Partial Ranking Models by Genetic Algorithms Variable Subset Selection (GA-VSS) approach for environmental priority settings

Partial order ranking (POR) strategies, which from a mathematical point of view are based on elementary methods of Discrete Mathematics, appear as an attractive and simple tool to perform 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, being a possible alternative to conventional QSAR methods. In fact, when data material is characterised by uncertainties, order methods can be used as alternative to statistical methods such as multi-linear regression (MLR), since they do not require specific functional relationship between the independent variables and the 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 variables. As in regression and classification models the variable selection is one of the main steps to find predictive models. In the present work, the Genetic Algorithm (GA-VSS) approach is proposed as the variable selection method to search for the best ranking models within a wide set of variables. The ranking models based on the selected subsets of variables are compared with the experimental ranking and evaluated by a set of similarity indices. A case study application is presented on a partial order ranking model developed for 23 chemicals selected as active ingredients used in agricultural practice and analysed according to their toxicity on Scenedesmus vacuolatus.