Otimização multi-objetivo envolvendo aproximadores de função via processos gaussianos e algoritmos híbridos que empregam otimização direta do hipervolume

Author(s)

Conrado Silva Miranda

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação
• Defense date: 2018-04-27

Examining board members

Fernando José Von Zuben; Felipe Campelo Franca Pinto; Myriam Regattieri De Biase da Silva Delgado; Romis Ribeiro de Faissol Attux; Guilherme Palermo Coelho

• Advisor: Fernando José Von Zuben

Abstract

The main purpose of this thesis is to bridge the gap between single-objective and multi- objective optimization and to show that connecting techniques from both ends can lead to improved results. To reach this goal, we provide contributions in three directions. First, we show the connection between optimality of a mean loss and the hypervolume when evaluating a single solution, proving optimality bounds when the solution from one is applied to the other. Furthermore, an evaluation of the gradient of the hypervolume shows that it can be interpreted as a particular case of the weighted mean loss, where the weights increase as their associated losses increases. We hypothesize that this can help to train a machine learning model, since samples with high error will also have high weight. An experiment with a neural network validates the hypothesis, showing improved performance. Second, we evaluate previous attempts at using gradient-based hypervolume optimization to solve multi-objective problems and why they have failed. Based on the analysis, we propose a hybrid algorithm that combines gradient-based and evolutionary optimization. Experiments on the benchmark functions ZDT show improved performance and faster convergence compared with reference evolutionary algorithms. Finally, we prove necessary and sufficient conditions for a function to describe a valid Pareto frontier. Based on this result, we adapt a Gaussian process to penalize violation of the conditions and show that it provides better estimates than other approximation algorithms. In particular, it creates a curve that does not violate the constraints as much as done by algorithms that do not consider the restrictions, being a more reliable performance indicator. We also show that a common optimization metric when approximating functions with Gaussian processes is a good indicator of the regions an algorithm should explore to find the Pareto frontier (AU)

• FAPESP's process: 15/09199-0 - Multi-Objective Optimization Involving Function Approximation via Gaussian Processes and Hybrid Algorithms that Employ Direct Hypervolume Otimization
• Grantee: Conrado Silva Miranda
• Support Opportunities: Scholarships in Brazil - Doctorate