A multi-objective optimisation evolutionary approach for the Multidimensional Scaling Problem

The Multidimensional Scaling (MDS) strategies allow visualising the similarity between different objects reducing the number of dimensions. MDS has been widely used to perform exploratory analyses in different fields of the knowledge. The current strategies designed to deal with the MDS problem are able to consider exclusively one measure in a same time, however, most of the real-life problems usually require to analyse more than one measure simultaneously. The multi-objective optimisation techniques have been successfully used to deal with in problems from different areas considering multiples criteria (two or three criteria). In this work, we propose a genetic algorithm to deal with the multi-objective MDS problem being evaluated by using classical data sets from the related literature. The results show that the proposed strategy is able to identify a Pareto set of solutions that include new representations which were non-dominated by solutions from the current state of the art single-objective optimisation approaches, and new solutions which combine the features of the different inputs. These results make our proposal a real alternative to deal with problems which require to visualise different similarity inputs.