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We consider the optimal downlink MISO scheduling design framework for a general class of convex utility functions. The access point or base station is equipped with nT transmit antennas. There are K mobiles in the system with single receive antenna. For practical reasons, we constraint the physical/link layer of the base station and mobile devices to linear processing complexity in signal transmission/reception respectively. We shall apply the design framework to two common utility functions, namely the maximum throughput and the proportional fair. The scheduling problem is a mixed nonlinear integer programming problem and therefore, the complexity of the optimal solution is enormous. Greedy algorithms is widely used in today's wireless data systems (3GIX, HDR, UMTS) and is optimal when nT = 1. However, we found that there is a large performance penalty of greedy algorithms (relative to optimal performance) when nT > 1 and this motivates the search for more efficient heuristics. In this paper, we address genetic-based heuristics and discuss their complexity-performance tradeoff.