The Maximum Bisection Problem (MBP) is a well-known combinatorial optimization problem that has been proven to be NP-hard. The maximum bisection of a graph is the partition of its set of vertices into two subsets with an equal number of vertices, where the weight of the edge cut is maximal. This work introduces a connected multidimensional generalization of the Maximum Bisection Problem. In this NP-hard problem, weights on edges are vectors of non-negative numbers, and subgraphs induced by partitions must be connected. A mixed integer linear programming (MILP) formulation is proposed with proof of its correctness. The MILP formulation of the problem has a polynomial number of variables and constraints

最大等分问题 （MBP） 是一个众所周知的组合优化问题，已被证明是 NP 困难的。图形的最大等分是将其顶点集划分为两个顶点数相等的子集，其中边切割的权重最大。这项工作介绍了最大等分问题的连通多维泛化。在这个 NP-hard 问题中，边上的权重是非负数的向量，分区诱导的子图必须连接起来。提出了一种混合整数线性规划 （MILP） 公式，并证明了其正确性。问题的 MILP 公式具有多项式数的变量和约束