Linear Ordering Problem (LOP) is a well know optimization problem attractive for its complexity (it is a NPhard problem), rich collection of testing data and variety of real world applications. In this paper, we investigate the usage and performance of two variants of Genetic Algorithms - Mutation Only Genetic Algorithms and Higher Level Chromosome Genetic Algorithms - on the Linear Ordering Problem. Both methods are tested and evaluated on a collection of real world and artificial LOP instances.