The rate of genetic gain in wheat must be doubled over the next 2-3 decades to secure global food supply. Production trends in growing regions worldwide suggest that current wheat breeding strategies need to be improved in order to achieve this goal. One of the most critical steps in a wheat breeding program is to select parents for targeted crossing but strategies for decision support in this regard are not readily available. Conventionally, parents are selected based on their performance per se or their breeding value which limits the inference that can be made about the probability for maximising the number of favourable chromosome segments in the offspring of a given cross. This is particularly challenging when a combination of quantitative traits (yield) and mono- or oligogenic traits (e.g. disease resistance, quality) are considered in parallel. This problem is well suited to evolutionary computation approaches, where algorithms inspired by biological evolution, such as reproduction, mutation, recombination, and selection are employed to find solutions to complex problems. In this ongoing study, we use evolutionary computing in a large commercial data set comprising more than 34,000 genotyped breeding lines which have been tested over multiple years and locations across Australia. The algorithms used predict optimal crosses that most efficiently stack complementary alleles important for quality, disease resistance and yield. Generated offspring from those crosses is advanced through “speed breeding” which allows an ultra-fast turnaround of several generations and breeding cycles per year. Finally, these approaches will be compared for efficiency with alternative breeding strategies, such as standard genomic selection and phenotypic selection.