We investigated the effectiveness of mate allocation strategies accounting for non-additive genetic effects to improve crossbred performance in a two-way crossbreeding scheme. We did this by computer simulation of 10 generations of evaluation and selection. QTL effects were simulated as correlated across purebreds and crossbreds, and (positive) heterosis was simulated as directional dominance. The purebred-crossbred correlation was 0.30 or 0.68 depending on the genetic variance component used. Dominance and additive marker effects were estimated simultaneously for purebreds and crossbreds by multiple trait genomic BLUP. Four scenarios that differ in the sources of information (only purebred data, or purebred and crossbred data) and mate allocation strategies (mating at random, minimizing expected future inbreeding, or maximizing the expected total genetic value of crossbred animals) were evaluated under different cases of genetic variance components. Selecting purebred animals for purebred performance yielded a response of 0.2 genetic standard deviations of the trait "crossbred performance" per generation, whereas selecting purebred animals for crossbred performance doubled the genetic response. Mate allocation strategy to maximize the expected total genetic value of crossbred descendants resulted in a slight increase (0.8%, 4% and 0.5% depending on the genetic variance components) of the crossbred performance. Purebred populations increased homozygosity, but the heterozygosity of the crossbreds remained constant. When purebred-crossbred genetic correlation is low, selecting purebred animals for crossbred performance using crossbred information is a more efficient strategy to exploit heterosis and increase performance at the crossbred commercial level, whereas mate allocation did not improve crossbred performance.