Latent variable analysis (LVA) often relies on a mono-objective formulation exploiting a given property of the desired information. For example, in classical blind source separation, most algorithms make use of a single separation criterion associated with a given property of the sources. However, in many practical situations, there is more than one property to be exploited and, as a consequence, a set of separation criteria may be used to recover the original signals. In this context, we consider an approach to deal with the separation problem based on multi-objective optimization. Such an approach provides the user a set of non-dominated solutions from which she can select one, for instance, according to prior knowledge on the problem. In order to verify the application of the proposed framework, we provided numerical experiments by considering both synthetic data and actual data acquired by chemical sensors. In a second application, we also introduce a multiobjective formulation of principal component analysis which can be used, for instance, in the context of fairness-aware machine learning.