A linearization method for quadratic minimum spanning tree problem

Abstract

The crisp and fuzzy quadratic minimum spanning tree (Q-MST) problem can be formulated as a linear model, and thus, the global optimum can be obtained by the proposed method. Conventionally, the Q-MST problem, which contains a quadratic term in the objective function, is solved by genetic algorithm and other heuristic methods. However, these methods cannot guarantee to obtain a global optimal solution. To address this issue, the proposed method transforms the quadratic term into linear formulations for crisp and fuzzy Q-MST problems, and yields the global optimum solutions by linear integer programming. Two examples are given to demonstrate the proposed method in greater detail.