Abstract
AbstractIn this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated via scalarization using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based multi-objective optimization method on the search space combined with an additional heuristic strategy to adapt parameters during the computations is proposed. The adaptive strategy aims to distribute the particles uniformly over the image space, in particular over the Pareto front, by using energy-based measures to quantify the diversity of the system. The resulting gradient-free metaheuristic algorithm is mathematically analyzed using a mean-field approximation of the algorithm iteration and convergence guarantees towards Pareto optimal points are rigorously proven. In addition, we analyze the dynamics when the Pareto front corresponds to the unit simplex, and show that the adaptive mechanism reduces to a gradient flow in this case. Several numerical experiments show the validity of the proposed stochastic particle dynamics, investigate the role of the algorithm parameters and validate the theoretical findings.
Funder
Ministero dell’Istruzione, dell’Università e della Ricerca
Deutsche Forschungsgemeinschaft
Germany’s Excellence Strategy EXC-2023
Banff International Research Station for Mathematical Innovation and Discovery
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Control and Optimization
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献