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Multiple-input-multiple-output (MIMO) systems are of interest for meeting the expected demand for higher data rates and lower delays in future wireless packet data systems. In such systems, it is optimal to simultaneously transmit to multiple users compared with a single user in a single-input-single-output system. In addition, multicarrier systems are of interest to combat frequency-selective fading that is experienced over the larger bandwidth that these future broadband systems will use. The use of dirty paper coding further complicates the matter, because the order in which the users are encoded will affect the rates that they can achieve. A well-designed cross-layer scheduling algorithm must take into account the multiple dimensions of this resource-allocation problem and other quality-of-service (QoS) parameters to fully exploit the communications channel. The scheduling problem is often expressed in terms of optimizing some utility function. Unfortunately, the search space for this optimization problem is extremely large, which prohibits an optimal exhaustive search. To this end, we investigate the use of genetic algorithms to reduce the complexity of the scheduling. This paper builds upon prior work that implements scheduling via genetic algorithms in the context of single-carrier systems using zero-forcing beamforming (ZFB). In this paper, we investigate how the genetic algorithm can be adapted to account for the effect of encoding order on the scheduling and how the scheduling can be extended to a multicarrier system. In particular, we investigate the maximum throughput and proportionally fair scheduling criteria. We demonstrate that the performance of the genetic algorithm is near optimal compared with an exhaustive search at a greatly reduced computational complexity. Furthermore, in the case of a multicarrier orthogonal frequency-division multiplexing (OFDM) system, an increase in capacity is shown relative to the single-carrier case.