Understanding genomic structural variation such as inversions and translocations is a key challenge in evolutionary genetics. We develop a novel statistical approach to comparative genetic mapping to detect large-scale structural mutations from low-level sequencing data. The procedure, called Genome Order Optimization by Genetic Algorithm (GOOGA), couples a Hidden Markov Model with a Genetic Algorithm to analyze data from genetic mapping populations. We demonstrate the method using both simulated data (calibrated from experiments on Drosophila melanogaster) and real data from five distinct crosses within the flowering plant genus Mimulus. Application of GOOGA to the Mimulus data corrects numerous errors (misplaced sequences) in the M. guttatus reference genome and confirms or detects eight large inversions polymorphic within the species complex. Finally, we show how this method can be applied in genomic scans to improve the accuracy and resolution of Quantitative Trait Locus (QTL) mapping.