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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 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.

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In this article, a distributed multiobjective optimization problem is formulated for the resource allocation of network-connected multiagent systems. The framework encompasses a group of distributed decision makers in the subagents, where each of them possesses a local preference index. Novel distributed algorithms are proposed to solve such a problem in a distributed manner. The weighted L p preference index is utilized in each agent since it can provide a robust Pareto solution to the problem. By using distributed fixed-time optimization methods, the L p preference index is constructed online without specifying the unknown parameters. Then, it is proved that the problem admits a unique Pareto solution. By exploiting consensus and gradient descent techniques, asymptotic convergence to the optimal solution is established via Lyapunov theories. Distinct from most of the current works, the proposed framework does not require any prior information in the formulation process, and private data can be well protected using this distributed approach. Numerical examples are included to validate the effectiveness of the proposed algorithms.