Scalable multi-objetive optimization

  1. Martí Orosa, Luis
Dirigée par:
  1. Antonio Berlanga de Jesús Directeur/trice
  2. José Manuel Molina López Directeur/trice

Université de défendre: Universidad Carlos III de Madrid

Fecha de defensa: 29 mars 2011

Jury:
  1. Pedro Isasi Viñuela President
  2. Jesús García Herrero Secrétaire
  3. Luis Miguel Parreira Correira Rapporteur
  4. Juan Luis Pavón Mestras Rapporteur
  5. Javier Bajo Pérez Rapporteur
  6. Pedro Larrañaga Múgica Rapporteur
  7. Francisco Javier Segovia Pérez Rapporteur

Type: Thèses

Résumé

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.