We consider the capacitated inverse optimal value problem on minimum spanning tree under Hamming distance. Given a connected undirected network \(G=(V,E)\) and a spanning tree \(T^0\), we aim to modify the weights of the edges such that \(T^0\) is not only the minimum spanning tree under the new weights but also the weight of \(T^0\) is equal to a given value K. The objective is to minimize the modification cost under bottleneck Hamming distance. We add a lower bound l and an upper bound u on the modification of weights and consider three cases (uncapacitated, lower bounded, capacitated) of the problem based on the bound vectors. Suppose \(l=-\,\infty , u=+\,\infty \) in the uncapacitated problem, \(l>-\,\infty , u=+\,\infty \) in the lower bounded problem and \(l>-\,\infty , u<+\,\infty \) in the capacitated problem. We present three mathematical models of these problems. After analyzing the properties, we develop three strongly polynomial time algorithms based on binary search to solve the problems. The time complexities for solving the uncapacitated, the lower bounded and capacitated problems are all \(O(|V| |E| \log |E|)\) time. Finally, we do some numerical experiments to show the effectiveness of the algorithms.

我们考虑了汉明距离下最小生成树上的容量逆最优值问题。给定连接的无向网络\（G =（V，E）\）和生成树\（T ^ 0 \），我们旨在修改边缘的权重，使得\（T ^ 0 \）不仅是根据新的权重最小生成树而且重量\（T ^ 0 \）是等于给定值ķ。目的是使瓶颈海明距离下的修改成本最小化。我们在权重的修改上添加了一个下限l和一个上限u，并基于绑定向量考虑了三种情况（无能力，下界，有能力）的问题。认为\（l =-\，\ infty，u = + \，\ infty \）在无能力的问题中，\（l>-\，\ infty，u = + \，\ infty \）在下界问题中和\ （l>-\，\ infty，u <+ \，\ infty \）。我们提出了这些问题的三个数学模型。在分析了这些特性之后，我们基于二进制搜索开发了三种强多项式时间算法来解决这些问题。解决无能力，下界和有能力问题的时间复杂度都是\（O（| V | | E | \ log | E |）\）时间。最后，我们进行了一些数值实验以证明算法的有效性。