In this study, we consider a combinatorial optimization problem that arises in plant breeding that involves selecting parent plants for crossing based on their genomic characteristics. We wish to ensure that individuals with the most desirable genomic characteristics are selected to increase the likelihood that desirable genetic materials will be passed on to the progeny. Unlike most of the approaches that use phenotypic values for parental selection and evaluate individuals separately, we use a criterion that relies on population genotypic information and evaluates the combination of a pair of individuals. Thus, we introduce the expected cross value (ECV) criterion that takes the vector of recombination frequencies between genes as an input and returns the expected number of desirable alleles for a gamete produced by two individuals of the population as selected parents. We use the ECV criterion to develop a mathematical optimization formulation for the parental selection problem. We target a single phenotypic trait for the genetic improvement program and optimally solving the mathematical formulation to find the best parental pair with maximum ECV. We propose a procedure to obtain multiple parental pairs by finding multiple pairs of (near) optimal solutions. Finally, we discuss how the ECV criterion can improve the genetic introgression process based on computational experiments.