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We address the problem of optimizing the delivery of multimedia services with different quality-of-service (QoS) requirements to mobile users. We assume that the network provides two distinct classes of service to which users may subscribe: Premium, or Economy. Subscribers to the Premium service pay more for their connections but receive a higher level of quality measured by a set of parameters such as call blocking probability, coding rate, and format of the multimedia services. By optimizing the delivery of the multimedia services, we mean that the network guarantees that all users receive their agreed-upon contractual level of quality, while maximizing the links' throughput, avoiding congestion, and maintaining the QoS requirements for each type of media (e.g., video, voice and data). Our proposed solution is based upon utilizing genetic algorithms to solve a multiobjective optimization function that adaptively selects the downloading bit-rate for each type of traffic flow subject to the constraints of the optimization function. A traffic flow is an abstract of aggregate traffic of the same type of media (e.g., voice, video, or data) that is downloaded to a group of users who share some common attribute such as the same class of service. The optimization function is adaptive in the sense that the selected downloading bit-rates are time-dependant according to the dynamics of the links' traffic-loads and users' requests. It is implemented on every output port of each node in the network. The function is used to control a filter that changes the coding rate of each media-type and, if necessary, performs transcoding of one, or more, media-types (i.e., video, voice, or data). Simulation results show significant improvement in terms of increasing the number of admitted users, while maintaining the QoS requirements, as well as target call blocking rates. An interesting result to report is that the performance improvement of the system (measured by the gain in the number of admitted users at a certain utilization factor) is not simply bounded by the maximum available link throughput. It is, rather, limited by the additional revenue gained by admitting more users. The increase in the revenue saturates at a certain offered traffic-load. Hence, it is not worth it,- from a service provider perspective, to admit additional users above this traffic load despite the fact that the filtering algorithm results indicate otherwise.