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Multi-hop broadcast is an important component in ad-hoc wireless networks. Some vehicular network (VANET) applications in particular use broadcast communications extensively. We propose using the distance-to-mean method to facilitate these applications. The performance of this method depends heavily on the value of the decision threshold, and it is difficult to choose a value for that threshold that results in good performance across a wide range of network scenarios. Node density, spatial distribution pattern, and wireless channel conditions all affect the optimal statistical threshold value. VANETs exhibit wide ranges of these factors, so protocols designed to support these applications must be adaptive to those variations. In this work we address this design challenge by using black-box optimization algorithms based on machine learning techniques such as genetic algorithms and particle swarm optimization to automatically discover a decision threshold value for the distance-to-mean method that is simultaneously adaptive to node density, node distribution pattern, and channel quality. The resulting decision surface is a function of the number of neighbors N, the quadrat statistic Q, and the Rician fading parameter K. The result is the Statistical Location-Assisted Broadcast (SLAB) protocol. Evaluations using JiST/SWANS show SLAB achieves high reachability and efficient bandwidth consumption in both urban and highway scenarios with varying node density.