An interactive GRASP algorithm for the multicriteria minimum spanning tree problem

This paper presents an interactive GRASP (Greedy Randomized Adaptive Search Procedure) algorithm for the multi-criteria minimum spanning tree problem, which is NP-hard. In this problem a vector of costs is defined for each edge of the graph and the problem is to determine a preferred pareto optimal (efficient) spanning tree (solution). In this paper based on the decision maker (DM) preferences, Analytic Hierarchy Process (AHP) is used for finding a weight vector corresponding to objective functions. This weight vector is used in the weighted utility function. The algorithm is based on the optimization of a weighted utility function. In the proposed algorithm, a solution is built using a greedy randomized constructive procedure. The solution procedure controls the search direction via updating weighting vector