This thesis is concerned with the three open in multi-objective optimization: (i) the development of strategies for dealing with problems with many objective functions; (ii) the comprehension and solution of the model-building issues of current MOEDAs, and; (iii) the formulation of stopping criteria for multi-objective optimizers. We argue about what elements of MOEDAs should be modified in order to achieve a substantial improvement on their performance and scalability. However, in order to supply a solid ground for that discussion, some other elements are to be discussed as well. In particular, this thesis: sketches the supporting theoretical corpus and the fundamentals of MOEA and MOEDA algorithms; analyzes the scalability issue of MOEAs from both theoretical and experimental points of view; discusses the possible directions of improvement for MOEAs’ scalability, presenting the current trends of research; gives reasons of why EDAs can be used as a foundation for achieving a sizable improvement with regard to the scalability issue; examines the model-building issue in depth, hypothesizing on how it affects MOEDAs performance; proposes a novel model-building algorithm, the model-building growing neural gas (MBGNG), which fulfill the requirements for a new approach derived from the previous debate, and; introduces a novel MOEDA, the multi-objective neural EDA, that is constructed using MB-GNG as foundation. The formulation of an strategy for stopping multi-objective optimizers became obvious and necessary as this thesis was developed. The lack of an adequate stopping criterion made the rendered any experimentation that had to do with many objectives a rather cumbersome task. That is why it was compulsory to deal with this issue in order to proceed with further studies. In this regard, the thesis: provides an updated and exhaustive state-of-the-art of this matter; examines the properties and characteristics that a given stopping criterion should exhibit; puts forward a new stopping criterion, denominated MGBM, after the authors last names, that has a small computational footprint, and; experimentally validates MGBM in a set of experiments. Theoretical discussions and algorithm proposals are experimentally contrasted with current state-of-the-art approaches when required.