On Integer Balancing of Digraphs

Limited Rate Distributed Weight-Balancing and Average Consensus Over Digraphs

Distributed quantized weight-balancing and average consensus over fixed digraphs are considered. A digraph with non-negative weights associated to its edges is weight-balanced if, for each node, the sum of the weights of its out-going edges is equal to that of its incoming edges. This paper proposes and analyzes the first distributed algorithm that solves the weight-balancing problem using only finite rate and simplex communications among nodes (compliant to the directed nature of the graph edges). Asymptotic convergence of the scheme is proved and a convergence rate analysis is provided. Buil…

Finite rate distributed weight-balancing and average consensus over digraphs

This paper proposes the first distributed algorithm that solves the weight-balancing problem using only finite rate and simplex communications among nodes, compliant with the directed nature of the graph edges. It is proved that the algorithm converges to a weight-balanced solution at sublinear rate. The analysis builds upon a new metric inspired by positional system representations, which characterizes the dynamics of information exchange over the network, and on a novel step-size rule. Building on this result, a novel distributed algorithm is proposed that solves the average consensus proble…

关于有向图与加权有向图中的 dijoin 装填

On packing dijoins in digraphs and weighted digraphs

本文研究有向图及加权有向图中 dijoines 的装填与划分，证明依据参数 $\rho$ 的三个加权装填结果，并说明各结果在相应条件下均为最优。

面向服装流水线平衡的混合整数线性规划（MILP）

A Mixed-Integer Linear Programming (MILP) for Garment Line Balancing

本文研究如何利用混合整数线性规划（MILP）结合精益方法论解决服装流水线平衡问题，并通过IBM CPLEX Studio案例验证其可将劳动力成本降低超过50%，同时有效管理资源与需求约束。

平衡电网效率与风险的双目标随机整数优化框架

A Framework for Balancing Power Grid Efficiency and Risk with Bi-objective Stochastic Integer Optimization

针对电网扩展规划中极端温度风险与效率的权衡，提出双目标随机整数优化模型及条件采样方法，结合空间相关温度模型，在真实数据案例中验证了其有效性。