Total order ranking (TOR) strategies, which are mathematically based on elementary methods of discrete mathematics, seem to be attractive and simple tools for performing data analysis. Moreover order-ranking strategies seem to be a very useful tool not only to perform data exploration but also to develop order ranking models, a possible alternative to conventional quantitative structure-activity relationship (QSAR) methods. In fact, when data material is characterised by uncertainties, order methods can be used as alternative to statistical methods such as multilinear regression (MLR), because they do not require specific functional relationships between the independent and dependent variables (responses). A ranking model is a relationship between a set of dependent attributes, experimentally investigated, and a set of independent attributes, i.e. model attributes, which are calculated attributes. As in regression and classification models, the variable selection model is one of the main steps in finding predictive models. In this work the genetic algorithm-variable subset selection (GA-VSS) approach is proposed as the variable selection method for searching for the best ranking models within a wide set of variables. The models based on the selected subsets of variables are compared with the experimental ranking and evaluated by the Spearman's rank index. A case study application is presented on a TOR model developed for polychlorinated biphenyl (PCB) compounds, which have been analysed according to some of their physicochemical properties which play an important role in their environmental impact.