermediary caching nodes on the delivery path can impact the Quality of Experience (QoE) perceived by the end user. In cache-assisted HAS, segments can be served from different origins based on the content of the caches, causing highly fluctuating throughput and Round-Trip Time (RTT) measurements, negatively impacting the stability and optimality of the quality decisions due to incorrect throughput estimations. In this paper, we propose heuristics that are able to use information on the streaming origin and intermediary cache contents to optimize the quality selection process. Using more accurate per origin throughput measurements, buffer starvations can be avoided. Moreover, including the cache state information in the decision process can positively impact the streaming quality. Furthermore, approximation techniques based on unsupervised incremental clustering are proposed to detect the streaming origin in absence of an external information channel. Similarly, a cache probability-based heuristic is proposed to predict the content of the expected delivery location when this information is not transferred. With perfect information, the proposed heuristics improve the QoE with 0.52 on a scale between 1 and 5, while the approximation techniques result in a performance gain between 0.04 and 0.36 for a dynamic scenario and a reduction of buffer starvations with a factor 3 to 7.