A Mathematical Programming Approach to Marker-Assisted Gene Pyramiding

In the crossing schedule optimization problem we are given an initial set of parental genotypes and a desired genotype, the ideotype. The task is to schedule crossings of individuals such that the number of generations, the number of crossings, and the required populations size are minimized. We present for the first time a mathematical model for the general problem variant and show that the problem is NP-hard and even hard to approximate. On the positive side, we present a mixed integer programming formulation that exploits the intrinsic combinatorial structure of the problem. We are able to solve a real-world instance to provable optimality in less than 2 seconds, which was not possible with earlier methods.

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