Models and hybrid algorithms for inverse minimum spanning tree problem with stochastic edge weights∗

An inverse minimum spanning tree problem is to make the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. In this paper, the inverse minimum spanning tree problem with stochastic edge weights is investigated. The concept of α-minimum spanning tree is initiated, and subsequently an α-minimum spanning tree model and a probability maximization model are presented to formulate the problem according to different decision criteria. In order to solve the two stochastic models, hybrid genetic algorithms and hybrid simulated annealing algorithms are designed and illustrated by some computational experiments.