During the past few decades, multi-agent optimization problems have drawn increased attention from the research community. When multiple objective functions are present among agents, many works optimize the sum of these objective functions. However, this formulation implies a decision regarding the relative importance of each objective: optimizing the sum is a special case of a multi-objective problem in which all objectives are prioritized equally. To enable more general prioritizations, we present a distributed optimization algorithm that explores Pareto optimal solutions for non-homogeneously weighted sums of objective functions. This exploration is performed through a new rule based on agents’ priorities that generates edge weights in agents’ communication graph. These weights determine how agents update their decision variables with information received from other agents in the network. Agents initially disagree on the priorities of objective functions, though they are driven to agree upon them as they optimize. As a result, agents still reach a common solution. The network-level weight matrix is (non-doubly) stochastic, contrasting with many works on the subject in which the network-level weight matrix is doubly-stochastic. New theoretical analyses are therefore developed to ensure convergence of the proposed algorithm. This paper provides a gradient-based optimization algorithm, proof of convergence to solutions, and convergence rates of the proposed algorithm. It is shown that agents’ initial priorities influence the convergence rate of the proposed algorithm and that these initial choices affect its long-run behavior. Numerical results performed with different numbers of agents illustrate the performance and effectiveness of the proposed algorithm.

在过去的几十年中，多主体优化问题引起了研究界的越来越多的关注。当代理之间存在多个目标函数时，许多工作会优化这些目标函数的总和。但是，这种表述意味着需要就每个目标的相对重要性做出决定：优化总和是多目标问题的一种特例，在该问题中，所有目标均被同等地优先考虑。为了实现更一般的优先级划分，我们提出了一种分布式优化算法，该算法探索目标函数的非均匀加权和的Pareto最优解。通过基于代理优先级的新规则执行此探索，该规则在代理的通信图中生成边缘权重。这些权重确定代理如何使用从网络中其他代理接收的信息更新其决策变量。代理最初不同意目标功能的优先级，尽管他们在优化时会被驱使达成一致。结果，代理仍然可以达到通用的解决方案。网络级权重矩阵是（非双重）随机的，这与网络级权重矩阵是双随机性的主题上的许多著作形成对比。因此，开发了新的理论分析以确保所提出算法的收敛性。本文提供了一种基于梯度的优化算法，解的收敛性证明以及该算法的收敛速度。结果表明，代理的初始优先级会影响所提出算法的收敛速度，并且这些初始选择会影响其长期行为。用不同数量的代理执行的数值结果说明了该算法的性能和有效性。