This paper considers distributed multi-objective optimisation problems with time-varying cost functions for network-connected multi-agent systems over switching graphs. The scalarisation approach is used to convert the problem into a weighted-sum objective. Fixed-time consensus algorithms are developed for each agent to estimate the global variables and drive all local copies of the decision vector to a consensus. The algorithm with fixed gains is first proposed, where some global information is required to choose the gains. Then, an adaptive algorithm is presented to eliminate the use of global information. The convergence of those algorithms to the Pareto solutions is established via Lyapunov theory for connected graphs. In the case of disconnected graphs, the convergence to the subsets of the Pareto fronts is studied. Simulation results are provided to demonstrate the effectiveness of the proposed algorithms.

中文翻译：

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通过固定时间一致性算法对切换图进行时变多目标优化

本文考虑了具有时变成本函数的分布式多目标优化问题，用于切换图上的网络连接多代理系统。标量化方法用于将问题转换为加权和目标。为每个代理开发了固定时间共识算法来估计全局变量并驱动决策向量的所有本地副本达成共识。首先提出固定增益的算法，其中需要一些全局信息来选择增益。然后，提出了一种自适应算法来消除全局信息的使用。这些算法与帕累托解的收敛性是通过连接图的李雅普诺夫理论建立的。在不连续图的情况下，研究了帕累托前沿子集的收敛性。