A Direct Multisearch Filter Method for Biobjective Optimization
Published in EUROPT 2022 - Workshop on Advances in Continuous Optimization, 2022
EUROPT 2022 - Workshop on Advances in Continuous Optimization
NOVA University of Lisbon, NOVA School for Science and Technology More information here
A Direct Multisearch Filter Method for Biobjective Optimization
Abstract: In practical applications, it is common to have several conflicting objective functions to optimize. Frequently, these functions are of black-box type, preventing the use of multiobjective derivative-based optimization techniques. Direct Multisearch (DMS) is a multiobjective derivative-free optimization class of methods, with a well-established convergence analysis and competitive computational implementations, often successfully used for benchmark of new algorithms and in practical applications. From the theoretical point of view, DMS is developed for Lipschitz continuous optimization with general constraints, making use of an extreme barrier approach, only evaluating feasible points. In this work, we propose the integration of a filter approach in DMS, to address biobjective optimization problems with linear and nonlinear constraints. The linear constraints are explicitly treated by the algorithm, by adapting the positive generating sets considered at each iteration to the geometry of the nearby constraints. The violations of the nonlinear constraints are aggregated in a third objective function and are treated as an additional objective to be minimized. We will describe the proposed algorithmic structure in detail, provide results on the theoretical properties of the method, and report numerical experiments that state the good performance of this approach to address nonlinear constraints.
Key words: Derivative-free Optimization, Multiobjective Optimization, Constrained Optimization, Direct Multisearch, Filter methods
Joint work with Ana L. Custódio
Acknowledgments: This research was financially supported by Fundação para a Ciência e a Tecnologia (FCT) (Portuguese Foundation for Science and Technology) through projects UIDB/00297/2020,UIDP/00297/2020, UI/BD/151246/2021 (Centro de Matemática e Aplicações - NOVA Math), and PTDC/MAT-APL/28400/2017 (NOVA Math).