This paper addresses the tradeoff problem between hit ratio and content quality in edge caching systems for multiuser adaptive bitrate streaming (ABS) services. A dynamic policy for cache decision and quality level selection for each ABS content during every cache cycle is proposed. Achieving this policy is NP-complete. For this, the considered problem is transformed into a nested multidimensional 0/1 knapsack optimization problem which is then resolved by a cooperative transfer learning-accelerated genetic algorithm. Performance evaluation demonstrates an adaptation of the proposed algorithm on various video stream popularity models in terms of algorithmic convergence and cache balancing.