论文标题
基于自适应共识的多目标优化方法，具有均匀的帕累托前近似值
An adaptive consensus based method for multi-objective optimization with uniform Pareto front approximation
论文作者
论文摘要
在这项工作中，我们对多目标优化的随机粒子方法感兴趣。该问题是使用同时解决的参数化的单目标子问题来提出的。为此，提出了基于共识的多目标优化方法，结合了在计算过程中适应参数的附加启发式策略。自适应策略旨在通过使用基于能量的措施来量化系统的多样性，在图像空间上均匀地分布粒子。严格证明，使用平均场近似值和收敛保证对最佳点进行了数学分析。另外，揭示和分析了自适应方法的参数空间中的梯度流结构。几个数值实验显示了提出的随机粒子动力学的有效性，并说明了理论发现。
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated 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 by using energy-based measures to quantify the diversity of the system. The resulting metaheuristic algorithm is mathematically analyzed using a mean-field approximation and convergence guarantees towards optimal points is rigorously proven. In addition, a gradient flow structure in the parameter space for the adaptive method is revealed and analyzed. Several numerical experiments shows the validity of the proposed stochastic particle dynamics and illustrate the theoretical findings.
