Global Optimality Integral Conditions and an Algorithm for Multiobjective Problems
Published in DFOS - Derivative-Free Optimization: Linking Algorithms and Applications, 2022
DFOS - Derivative-Free Optimization: Linking Algorithms and Applications
University of British Columbia Okanagan (UBCO), Canada
Global Optimality Integral Conditions and an Algorithm for Multiobjective Problems
Abstract: In this work, we propose global optimality integral conditions for multiobjective problems, not necessarily differentiable. The integral characterization, already known for single objective optimization problems, is extended to multiobjective optimization, by the weighted sum and the Chebyshev weighted scalarizations. Using this last scalarization, we propose an algorithm for obtaining an approximation to the weak Pareto front, whose effectiveness is illustrated by solving a collection of multiobjective test problems.
Key words: Multiobjective optimization, Pareto front, Weighted sum scalarization, Chebyshev weighted scalarization, Global optimality integral conditions.
Joint work with Elizath W. Karas and Lucelina B. Santos
Acknowledgments: This work was partially supported by CAPES - Brazil and Fundação para a Ciência e a Tecnologia (FCT) through the projects PTDC/MAT-APL/28400/2017, UI/BD/151246/2021, UIDB/00297/2020 and UIDP/00297/2020 (NOVA Math), Portugal.