Multi-Objective Optimization Involving Function Approximation via Gaussian Processes and Hybrid Algorithms that Employ Direct Hypervolume Otimization

• Grant number: 15/09199-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: January 01, 2016
• End date: July 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Fernando José von Zuben
• Grantee: Conrado Silva Miranda
• Host Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Hypervolume optimization and objective-function approximators have been receiving considerable highlight in multi-objective optimization (MOO), as they provide increase in performance both in reducing the number of objective evaluations and in quality of the obtained solution. This thesis aims to contribute in these two fronts, proposing hybrid solutions for hypervolume maximization, which seek to use explotative and explorative optimization approaches, and defining function approximators that are able to consider the multi-objetive nature of the problem.The hypervolume is an effective measure for performance evaluation, to the point that MOO can be described by a single-objective optimization (SOO) of the hypervolume. In SOO, gradient optimization methods may be able to provide locally optimal solutions using few computational resources, motivating its research in MOO, which is dominated by evolutionary algorithms. The hybrid algorithms to be proposed must aggregate the main advantages of the gradient methods and the evolutionary algorithms, trying to overcome some limitations already verified in the literature, such as the loss of efficiency of solutions that initially were efficient in methods using hypervolume gradient.Aiming at reducing the number of objective evaluations required, this project intends to use function approximatos. Predominates in the literature the direct use of traditional approximators in the multi-objective context. Thus, this research will try to improve the state of the art in using approximators in MOO, adapting or introducing techniques that take into account: (1) The necessary and sufficient conditions that efficient solutions must obey, whose formalization will also be a part of this research; and (2) The possible interdependencies of the objectives. Gaussian processes will be taken for the approximators synthesis, particularly for its ability of synthesis of functions that consider formally the items (1) and (2) mentioned.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MIRANDA, CONRADO S.; VON ZUBEN, FERNANDO J.. Necessary and Sufficient Conditions for Surrogate Functions of Pareto Frontiers and Their Synthesis Using Gaussian Processes. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, v. 21, n. 1, p. 1-13, FEB 2017. (15/09199-0)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

MIRANDA, Conrado Silva. Otimização multi-objetivo envolvendo aproximadores de função via processos gaussianos e algoritmos híbridos que empregam otimização direta do hipervolume. 2018. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação Campinas, SP.