Cláudio’s Thesis Proposal
DOMINANCE MOVE: CONCEPT, ADVANCES AND APPLICATIONS IN MULTI- AND MANY-OBJECTIVE OPTIMIZATION PROBLEMS
Advisor: Flávio Vinícius Cruzeiro Martins
Co-Advisor: Elizabeth Fialho Wanner
EXAMINING BOARD:
Carlos M. Fonseca – University of Coimbra.
Ricardo H. C. Takarashi – UFMG
Elisangela Martins de Sá – CEFET-MG
Adriano Chaves Lisboa – CEFET-MG
May 25, 2021 – 10h – link
ABSTRACT:
Dominance move (DoM) is a concept that expresses an ‘effort’ that a solution set must employ to dominate or become another solution set. It can be used, for example, in a binary quality indicator in multi-objective and many-objective optimization, comparing two solution sets obtained from different algorithms. As the concept brings additional information, stated here as the new solution set generated by its calculation, this new information can be used in multiple other scenarios, which will be discussed here.
DoM as quality indicator can differentiate the sets for certain important features, such as convergence, spread, uniformity, and cardinality. Despite the aforementioned properties, DoM is hard to calculate, particularly in higher dimensions. There is an efficient and exact method to calculate it in a bi-objective case only. The first work’s contribution proposes novel approaches to calculate DoM using an assignment problem formulation and a mixed integer programming (MIP) approach, which can handle sets with three or more objectives. Some bi-objective space experiments are done to verify the model’s correctness. Furthermore, other experiments, using 3, 5, 10, 15, 20, 25, and 30-objective problems, are performed to show how the model behaves in higher-dimensional cases. Algorithms, such as IBEA, MOEA/D, NSGA-III, NSGA-II, and SPEA2 are used to generate the solution sets (however, any other algorithms can also be used with the proposed DoM indicator), and the results are discussed, showing the effectiveness of DoM in problems with over three objective functions.
The dominance move shows to overcome the epsilon-indicator’s information loss, not only as a quality indicator but as a concept. As said before, it can be employed not only as a quality indicator but also in multiple other situations. As our next steps, we are trying to use the dominance move to solve other relevant questions in multi- and many-objective optimization: I)It can be used as an accelerator operator in an evolutionary process, helping solutions with fast convergence in many-objective problems; II) we are trying to calculate DoM using an approximate approach using some machine learning ideas and the mixed-integer programming approach; III)it can be used in the selection operator and helps measure each individual’s contribution towards the convergence; and, IV)the extra information generated by DoM can be used as `direction’ in the objective space search.
In this sense, the work’s contribution tries to clarify the DoM utility, and how the concept can tackle many-objective problems and extend the Pareto Dominance relation. In general, our proposal involves present the dominance move as a suitable way to measure, compare, and use solution sets features in indicators and algorithms, showing scenarios that are benefited from its application.