发表机构
State University of Campinas (UNICAMP); Delft University of Technology; Vanderbilt University（坎皮纳斯州立大学; 代尔夫特理工大学; 范德堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于流的连通性约束用于网络化多智能体系统的MILP轨迹规划，相比SEC方法降低约束增长，但k跳流模型虽减少二元变量，平均性能未显著提升。
AI 中文摘要
本文研究了在网络化多智能体系统（MAS）的混合整数线性规划（MILP）轨迹规划与决策模型中，使用基于流的连通性保持约束的方法。我们将标准连通性和k跳连通性的基于流的编码集成到广泛与滚动时域规划策略结合使用的MILP多车辆机动模型中。我们证明了这些约束的必要性和充分性，确保了对潜在网络拓扑的完整覆盖。与最先进的子回路消除（SEC）方法相比，标准连通性的流模型将所需不等式约束的增长从指数级降低为关于MAS规模的多项式级。基于流的k跳连通性约束减少了所需二元变量的数量，并将其增长与跳数解耦。然而，由于引入了大量连续流优化变量，以及在k跳连通性情况下额外的不等式约束，这些公式对性能的影响并非直接明了。我们通过使用常规的分支定界商业求解器，以及在随机化环境中对日益增大的MAS进行的试验，对成本和优化时间进行统计评估来研究这种权衡。结果表明，在标准连通性问题中，流模型优于SEC，使得在设定的优化时间限制内能够为更大的MAS计算解决方案。k跳流模型所实现的二元变量数量减少，降低了分支定界算法计算全局最优解所需的理论最坏情况迭代次数。我们的结果表明，与基线相比，这一优势并未转化为平均性能的提升。
英文摘要
This work investigates the use of flow-based connectivity maintenance constraints in mixed-integer linear programming (MILP) trajectory planning and decision-making models for networked multi-agent systems (MAS). We integrate flow-based encodings for standard and k-hop connectivity into MILP multi-vehicle maneuvering models that are widely used alongside receding horizon planning strategies. Their necessity and sufficiency is demonstrated, guaranteeing full coverage of potential network topologies. The flow formulation for standard connectivity decreases the growth of the required inequality constraints from exponential to polynomial w.r.t. the size of the MAS when compared to the state-of-the-art subtour elimination (SEC) method. The flow-based k-hop connectivity constraints decrease the number of required binary variables and decouple its growth from the number of hops. However, the impact of these formulations in performance is not straightforward due to the introduction of a substantial number of continuous flow optimization variables and, in the case of k-hop connectivity, additional inequality constraints. We investigate this trade-off through a statistical evaluation of costs and optimization times using a conventional branch-and-bound commercial solver and trials performed with randomized environments for increasingly larger MAS. The results show that the flow formulation outperforms SEC in standard connectivity problems, enabling the solutions to be computed for larger MAS considering the imposed optimization time limit. The reduction in number of binary variables enabled by the k-hop flow formulations decreases the theoretical worst-case number of iterations required by the branch-and-bound algorithm to compute the global optimal solution. Our results show that this advantage did not translate into improvements in the average performance when compared to the baseline.
