Empirical study of exact algorithms for the multi-objective spanning tree

The multi-objective spanning tree ( MoST ) is an extension of the minimum spanning tree problem ( MST ) that, as well as its single-objective counterpart, arises in several practical applications. However, unlike the MST , for which there are polynomial-time algorithms that solve it, the MoST is NP-hard. Several researchers proposed techniques to solve the MoST , each of those methods with specific potentialities and limitations. In this study, we examine those methods and divide them into two categories regarding their outcomes: Pareto optimal sets and Pareto optimal fronts. To compare the techniques from the two groups, we investigated their behavior on 2, 3 and 4-objective instances from different classes. We report the results of a computational experiment on 8100 complete and grid graphs in which we analyze specific features of each algorithm as well as the computational effort required to solve the instances.

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