Scalable multi-objetive optimization

Abstract

This thesis is mainly concerned with the two open in multi-objective optimization; that is, * the comprehension and solution of the model-building issues of current MOEDAs, and; * the formulation of stopping criteria for multi-objective optimizers. With regard to the first issue, 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, we: * sketch the supporting theoretical corpus and the fundamentals of MOEA and MOEDA algorithms; * analyze the scalability issue of MOEAs from both theoretical and experimental points of view; * discuss the possible directions of improvement for MOEAs' scalability, presenting the current trends of research; * give reasons of why EDAs can be used as a foundation for achieving a sizable improvement with regard to the scalability issue; * examine the model-building issue in depth, hypothesizing on how it affects MOEDAs performance, and; * propose 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; * propose a novel MOEDA, the multi-objective neural EDA, that is constructed on top of MB-GNG. Theoretical discussions and algorithm proposals are experimentally contrasted with current state-of-the-art approaches when required. 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 we: * provide an updated and exhaustive state-of-the-art of this matter; * examine the properties and characteristics that a given stopping criterion should exhibit; * put forward a new stopping criterion, denominated MGBM, after the authors last names, that has a small computational footprint, and; * we experimentally validate MGBM in a set of experiments.